Math in Focus

Go through the Math in Focus Grade 6 Workbook Answer Key Chapter 1 Lesson 1.5 Cubes and Cube Roots to finish your assignments.

Math in Focus Grade 6 Course 1 A Chapter 1 Lesson 1.5 Answer Key Cubes and Cube Roots

Math in Focus Grade 6 Chapter 1 Lesson 1.5 Guided Practice Answer Key

Find a cube of a whole number.

a) A cube has edges 2 centimeters long. Find its volume.

Volume of cube = 2 × 2 × 2 = 8 cm³
2 × 2 × 2 is called the cube of 2.
You can write 2 × 2 × 2 as 2³.
So, 2³ = 8.

The number 3 in 2³ is the exponent. The number 2 is the base.
The cube of a whole number is called a perfect cube.
Since 8 = 2 × 2 × 2, 8 is a perfect cube.

b) Find the cube of 7.
7³ = 7 × 7 × 7
= 343
The cube of 7 is 343.

I can relate this to finding the volume of a cube with edges of length 7 units.

Find the cube of each number.

Question 1.
5
Answer:
125

Explanation:
I can relate this to finding the volume of a cube with edges of length 5 units.
^{5³ = 5 x 5 x 5}
= 125
The cube of 5 is 125.

Question 2.
6
Answer:
216

Explanation:
I can relate this to finding the volume of a cube with edges of length 7 units.
^{7³ = 7 x 7 x 7}
= 216
The cube of 6 is 216.

Question 3.
9
Answer:
729

Explanation:
I can relate this to finding the volume of a cube with edges of length 9 units.
^{9³ = 9 x 9 x 9}
= 729
The cube of 5 is 729.

Find a cube root of a perfect cube.

a) A cube has a volume of 27 cubic meters. Find the length of each edge of the cube.

You know that
Volume of cube = edge × edge × edge.
To find the length of the edge of the cube, you need to find a number whose cube is 27.
You know that 3 × 3 × 3 = 27.
So, the length of each edge of the cube is 3 meters. 3 is called the cube root of 27. This can be written as
\(\sqrt[3]{27}\) = 3
Finding the cube root of a number is the inverse of finding the cube of a number.

b) Find the cube root of 64.
By prime factorization,

I can relate this to finding the length of an edge of a cube, when I know it has a volume of 64 units³.

Find the cube root of each number.

Question 4.
216
Answer:
6

Explanation:
Finding the cube root of a number is the inverse of finding the cube of a number
prime factorization of 216 = 2 x 2 x 2 x 3 x 3 x 3
= (2.3)³
=6³
so, cube root of 216 is 6.

Question 5.
343
Answer:
7

Explanation:
Finding the cube root of a number is the inverse of finding the cube of a number
prime factorization of 343 = 7 x 7 x 7
=7³
so, cube root of 343 is 7.

Question 6.
1,000
Answer:
10

Explanation:
Finding the cube root of a number is the inverse of finding the cube of a number
prime factorization of 1000 = 2 x 2 x 2 x 5 x 5 x 5
= (2.5)³
=10³
so, cube root of 1000 is 10.

Complete.

Question 7.
Find the values of 5² + 5³ and 5 • 5 • 5 • 5 • 5.

Answer:

Find the value of each of the following.

Question 8.
6³ + 4²
Answer:
232

Explanation:
6³ = 6 x 6 x 6= 216
4² = 4 x 4 = 16
6³ + 4² =  216 + 16 = 232
6³ + 4²  = 232

Question 9.
7³ – 4³
Answer:
279

Explanation:
7³ = 7 x 7 x 7 = 343
4³ = 4 x 4 x 4 = 64
7³ – 4³ = 343 – 64 = 279
7³ – 4³ = 279

Question 10.
3² × 5³ + 9²
Answer:
215

Explanation:
3² = 3 x 3 = 9
5³ = 5 x 5 x 5 = 125
9² = 9 x 9 = 81
3² x 5³ x 9² = 9+125+81 = 215.
3² x 5³ x 9²  = 215.

Question 11.
8³ ÷ 4² – 5²
Answer:
7

Explanation:
8³ = 8 x 8 x 8 = 512
4² = 4 x 4 = 16
5² = 5 x 5 = 25
8³ ÷ 4² – 5² = 512 ÷ 16 – (25)
= 32 – 25
= 7

8³ ÷ 4² – 5² = 7

Question 12.
7² + 6³ ÷ 2³
Answer:
76

Explanation:
7²  = 7 x 7 = 49
6³ = 6 x 6 x 6 = 216
2³ = 2 x 2 x 2 = 8
7² + 6³ ÷ 2³ = 49 + (216 ÷ 8)
= 49 + 27
= 76
7² + 6³ ÷ 2³ = 76

Question 13.
9³ – 4² × 3³
Answer:
297

Explanation:
9³ = 9 x 9 x 9 = 729
4² = 4 x 4 = 16
3³ = 3 x 3 x 3 = 27
9³ – 4² + 3³ = 729 – (16 x 27)
= 729 – 432
= 279
9³ – 4² + 3³ = 279.

Math in Focus Course 1A Practice 1.5 Answer Key

Find the cube of each number.

Question 1.
8
Answer:
512

Explanation:
I can relate this to finding the volume of a cube with edges of length 8 units.
^{8³ = 8 x 8 x 8}
= 64 x 8
= 512
The cube of 8 is 512.

Question 2.
3
Answer:
27

Explanation:
I can relate this to finding the volume of a cube with edges of length 3 units.
^{3³ = 3 x 3 x 3}
9 x 3
= 27
The cube of 3 is 27.

Question 3.
10
Answer:
1000

Explanation:
I can relate this to finding the volume of a cube with edges of length 10 units.
^{10³ = 10 x 10 x 10}
=100 x 10
= 1000
The cube of 10 is 1000.

Find the cube root of each number.

Question 4.
125
Answer:
5

Explanation:
Finding the cube root of a number is the inverse of finding the cube of a number
prime factorization of 125 = 5 x 5 x 5
=5³
so, cube root of 125 is 5.

Question 5.
512
Answer:
8

Explanation:
Finding the cube root of a number is the inverse of finding the cube of a number
prime factorization of 512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
= (2.2.2)³
=8³
so, cube root of 512 is 8.

Question 6.
729
Answer:
9

Explanation:
Finding the cube root of a number is the inverse of finding the cube of a number
prime factorization of 729 = 3 x 3 x 3 x 3 x 3 x 3
= (3.3)³
=9³
so, cube root of 729 is 9.

Solve.

Question 7.
List the perfect cubes that are between 100 and 600.
Answer:
125, 216, 343 and 512.

Explanation:
125, 216, 343 and 512 are the perfect cubes between 100 and 600.

Question 8.
Math Journal Find the value of each expression. Then describe any patterns you see.
a) 2² – 1²
Answer:
3

Explanation:
2² = 2 x 2 = 4
1² = 1 x 1 = 1
2² – 1² = 4 – 1
= 3
2² – 1² = 3.

b) 3² – 2²
Answer:
5

Explanation:
3² = 3 x 3 = 9
2² = 2 x 2 = 4
3² – 2² = 9 – 4
= 5
3² – 2² = 5.

c) 4² – 3²
Answer:
7

Explanation:
4² = 4 x 4 = 16
3² = 3 x 3 = 9
4² – 3² = 16 – 9
= 7
4² – 3² = 7.

d) 5² – 4²
Answer:
9

Explanation:
5² = 5 x 5 = 25
4² = 4 x 4 = 16
5² – 4² = 25 – 16
= 9
5² – 4² = 9.

Question 9.
Find two consecutive numbers whose squares differ by 17.
Answer:
8 and 9

Explanation:
The square of 8 is 64
The square of 9 is 81
81 – 64 = 17
So, 8 and 9 are two consecutive numbers whose squares differ by 17.

Find the value of each of the following.

Question 10.
8³ + 5²
Answer:
537

Explanation:
8³ = 8 x 8 x 8 = 512
5² = 5 x 5 = 25
8³ + 5² = 512 + 25
= 537
8³ + 5² = 537.

Question 11.
10³ – 6²
Answer:
964

Explanation:
10³ = 10 x 10 x 10 = 1000
6² = 6 x 6 = 36
10³ – 6² = 1000 – 36
= 964
10³ – 6² = 964.

Question 12.
3³ × 9²
Answer:
2187

Explanation:
3³ = 3 x 3 x 3 = 27
9² = 9 x 9 = 81
3³ x 9² = 27 x 81
= 2187
3³ x 9² = 2187

Question 13.
9³ – 5² + 6²
Answer:
740

Explanation:
9³ = 9 x 9 x 9 = 729
5² = 5 x 5 = 25
6² = 6 x 6 = 36
9³ –  5² + 6² = 729 – 25 + 36
= 740
9³ – 5² + 6² = 740.

Question 14.
7² + 8³ – 4²
Answer:
545

Explanation:
7² = 7 x 7 = 49
8³ = 8 x 8 x 8 = 512
4² = 4 x 4 = 16
7² + 8³ – 4² = 49 + 512 – 16
= 545
7² + 8³ – 4² = 545

Question 15.
9³ – 5² + 6²
Answer:
740

Explanation:
9³ = 9 x 9 x 9 = 729
5² = 5 x 5 = 25
6² = 6 x 6 = 36
9³ – 5² + 6² = 729 – 25  + 36
= 740
9³ – 5² + 6² = 740

Question 16.
8³ × 5³ ÷ 5²
Answer:
2560

Explanation:
8³ = 8 x 8 x 8 = 512
5³ = 5 x 5 x 5 = 125
5² = 5 x 5 = 25
8³ × 5³ ÷ 5² = 512 x 125 ÷ 25
= 2560
8³ × 5³ ÷ 5² = 2560

Question 17.
10³ ÷ 8² × 4²
Answer:
250

Explanation:
10³ = 10 x 10 x 10 = 1000
8² = 8 x 8 = 64
4² = 4 x 4 = 16
10³ ÷ 8² x 4² = 1000 ÷ 64 x 16
= 250
10³ ÷ 8² x 4² = 250.

Question 18.
7³ – 10² ÷ 2²
Answer:
318

Explanation:
7³ = 7 x 7 x 7 = 343
10² = 10 x 10 = 100
2² = 2 x 2 = 4
7³ – 10² ÷ 2² = 343 – (100 ÷ 4 )
= 343 – 25
= 318
7³ – 10² ÷ 2² = 318

Question 19.
3³ + 4³ × 6²
Answer:
2331

Explanation:
3³ = 3 x 3 x 3= 27
4³ = 4 x 4 x 4 = 64
6² = 6 x 6 = 36
3³ + 4³ × 6² = 27 + (64 x 36 )
= 27 + 2304
= 2331
3³ + 4³ × 6² = 2331.

Find the value of each of the following.

Question 20.
17³
Answer:
4913

Explanation:
I can relate this to finding the volume of a cube with edges of length 17 units.
17³ = 17 x 17 x 17
= 289 x 17
= 4913
The cube of 17 is 4913.

Question 21.
16³
Answer:
4096

Explanation:
I can relate this to finding the volume of a cube with edges of length 16 units.
16³ = 16 x 16 x 16
= 256 x 16
= 4096
The cube of 16 is 4096.

Question 22.
18³
Answer:
5832

Explanation:
I can relate this to finding the volume of a cube with edges of length 18 units.
18³ = 18 x 18 x 18
= 324 x 18
= 5832
The cube of 18 is 5832.

Question 23.

Answer:
12

Explanation:
Finding the cube root of a number is the inverse of finding the cube of a number
prime factorization of 1728 = 2 x 2x 2 x 2 x 2 x 2 x 3 x 3 x 3
= (2.2.3)³
=12³
So, cube root of 1728 is 12.

Question 24.

Answer:
20

Explanation:
Finding the cube root of a number is the inverse of finding the cube of a number
prime factorization of 8000 = 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5 x 5
= (2.2.5)³
=20³
So, cube root of 8000 is 20.

Question 25.

Answer:
15

Explanation:
Finding the cube root of a number is the inverse of finding the cube of a number
prime factorization of 3375 = 3 x 3 x 3 x 5 x 5 x 5
= (3.5)³
=15³
So, cube root of 3375 is 15.

Solve.

Question 26.
Given that 11³ = 1,331, find the cube of 110.
Answer:
1,331,000

Explanation:
If 11³ = 1,331 then 110³ will be 1,331,000.

Question 27.
Given that 14³ = 2,744, find the cube root of 2,744,000.
Answer:
140³

Explanation:
If 14³ = 2,744 then cube root of 2,744,000 is 140³.

Question 28.
Given that = 16, evaluate 160³.
Answer:
4,096,000

Explanation:
If cube root 4096 is 16 then 160³ will be 4,906,000.

Question 29.
Evaluate 13² + 20³ – 18².
Answer:
7845

Explanation:
13² = 13 x 13 = 169
20³ = 20 x 20 x 20 = 8000
18² = 18 x 18 = 324
13² + 20³ – 18² = 169 + 8000 – 324
= 7845
13² + 20³ – 18² = 7845.

Question 30.
Evaluate the cube root of 12³ × 5³ + 8³.
Answer:
68

Explanation:
Cube root of 12³ × 5³ + 8³ will be the number itself
So, 12 x 5 + 8 = 68 is cube root of 12³ × 5³ + 8³.

Question 31.
Find three consecutive numbers whose cubes have a sum of 2,241.
Answer:
8, 9, 10

Explanation:
8³ = 512
9³ = 729
10³ = 1000
512 + 729 + 1000 = 2241
So, the three consecutive numbers whose cubes have a sum of 2241 are 8, 9 and 10.

Question 32.
A cubic crate with an edge length of 16 feet will be used to contain cubic wooden boxes. Each wooden box has an edge length of 4 feet. How many wooden boxes can the crate contain?
Answer:
4 wooden boxes

Explanation:
A cubic crate with an edge length of 16 feet will be used to contain cubic wooden boxes.
Each wooden box has an edge length of 4 feet
4 x 4 = 16
S0, the wooden crate can contain 4 wooden boxes.

Brain @ Work

Mr. Henderson wants to tile his patio that is rectangular in shape. His patio measures 108 inches by 144 inches. Find the fewest square tiles he can use without cutting any of them. (Hint: First find the largest size tile he can use.)

Answer:
21 tiles of 12 inches square tile

Explanation:
Mr. Henderson wants to tile his patio that is rectangular in shape.
His patio measures 108 inches by 144 inches
The largest size tile he can use is 12 inches
12 in x 12 tiles = 144 in
12 in x 9 tiles = 108 in
So, Mr. Henderson wants 21 tiles of 12 inches to tile his patio in rectangular shape without cutting any square tile.

Go through the Math in Focus Grade 6 Workbook Answer Key Chapter 1 Lesson 1.1 The Number Line to finish your assignments.

Math in Focus Grade 6 Course 1 A Chapter 1 Lesson 1.1 Answer Key The Number Line

Math in Focus Grade 6 Chapter 1 Lesson 1.1 Guided Practice Answer Key

Draw a horizontal number line to represent each set of whole numbers.

Question 1.
Positive whole numbers less than 5
Answer:
0, 1, 2, 3 and 4 are the positive whole numbers less than 5.

Question 2.
Whole numbers greater than 9 but less than 14
Answer:
10, 11, 12, 13 are the whole numbers greater than 9 but less than 14.

Draw a vertical number line to represent each set of whole numbers.

Question 3.
Odd numbers between 1 and 10
Answer:
1, 3, 5, 7 and 9 are the odd numbers between 1 and 10.

Question 4.
Positive odd numbers < 15
Answer:
1, 3, 5, 7, 9, 11, 13  are the positive odd numbers < 15.

Represent fractions, mixed numbers, and decimals on a horizontal number line.

a) Represent the fractions \(\frac{1}{4}\), \(\frac{2}{4}\), and \(\frac{3}{4}\) on a number line.

To represent \(\frac{1}{4}\)s, subdivide each interval between two consecutive whole numbers into four equal intervals using three tick marks.

Answer:

b) Represent the decimals from 0.1 to 0.9 on a horizontal number line. Use an interval of 0.1 between each decimal.

To represent decimals in tenths, subdivide each interval between two consecutive whole numbers into ten equal intervals.

Answer:

Complete each with the correct value, and each with > or <.

Question 5.
Fill in the missing fractions and mixed numbers on the number line. Then complete the statements of inequality.

Answer:

Draw a horizontal number line to represent each set of numbers.

Question 6.
Mixed numbers greater than 10 but less than 11 Use an interval of \(\frac{1}{4}\) between each pair of mixed numbers.
Answer:

Question 7.
Mixed numbers from 3 to 4, with an interval of \(\frac{1}{10}\) between each pair of mixed numbers.
Answer:

Question 8.
Decimals between 0 and 1, with an interval of 0.25 between each pair of decimals
Answer:

Question 9.
Decimals greater than 8.0 but less than 12.0
Use an interval of 0.8 between each pair of decimals.
Answer:

Represent fractions1 mixed numbers, and decimals on a vertical number line.

a) Represent the fractions \(\frac{1}{5}\), \(\frac{2}{5}\), \(\frac{3}{5}\), \(\frac{4}{5}\) on a vertical number line.
To represent these fractions on the number line, subdivide the interval between 0 and 1 into five smaller intervals.

Answer:

b) Represent the decimals 2.0, 2.2, 2.4, 2.6, …, 4.0 on a vertical number line.
To represent these decimals, subdivide the interval from 2.0 to 4.0 into ten equal intervals of 0.2.

To decide how many tick marks to show on the number line, you can 3.6 count up by 0.2s, marking them as you go:
2.0, 2.2, 2.4, 2.6, 2.8, 3.0, 3.2, 3.4, 3.2, 3.6, 3.8, 4.0.

Answer:

Write statements of inequality comparing two fractions or two decimals using the symbols > and <.

You can use a number line to compare fractions and decimals.

a) Compare the two fractions, \(\frac{2}{3}\) and \(\frac{5}{6}\).
Use a number line to compare \(\frac{2}{3}\) and \(\frac{5}{6}\).

The numbers \(\frac{2}{3}\) and \(\frac{4}{6}\) are equivalent and are represented by the same point on a number line.

The fraction \(\frac{5}{6}\) lies to the right of \(\frac{2}{3}\). This means that \(\frac{5}{6}\) is greater than \(\frac{2}{3}\).
This can be represented as:
\(\frac{5}{6}\) > \(\frac{2}{3}\).

b) Compare the two decimals, 1.3 and 1.15. Use a number line to help you.

The decimal 1.15 lies to the left of 1.3. This means that 1.15 is less than 1.3. This can be represented by:
1.15 < 1.3.
Answer:

Complete each with the correct value, and each with > or <.

Question 10.
a) Fill in the missing decimals on the number line.

Answer:

b) Compare each pair of decimals using < or >. Use the number line in a) to help you.
0.1 0.05 0.02 0.07
Answer:

Draw a vertical number line to represent each set of numbers.

Question 11.
Mixed numbers greater than 6 but less than 7
Use an interval of \(\frac{1}{6}\) between each pair of mixed numbers.
Answer:

Question 12.
Positive fractions less than 1, with an interval of \(\frac{1}{12}\) between each pair of fractions.
Answer:

Question 13.
Decimals between 11.4 and 15.0, with an interval of 0.4 between each pair of decimals
Answer:

Question 14.
Decimals greater than 7.2 but less than 9.6
Use an interval of 0.3 between each pair of decimals.
Answer:

Question 15.
Positive decimals less than 7.5, with an interval of 0.75 between each pair of decimals
Answer:

Compare each pair of numbers using > or <. Use a number line to help you.

Question 16.
3\(\frac{9}{10}\) 3\(\frac{3}{10}\)
Answer:

Question 17.
2.17 2.71
Answer:

Question 18.
14.4 13.38
Answer:

Question 19.
8\(\frac{5}{12}\) \(\frac{100}{12}\)
Answer:

Compare numbers in different forms.

Look at these number lines.

Every whole number, fraction, and decimal can be represented on the number line. A given point on a number line can be written ¡n different forms. For example,
\(\frac{1}{2}\) = 0.5 and \(\frac{3}{4}\) = 0.75.

You can see that \(\frac{1}{4}\) = 0.25, \(\frac{1}{2}\) = 0.5, and \(\frac{3}{4}\) = 0.75.
You can also see that \(\frac{1}{5}\) = 0.2, \(\frac{2}{5}\) = 0.4, \(\frac{3}{5}\) = 0.6, and \(\frac{4}{5}\) = 0.8.

a) Which is greater, \(\frac{1}{4}\) or 0.3?
\(\frac{1}{4}\) = 0.25
0.25 lies to the left of 0.3
So, 0.3 > \(\frac{1}{4}\)
Answer:

b) Which is lesser, 0.62 or \(\frac{3}{5}\)?

Answer:

Complete.

Question 20.
Which is greater, \(\frac{1}{2}\) or 0.55?

Answer:

Compare each using > or <. Use a number line to help you.

Question 21.
0.2 \(\frac{1}{4}\)
Answer:

Question 22.
\(\frac{3}{4}\) 0.7
Answer:

Question 23.
0.89 \(\frac{4}{5}\)
Answer:

Question 24.
0.25 \(\frac{1}{5}\)
Answer:

Question 25.
\(\frac{2}{5}\) 0.3
Answer:

Question 26.
3.26 3\(\frac{5}{8}\)
Answer:

Math in Focus Course 1A Practice 1.1 Answer Key

Copy and complete each number line by filling in the missing values.

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Draw a horizontal number line to represent each set of numbers.

Question 4.
Odd numbers from 11 to 21
Answer:

Question 5.
Positive whole numbers less than 9
Answer:

Question 6.
Whole numbers greater than 12 but less than 18
Answer:

Question 7.
Mixed numbers between 0 and 2, with an interval of \(\frac{1}{3}\) between each pair of mixed numbers
Answer:

Question 8.
Decimals from 7.0 to 8.4, with an interval of 0.2 between each pair of decimals
Answer:

Draw a vertical number line to represent each set of numbers.

Question 9.
Even numbers between 20 and 32
Answer:

Question 10.
Positive whole numbers less than 13
Answer:

Question 11.
Whole numbers greater than 6 but less than 16
Answer:

Question 12.
Positive fractions less than 1, with an interval of \(\frac{1}{8}\) between each pair of fractions
Answer:

Question 13.
Decimals between 10 and 15, with an interval of 0.75 between each pair of decimals
Answer:

Compare each pair of numbers using > or <. Use a number line to help you.

Question 14.
2\(\frac{3}{7}\) 1\(\frac{9}{7}\)
Answer:

Question 15.
\(\frac{17}{25}\) 1\(\frac{7}{25}\)
Answer:

Question 16.
1\(\frac{4}{5}\) 1\(\frac{2}{3}\)
Answer:

Question 17.
33.61 36.13
Answer:

Question 18.
59.05 59.5
Answer:

Question 19.
98.072 98.027
Answer:

Draw a horizontal number line from 2 to 3 to represent each set of numbers.

Question 20.
2\(\frac{4}{5}\), 2\(\frac{3}{20}\), 2\(\frac{1}{2}\), 2\(\frac{11}{20}\), and 2\(\frac{9}{20}\)
Answer:

Question 21.
2.5, 2.125, 2.375, and 2.875
Answer:

Draw a horizontal number line from 0 to 1 to represent each set of numbers.

Question 22.
\(\frac{1}{3}\), \(\frac{1}{4}\), \(\frac{3}{8}\), \(\frac{3}{4}\), \(\frac{7}{8}\) and \(\frac{5}{6}\)
Answer:

Question 23.
0.1, 0.25, 0.05, 0.8, 0.75, and 0.95
Answer:

Compare each pair of numbers using > or <. Use a number line to help you.

Question 24.
0.8 \(\frac{1}{10}\)
Answer:

Question 25.
\(\frac{1}{5}\) 0.25
Answer:

Question 26.
\(\frac{3}{5}\) 0.35
Answer:

Question 27.
0.14 \(\frac{1}{4}\)
Answer:

Question 28.
\(\frac{2}{5}\) 0.3
Answer:

Question 29.
0.64 \(\frac{9}{10}\)
Answer:

Question 30.
0.2 \(\frac{1}{6}\)
Answer:

Question 31.
\(\frac{7}{8}\) 0.87
Answer:

Solve.

Question 32.
The wingspan of one butterfly is 1\(\frac{9}{16}\) inches. The wingspan of another butterfly is 1\(\frac{5}{8}\) inches. Write an inequality comparing the two wingspans.
Answer:

Question 33.
For a class project, Jina made a model of the Empire State Building that was 23.7 centimeters tall. Her friend Caleb made a model that was 23\(\frac{3}{5}\) centimeters tall. Whose model was taller? How much taller was it?
Answer:

Go through the Math in Focus Grade K Workbook Answer Key Chapter 16 Classifying and Sorting to finish your assignments.

Math in Focus Kindergarten Chapter 16 Answer Key Classifying and Sorting

Lesson 1 Classifying Things by One Attribute

Sort and match.

Question 1.


Answer:

Explanation:
Here are 2 things one is circle and the other is circle
so matched with one attribute

Question 2.


Answer:

Explanation:
Here are pictures with colors matched with the correct color
so matched with one attribute

Question 3.


Answer:

Explanation:
Here are pictures with colors matched with the correct color
so matched with one attribute

Question 4.


Answer:

Explanation:
Here are pictures with colors matched with the correct pattern
so matched with one attribute

Make an X on the item that does not belong.

Question 1.

Answer:

Explanation:
The both are in red green is odd
so, crossed out the green

Question 2.

Answer:

Explanation:
The orange is not in the above attributes

Question 3.

Answer:

Explanation:
The blue color is crossed because the bird and baby is in yellow color

Question 4.

Answer:

Explanation:
Cap and quilt in same pattern so crossed the shirt

Lesson 2 Classifying and Sorting Things by Two Attributes

Match.

Answer:

Explanation:
Matched with two attributes for the shapes.

Make an X on the wrong common attribute.

Question 1.

Answer:

Explanation:
Both are triangle and red in color so crossed the small

Question 2.

Answer:

Explanation:
The above shapes are green and small
so, crossed the square

Question 3.

Answer:

Explanation:
The above are all circles and big
so, crossed the purple.

Go through the Math in Focus Grade K Workbook Answer Key Chapter 14 Number Facts to finish your assignments.

Math in Focus Kindergarten Chapter 14 Answer Key Number Facts

Lesson 1 Number Facts to 10

Count, write, and circle.

Question 1.

How many in all?
2
4
6
Answer:
Count the blue bottles and yellow bottles.
The total number of blue bottles=4
The total number of yellow bottles=2
The total number of blue and yellow bottles combine=4+2=6

Question 2.

How many in all?
3
6
7
Answer: 6
Count the blue bottles and yellow bottles.
The total number of blue bottles=5
The total number of yellow bottles=1
The total number of blue and yellow bottles combine=5+1=6

Question 3.

How many in all?
8
9
10
Answer: 8
Count the blue bottles and yellow bottles.
The total number of blue bottles=3
The total number of yellow bottles=5
The total number of blue and yellow bottles combine=3+5=8

Question 4.

How many in all?
7
8
10
Answer: 10
Count the blue bottles and yellow bottles.
The total number of blue bottles=2
The total number of yellow bottles=8
The total number of blue and yellow bottles combine=2+8=10

Question 5.

How many in all?
10
11
12
Answer:
Count the blue bottles and yellow bottles.
The total number of blue bottles=7
The total number of yellow bottles=3
The total number of blue and yellow bottles combine=7+3=10

Color, count and write. Write the number sentence.

Question 1.

5 is _________ and ________.
Answer:
The sum of two positive integers 3 and 2 is 5
3+2=5
3 and 2 make 5
In the above-given diagram:
The uncoloured boxes are given.
The number of uncoloured boxes=5
We need to colour them red and green.
So we can colour 3 red boxes and 2 green boxes.

Question 2.

5 is _________ and ________.
Answer:
The sum of two positive integers 4 and 1 is 5
4+1=5
4 and 1 make 5
In the above-given diagram:
The uncoloured boxes are given.
The number of uncoloured boxes=5
We need to colour them red and green.
So we can colour 4 red boxes and 1 green box.

Question 3

7 is _________ and ________.
Answer:
The sum of two positive integers 3 and 4 is 7
3+4=7
3 and 4 make 7
In the above-given diagram:
The uncoloured boxes are given.
The number of uncoloured boxes=7
We need to colour them red and green.
So we can colour 3 red boxes and 4 green boxes.

Question 4.

9 is _________ and ________.
Answer:
The sum of two positive integers 4 and 5 is 9
4+5=9
4 and 5 make 9
In the above-given diagram:
The uncoloured boxes are given.
The number of uncoloured boxes=9
We need to colour them red and green.
So we can colour 4 red boxes and 5 green boxes.

Question 5.

9 is _________ and ________.
Answer:
The sum of two positive integers 8 and 1 is 9
8+1=9
8 and 1 make 9
In the above-given diagram:
The uncoloured boxes are given.
The number of uncoloured boxes=9
We need to colour them red and green.
So we can colour 8 red boxes and 1 green box.

Lesson 2 Combining Sets

Count and write.

Question 1.

Count how many. ____________
How many more to make 10? ___________
Answer:
The total number of apples=9
We need to find out the number of more apples needed to make 10=X
X=10-9
X=1
Therefore, 1 more apple is needed to make 10.

Question 2.

Count how many. ____________
How many more to make 10? ___________
Answer:
The total number of glasses=5+3=8
We need to find out the number of more glasses needed to make 10=X
X=10-8
X=2
Therefore, 2 more glasses are needed to make 10.

Question 3.

Count how many. ____________
How many more to make 10? ___________
Answer:
The total number of pizzas=2+1=3
We need to find out the number of more pizzas needed to make 10=X
X=10-3
X=7
Therefore, 7 more pizzas are needed to make 10.

Question 4.

Count how many. ____________
How many more to make 10? ___________
Answer:
The total number of sandwiches=6+3=9
We need to find out the number of more sandwiches needed to make 10=X
X=10-9
X=1
Therefore, 1 more sandwich is needed to make 10.

Question 5.

Count how many. ____________
How many more to make 10? ___________
Answer:
The total number of toys=3+2=5
We need to find out the number of more toys needed to make 10=X
X=10-5
X=5
Therefore, 5 more toys are needed to make 10.

Lesson 3 Composing and Decomposing Numbers to 20

Count and write. Write the number sentence.

Question 1.

Answer:

5+2=7
The sum of two positive integers 5 and 2 is 7.

Question 2.

_________ and __________ make ___________.
Answer:
The sum of two positive integers 0 and 5 is 5
0+5=5

Question 3.

_________ and __________ make ___________.
Answer:
The sum of two positive integers 5 and 5 is 10
5 and 5 make 10.

Question 4.

_________ and __________ make ___________.
Answer:
The sum of two positive integers 10 and 2 is 12
10+2=12
10 and 2 make 12.

Question 5.

_________ and __________ make ___________.
Answer:
The sum of two positive integers 10 and 5 is 15
10+5=15
10 and 5 make 15

Question 6.

_________ and __________ make ___________.
Answer:
The sum of two positive integers 10 and 7 is 17
10+7=17
10 and 7 make 17

Draw . Write the number sentence.

Question 1.

Answer:

5+2=7
So we can write in sentences,
adding 5 and 2 we get 7.

Question 2.

__________ is __________ and ___________.
Answer: 9 is 5 and 4

5+4=9
And some other ways we can write 9 is:
4+5=9
6+3=9
7+2=9
8+1=9
So we can write in sentences,
by adding above all we get 9.

Question 3.

__________ is __________ and ___________.
Answer:

5 is 4 and 1
and there are some other ways we can write 5:
2+3=5
3+2=5
4+1=5
So we can write in sentences,
by adding above all we get 5.

Question 4.

__________ is __________ and ___________.
Answer:
16 is 10 and 6

and there are some other ways we can write 16:
10+6=16
8+8=16
15+1=16
14+2=16
13+3=16
12+4=16
11+5=16
9+7=16
So we can write in sentences,
by adding above all we get 16.

Question 5.

__________ is __________ and ___________.
Answer:
14 is 10 and 4

and there are some other ways we can write 14:
2+12=14
13+1=14
11+3=14
10+4=14
9+5=14
8+6=14
7+7=14
6+8=14
5+9=14
So we can write in sentences,
by adding above all we get 14.

Lesson 4 Counting On

Count and write.

Question 1.

Count how many. ____________
How many more to make 15? __________
Answer:
The number of honey bees = 6
We need to find out the number of more honey bees to make 15=X
X=15-6
X=9
Therefore, 9 more honey bees are needed to make 15.

Question 2.

Count how many. ____________
How many more to make 15? __________
Answer:
The number of ants = 11
We need to find out the number of more ants to make 15=X
X=15-11
X=4
Therefore, 4 more ants are needed to make 15.

Question 3.

Count how many. ____________
How many more to make 15? __________
Answer:
The number of snails = 12
We need to find out the number of more snails to make 15=X
X=15-12
X=3
Therefore, 3 more snails are needed to make 15.

Question 4.

Count how many. ____________
How many more to make 15? __________
Answer:
The number of flies = 9
We need to find out the number of more flies to make 15=X
X=15-9
X=6
Therefore, 6 more flies are needed to make 15.

Question 5.

Count how many. ____________
How many more to make 15? __________
Answer:
The number of caterpillars = 5
We need to find out the number of more caterpillars to make 15=X
X=15-5
X=10
Therefore, 10 more caterpillars are needed to make 15.

Count and write.

Question 1.

Count how many. ____________
How many more to make 15? __________
Answer:
The number of flies is 8

The number of flies is needed to make 15 is ‘X’.
X=15-8
X=7
Therefore, 7 more are needed to make 15.

Question 2.

Count how many. ____________
How many more to make 15? __________
Answer:
The number of flies=6
The number of flies is needed to make 15 is ‘X’.
X=15-6
X=9
Therefore, 9 more are needed to make 15.

Question 3.

Count how many. ____________
How many more to make 15? __________
Answer:
The number of leaves=10
The number of leaves is needed to make 15 is ‘X’.
X=15-10
X=5
Therefore, 5 more are needed to make 15.

Question 4.

Count how many. ____________
How many more to make 15? __________
Answer:
The number of snails=5
The number of snails is needed to make 15 is ‘X’.
X=15-5
X=10
Therefore, 10 more are needed to make 15.

Question 5.

Count how many. ____________
How many more to make 15? __________
Answer:
The number of ants=13
The number of ants is needed to make 15 is ‘X’.
X=15-13
X=2
Therefore, 2 more are needed to make 15.

Go through the Math in Focus Grade K Workbook Answer Key Chapter 15 Length and Height to finish your assignments.

Math in Focus Kindergarten Chapter 15 Answer Key Length and Height

Lesson 1 Comparing Lengths

Draw a long tail.

Answer:

The question asked was to draw a long tail.

Draw a short tail.

Answer:

The question asked was to draw a short tail.

Draw a longer object.

Question 1.

Answer:

Question 2.

Answer:

Draw a shorter object.

Question 1.

Answer:

Question 2.

Answer:

Make an X on the kite with the longest tail. Circle the kite with the shortest tail.

Answer:

Lesson 2 Comparing Lengths Using Nonstandard Units

Measure, count and write.

Question 1.

The pencil is about ___________ cubes long.
Answer:
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.

The pencil is 2 cubes long.

Question 2.

The spoon is about ___________ cubes long.
Answer:
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes

The spoon is 3 cubes long.

Question 3.

The toothbrush is about ____________ cubes long.
Answer:
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes

The tooth brush is about 5 cubes long.

Question 4.

The comb is about ____________ cubes long.
Answer:
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes

The comb is about 3 cubes long.

Question 5.

The tube is about ____________ cubes long.
Answer:
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.

The tube is about 2 cubes long.

Question 6.

The paintbrush is about ____________ cubes long.
Answer:
The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.

The paint brush is about 7 cubes long.

Count and write.

Question 1.

The pencil is about __________ long.

The crayon is about ____________ long.
The pencil is about ____________ longer than the crayon.
Answer:
The pencil is about 7 cubes long.
The crayon is about 4 cubes long.
The pencil is about ‘X’ longer than the crayon.
X=7-4
X=3
The pencil is about 3 cubes longer than a crayon.

Question 2.

The leaf is about ___________ long.

The carrot is about __________ long.
The leaf is about ____________ shorter than the carrot.
Answer:
The leaf is about 6 long
The carrot is about 9 long.
The leaf is about ‘X’ shorter than the carrot.
X=9-6
X=3
The leaf is about 3 shorter than the carrot.

Lesson 3 Comparing Heights Using Nonstandard Units

Count and write. Make an X on the taller vase.

Answer:
I crossed vase A because it is a taller one.


Count the circles present in vase A.

Answer:
Count the circles in vase B.

Count and write. Circle the shorter flower.

Answer:

Answer:
Count the circles in the flower B.

Go through the Math in Focus Grade K Workbook Answer Key Chapter 11 Calendar Patterns to finish your assignments.

Math in Focus Kindergarten Chapter 11 Answer Key Calendar Patterns

Lesson 1 Days of the Week

What day is it today? Color green. What day was it yesterday? Color blue. What day will it be tomorrow? Color yellow.

Answer:

Explanation:
There are 7 days a week. They are Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday
Today is a Monday so I coloured green.
Yesterday was Sunday so I coloured blue.
Tomorrow is a  Tuesday so I coloured yellow.

Read and circle.

Answer:
Explanation:
There are 7 days a week. They are Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday.
Saturday after Sunday.
Monday before Sunday.

Lesson 2 Months of the Year

Make an X on the month before August. Circle the month after February. Color the month between October and December.

Answer:
There are 12 months in a year. They are January, February, March, April, May, June, July, August, September, October, November, December.
– The month before August is July.
– The month after February is March.
– The month between October and December is November.

Go through the Math in Focus Grade K Workbook Answer Key Chapter 6 Numbers 0 to 20 to finish your assignments.

Math in Focus Kindergarten Chapter 6 Answer Key Numbers 0 to 20

Lesson 1 All About 10

Sing.

Answer:

Count and write.

Answer:

Explanation:
There are 2 giraffe
10 sheep and
4 cocks

Answer:

Explanation:
There are 9 cherries
3 cows
5 ducks

Count and write.

Answer:

Explanation:
Counted the fingers which are open

Count and write.

Question 1.

Answer:

Explanation:
Counted the blocks and Written the number
There are 10 blocks

Question 2.

Answer:

Explanation:
Counted the blocks and Written the number
There are 9 blocks

Question 3.

Answer:

Explanation:
Counted the blocks and Written the number
There are 8 blocks

Question 4.

Answer:

Explanation:
Counted the blocks and Written the number
There are 10 blocks

Question 5.

Answer:

Explanation:
Counted the blocks and Written the number
There are 9 blocks

Question 6.

Answer:

Explanation:
Counted the blocks and Written the number
There are 10 blocks

Lesson 2 Numbers 10 to 12

Count and write.

Question 1.

Answer:
Explanation:
counted the flowers and written the number
there are 11 flowers

Question 2.

Answer:
Explanation:
counted the bells and written the number
there are 12 bells

Question 3.

Answer:
Explanation:
counted the bees and written the number
there are 12 bees

Question 4.

Answer:
Explanation:
counted the eggs  and written the number
there are 11 eggs

Question 5.

Answer:
Explanation:
counted the bells and written the number
there are 12 bells

Question 6.

Answer:
Explanation:
counted the glasses and written the number
there are 12 glasses

Question 7.

Answer:
Explanation:
counted the ants and written the number
there are 11 ants

Question 8.

Answer:
Explanation:
counted the leaves and written the number
there are 11 leaves

Read and draw . Count and write.

Question 1.

How many in all? __________
Answer:

Explanation:
Counted and written the number
10 and  1 is 11
There are 11 in all

Question 2.

How many in all? __________
Answer:

Explanation:
Counted and written the number
There are 10 in all

Question 3.

How many in all? __________
Answer:

Explanation:
Counted and written the number
There are 8 in all

Question 4.

How many in all? __________
Answer:

Explanation:
Counted and written the number
There are 12 in all

Lesson 3 Numbers 13 to 16

Count and write.

Question 1.

Answer:

Explanation:
Counted the cups and written the number
there are 11 cups

Question 2.

Answer:

Explanation:
Counted the snails and written the number
there are 12 snails

Question 3.

Answer:

Explanation:
Counted the ducks and written the number
there are 13 ducks

Question 4.

Answer:

Explanation:
Counted the stars and written the number
there are 15 stars

Question 5.

Answer:

Explanation:
Counted the balls and written the number
there are 15 balls

Question 6.

Answer:

Explanation:
Counted the ants and written the number
there are 16 ants

Count and write.

Question 1.

Answer:

Explanation:
Counted the butterflies and written the number
there are 13 butterflies

Question 2.

Answer:

Explanation:
Counted the hats and written the number
there are 16 hats

Question 3.

Answer:

Explanation:
Counted the spoons and written the number
there are 15 spoons

Question 4.

Answer:

Explanation:
Counted the pencils and written the number
there are 14 pencils

Lesson 4 Numbers 17 to 20

Count and write.

Question 1.

Answer:

Explanation:
Counted the sparrows and written the number
there are 15 sparrows

Question 2.

Answer:

Explanation:
Counted the cherries and written the number
there are 16 cherries

Question 3.

Answer:

Explanation:
Counted the glosses and written the number
there are 17 glosses

Question 4.

Answer:

Explanation:
Counted the bricks and written the number
there are 18 bricks

Question 5.

Answer:

Explanation:
Counted the oranges and written the number
there are 19 oranges

Question 6.

Answer:

Explanation:
Counted the cups and written the number
there are 20 cups

Count and write.

Question 1.

Answer:

Explanation:
Counted the leaves and written the number
there are 20 leaves

Question 2.

Answer:

Explanation:
Counted the carrots and written the number
there are 18 carrots

Question 3.

Answer:

Explanation:
Counted the marbles and written the number
there are 19 marbles

Question 4.

Answer:

Explanation:
Counted the mice and written the number
there are 17 mice

Read and draw . Count and write.

Question 1.

How many in all? ___________
Answer:

Explanation:
Counted and written the number
There are 18 in all

Question 2.

How many in all? ___________
Answer:

Explanation:
Counted and written the number
There are 16 in all

Question 3.

How many in all? ___________
Answer:

Explanation:
Counted and written the number
There are 20 in all

Question 4.

How many in all? ___________
Answer:

Explanation:
Counted and written the number
There are 17 in all

Read and draw . Count and write.

Question 5.

How many in all? ___________
Answer:

Explanation:
Counted and written the number
There are 15 in all

Question 6.

How many in all? ___________
Answer:

Explanation:
Counted and written the number
There are 19 in all

Join the dots.

Answer:

Explanation:
Joined the dots by tracing the numbers.

Lesson 5 Compare and Order

Count and write. Color the group with more.

Answer:

Explanation:
Number of stars more than the hearts. So color the stars

Count and write. Color the group with fewer.

Answer:

Explanation:
Number of glass fewer than the cups. So color the glasses

Draw the same number.

Answer:

Explanation:
Counted  the circles there are 8. So drawn the 8 circles.

Draw more.

Answer:

Explanation:
Counted  the circles there are 12. So drawn the 15 circles.
Since 15 is more than 12.

Draw fewer.

Answer:

Explanation:
Counted  the circles there are 20. So drawn the 12 circles.
Since 12 is fewer than 20.

Go through the Math in Focus Grade K Workbook Answer Key Chapter 2 Numbers to 10 to finish your assignments.

Math in Focus Kindergarten Chapter 2 Answer Key Numbers to 10

Lesson 1 All about 6

Match.

Answer:

Explanation:
Counted the number of wheels and  counted and matched the same number of wheels

Draw.

Answer:

Explanation:
counted and  Drawn the number of dots

Trace.

Answer:

Explanation:
Traced the numbers from 1 to 6

Count and Write.

Question 1.

Answer:

Explanation:
Counted and written number of wheels
There are 6 wheels

Question 2.

Answer:

Explanation:
Counted and written number of cups
There are 6 cups

Question 3.

Answer:

Explanation:
Counted and written number of flags
There are 6 flags

Question 4.

Answer:

Explanation:
Counted and written number of oranges
There are 6 oranges

Question 5.

Answer:

Explanation:
Counted and written number of lemons
There are 6 lemons

Question 6.

Answer:

Explanation:
Counted and written number of onions
There are 6 onions

Lesson 2 All about 7

Sing.

Circle the groups of seven bees.

Explanation:

Circled the group of seven bees

Match.

Explanation:

Counted the number of hives and matched with the same number of hives

Draw.

Explanation:

Counted and drawn the circles

Trace.

Explanation:

Traced the numbers from 6 and 7

Look and Say.

Count and Write.

Question 1.

Answer:
Explanation:
Counted and written number of hives
There are 7 hives

Question 2.

Answer:
Explanation:
Counted and written number of glasses
There are 7 glasses

Question 3.

Answer:
Explanation:
Counted and written number of cups
There are 7 cups

Question 4.

Answer:
Explanation:
Counted and written number of forks
There are 7 forks

Question 5.

Answer:
Explanation:
Counted and written number of bees
There are 7 bees

Question 6.

Answer:
Explanation:
Counted and written number of pencils
There are 7 pencils

Lesson 3 All about 8

Color.

Explanation:

According to the number colored the dots

Explanation:

According to the number colored the dots

Draw.

Explanation:

According to the numbers drawn the apples

Match.

Explanation:
Counted the number of oranges and matched according to the same number of oranges

Draw.

Explanation:

Counted and drawn the same number of dots

Trace.

Explanation:

Written and traced the numbers from 1 to 4

Trace.

Explanation:

Written and traced the numbers from 5 to 8

Count and write.

Question 1.

Answer:

Explanation:
Counted and written number of balls
There are 8 balls

Question 2.

Answer:

Explanation:
Counted and written number of fishes
There are 8 fishes

Question 3.

Answer:

Explanation:
Counted and written number of bells
There are 8 bells

Question 4.

Answer:

Explanation:
Counted and written number of glasses
There are 8 glasses

Question 5.

Answer:

Explanation:
Counted and written number of spoons
There are 8 spoons

Question 6.

Answer:

Explanation:
Counted and written number of oranges
There are 8 oranges

Lesson 4 Numbers 0 to 9

Match.

Explanation:

Counted and matched the numbers from 1 to 9

Draw.

Explanation:

Drawn the same number of dots by counting the dots

Trace.

Explanation:

Traced the numbers from 1 to 5

Explanation:

Traced the numbers from 6 to 9

Write the missing numbers.

Explanation:

Written the missing numbers

Explanation:

Written the missing numbers

Count and write

Explanation:

The second boy is holding only one glass

Explanation:

In the above picture the first boy is catching 9 balloons
the second boy is catching 4 bottles and the third boy is catching 5 balls

Count and write.

Question 1.

Answer:

Explanation:
Counted and written number of Balls
There are 9 balls

Question 2.

Answer:

Explanation:
Counted and written number of birds
There are 9 birds

Question 3.

Answer:

Explanation:
Counted and written number of Eggs
There are 9 eggs

Question 4.

Answer:

Explanation:
Counted and written number of Carrots
There are 9 carrots

Question 5.

Answer:

Explanation:
Counted and written number of sticks
There are 9 sticks

Question 6.

Answer:

Explanation:
Counted and written number of Cheese
There are 9 cheese

Circle the group of 9 players.

Explanation:
In the above picture there are 10 boys circled 9 of them

Lesson 5 Pairing Sets with Numbers

Read, count, and circle.

Question 1.

Answer:
Explanation:
3 + 1 = 4
Circled the 4 birds

Question 2.

Answer:
Explanation:
4 – 1 = 3
Circled 3 fishes

Question 3.

Answer:
Explanation:
Circled the same number that is 2

Lesson 6 Pairing One-to-One

What is missing? Complete the set.

Explanation:
For cups saucer is missing
For bottles straw is missing
For cats tails are missing

Circle, Count, and write.

Question 1.
There is cheese for 6 mice.

How many mice will be hungry? ____
Answer:
3 will be hungry
Explanation:
There are 9 mice but only 6 cheese are there so 3 are missing

Question 2.
3 boys have coats.

How many boys will be cold? ____
Answer:
2 boys will be cold
Explanation:
There are 5 boys out of them 3 having coats
so 2 will be cold

Question 3.
There are 6 egg holders.

How many eggs are needed to fill all the egg holders? _____
Answer:
4 eggs are needed to fill all the egg holders
Explanation:
There are 6 egg holders out of them there are only 2 eggs
so 4 will be empty

Practice the problems of Math in Focus Grade 6 Workbook Answer Key Cumulative Review Chapters 4-7 to score better marks in the exam.

Math in Focus Grade 6 Course 1 A Cumulative Review Chapters 4-7 Answer Key

Concepts and Skills

Write each ratio in simplest form. (Lesson 4.2)

Question 1.
12 : 28
Answer:
4 : 7
Explanation:
To find the simplest form of ratios we can use,
prime factor method or greatest common factor method.
12 : 28
common factor for both the numbers is 3
so, divided both sides with 3
12 : 28 = 4 : 7

Question 2.
32 : 18
Answer:
16 : 9
Explanation:
To find the simplest form of ratios we can use,
prime factor method or greatest common factor method.
32 : 18
common factor for both the numbers is 2
so, divided both sides with 2
32 : 18 = 16 : 9

Question 3.
36 : 81
Answer:
4 : 9
Explanation:
To find the simplest form of ratios we can use,
prime factor method or greatest common factor method.
36 : 81
common factor for both the numbers is 9
so, divided both sides with 9
36 : 81 = 4 : 9

Question 4.
64 : 40
Answer:
8 : 5
Explanation:
To find the simplest form of ratios we can use,
prime factor method or greatest common factor method.
64 : 40
common factor for both the numbers is 8
so, divided both sides with 8
64 : 40 = 8 : 5

Find the missing term in each pair of equivalent ratios. (Lesson 4.2)

Question 5.
35 : 25 = : 5
Answer:
Missing term is 7
Explanation:
product of extremes = product of means
a:b = c:d
ab = cd
ad = bc
a = 35, b = 25, c = x, d = 5
35 x 5 = 25x
25x = 175
x = 175 ÷ 25
x = 7

Question 6.
48 : 33 = 16 :
Answer:
Missing term is 11
Explanation:
product of extremes = product of means
a:b = c:d
ab = cd
ad = bc
a = 48, b = 33, c = 16, d = x
48x  = 33 x 16
48x = 528
x = 528 ÷ 48
x = 11

Question 7.
18 : = 9 : 12
Answer:
Missing term is 24
Explanation:
product of extremes = product of means
a:b = c:d
ab = cd
ad = bc
a = 18, b = x, c = 9, d = 12
18 x 12 = 9x
9x = 216
x = 216 ÷ 9
x = 24

Question 8.
: 24 = 21 : 14
Answer:
Missing term is 36
Explanation:
product of extremes = product of means
a:b = c:d
ab = cd
ad = bc
a = x, b = 24, c = 21, d = 14
14x = 24 x 21
14x = 504
x = 504 ÷ 14
x = 36

Express each percent as a fraction in simplest form. (Lesson 6.1)

Question 9.
58%
Answer:
= \(\frac{29}{50}\)
Explanation:
= \(\frac{58}{100}\)
= \(\frac{29}{50}\)

Question 10.
24\(\frac{1}{3}\)%
Answer:
2433.33
Explanation:
24 \(\frac{1}{3}\) x 100
= \(\frac{73}{3}\) x 100
= \(\frac{73 x 100}{3}\)
= \(\frac{7300}{3}\)
= 2433.33
Question 11.
9.4%
Answer:
\(\frac{29}{50}\)
Explanation:
9.4% = \(\frac{9.4}{100}\)
multiply the numerator and denominator with 10,
as numerator has decimal
= \(\frac{94}{1000}\)
Divided numerator and denominator with 2
= \(\frac{47}{500}\)

Express each percent as a decimal. (Lesson 6.1)

Question 12.
37%
Answer:
0.37
Explanation:
37% = \(\frac{37}{100}\)
= 0.37

Question 13.
67%
Answer:
0.67
Explanation:
67% = \(\frac{67}{100}\)
= 0.67

Question 14.
8.9%
Answer:
0.089
Explanation:
8.9% = \(\frac{8.9}{100}\)
= 0.089

Express each fraction as a percent. (Lesson 6.2)

Question 15.
\(\frac{19}{20}\)
Answer:
95%
Explanation:
\(\frac{19}{20}\)
= \(\frac{19}{20}\) × 100%
= \(\frac{1900}{20}\) %
= 95%

Question 16.
\(\frac{23}{25}\)
Answer:
92%
Explanation:
\(\frac{23}{25}\)
= \(\frac{23}{25}\) × 100%
= \(\frac{2300}{25}\) %
= 92%

Question 17.
\(\frac{360}{400}\)
Answer:
90%
Explanation:
\(\frac{360}{400}\)
= \(\frac{360}{400}\) × 100%
= \(\frac{36000}{400}\) %
= 90%

Express each decimal as a percent. (Lesson 6.2)

Question 18.
0.07
Answer:
7%
Explanation:
Express 0.04 as a percent.
Converting from a decimal to a percentage is done by multiplying the decimal value by 100 and adding %.
0.07 = \(\frac{7}{100}\)
= 0.07 x 100 = 7

Question 19.
0.62
Answer:
62%
Explanation:
Express 0.62 as a percent.
Converting from a decimal to a percentage is done by multiplying the decimal value by 100 and adding %.
0.62= \(\frac{62}{100}\)
= 0.62 x 100
= 62

Question 20.
0.8
Answer:
80%
Explanation:
Express 0.8 as a percent.
Converting from a decimal to a percentage is done by multiplying the decimal value by 100 and adding %.
0.8 = \(\frac{8}{100}\)
= 0.8 x 100
= 80

Find the quantity represented by each percent. (Lesson 6.3)

Question 21.
55% of 600 liters
Answer:
330 liters
Explanation:
55% of 600 liters
= \(\frac{55}{100}\) × 600
= 330
66% of 740 is 330.

Question 22.
73% of $3,900
Answer:
$2,847
Explanation:
73% of $3,900
= \(\frac{73}{100}\) × 3,900
= 2,847
73% of 740 is $2,847.

Write an algebraic expression for each of the following. (Lesson 7.1)

Question 23.
A number that is 7 more than 3 times x
Answer:
3x + 7
Explanation:
x + 7 is an algebraic expression in terms of x.
x and 7 are the terms of expression.
A number that is 7 more than 3 times x
3x + 7

Question 24.
The total cost, in cents, of 8 apples and 9 oranges if each apple costs 2y cents and each orange costs 3y cents
Answer:
43y cents
Explanation:
each apple costs 2y cents
each orange costs 3y cents
8 x 2y + 9 x 3y
= 16y + 27y
= 43y

Question 25.
The perimeter of a rectangle whose sides are of lengths (4z + 3) units and (3z + 5) units
Answer:
14z + 16 units
Explanation:
The perimeter of a rectangle = 2(Length + Breadth)
= 2 ( (4z + 3) + (3z + 5))
= 2 (4z + 3z + 3 + 5)
= 2 (7z + 8)
= 14z + 16

Evaluate each expression for the given value of the variable. (Lesson 7.2)

Question 26.
4(x + 5) – \(\frac{2x}{3}\) when x = 6
Answer:
40
Explanation:
by substituting  x value = 6 in the given algebraic equation
4(x + 5) – \(\frac{2x}{3}\)
= 4(6 + 5) – \(\frac{2 x 6}{3}\)
= (24 + 20) – \(\frac{12}{3}\)
= 44 – \(\frac{12}{3}\)
= (132 – 12) ÷ 3
= 120 ÷ 3
= 40

Question 27.
\(\frac{6 y+7}{3}\) + \(\frac{3 y+4}{4}\) when y = 8
Answer:
\(\frac{152}{6}\)  or 25.33
Explanation:
\(\frac{6 y+7}{3}\) + \(\frac{3 y+4}{4}\) when y = 8
= \(\frac{6 x 8+7}{3}\) + \(\frac{3 x 8+4}{4}\)
= \(\frac{48+7}{3}\) + \(\frac{24+4}{4}\)
= \(\frac{55}{3}\) + \(\frac{28}{4}\)
= \(\frac{304}{12}\)
= \(\frac{152}{6}\)  or 25.33

Simplify each expression. (Lesson 7.3)

Question 28.
36a + 12 – 6a – 7
Answer:
30a + 5
Explanation:
36a + 12 – 6a – 7
= 36a – 6a + 12 – 7
= 30a + 5

Question 29.
21 + 34b – 8 – 5b + 8 + 23b
Answer:
Explanation:
21 + 34b – 8 – 5b + 8 + 23b
= 21 – 8 + 8 + 34b – 5b + 23b
= 21 + 52b

Expand each expression. (Lesson 7.4)

Question 30.
6(m + 4) + 3(m + 9)
Answer:
9m + 51
Explanation:
6(m + 4) + 3(m + 9)
= 6m + 24 + 3m + 27
= 9m + 51

Question 31.
8(n + 4) + 5(6 + n)
Answer:
13n + 62
Explanation:
8(n + 4) + 5(6 + n)
= 8n + 32 + 30 + 5n
= 13n + 62

Factor each expression. (Lesson 7.4)

Question 32.
6a – 42
Answer:
6(a – 7)
Explanation:
6a – 42
In the above expression 6 is a common factor
= 6(a – 7)

Question 33.
56 – 8b
Answer:
8(7 – b)
Explanation:
56 – 8b
In the above expression 8 is a common factor
= 8(7 – b)

Question 34.
23c + 37 – 5c + 8
Answer:
9(2c + 5)
Explanation:
23c + 37 – 5c + 8
= 23c – 5c + 37 + 8
= 18c + 45
= 9(2c + 5)

Question 35.
58 + 40d – 9 – 19d
Answer:
7(7 – 4d)
Explanation:
58 + 40d – 9 – 19d
= 58 – 9 + 40d – 19d
= 49 – 28d
= 7(7 – 4d)

Problem Solving

Solve. Show your work.

Question 36.
A factory produces 550 bottles of water in 25 minutes. How many bottles can it produce in 3 minutes? (Chapter 5)
Answer:
66 water bottles
Explanation:
A factory produces 550 bottles of water in 25 minutes.
Number of bottles can it produce in 3 minutes
= (550 x 3) ÷ 25
= 1650 ÷ 25 = 66

Question 37.
A machine can stamp 75 caps per minute. At this rate, how long will it take to stamp 3,000 caps? (Chapter 5)
Answer:
40 minutes
Explanation:
A machine can stamp 75 caps per minute
At this rate, how long will it take to stamp 3,000 caps
= 3000 ÷ 75
= 40 minutes

Question 38.
There were 65 students in the hall. 80% of them were girls. How many girls were in the hall? (Chapter 6)
Answer:
52 girls
Explanation:
There were 65 students in the hall.
80% of them were girls.
Number of  girls in the hall
= 80% 0f 65
= \(\frac{80}{100}\) X 65
= \(\frac{5200}{100}\)
= 52

Question 39.
Kenneth had $1,800. He spent 34% of it on a watch. How much did he pay for the watch? (Chapter 6)
Answer:
$612
Explanation:
Kenneth had $1,800.
He spent 34% of it on a watch.
Amount he paid for the watch
= 34% 0f 1800
= \(\frac{34}{100}\) X 1800
= 34 X 18 = 612

Question 40.
28% of a number is 168. Find the number. (Chapter 6)
Answer:
number is 200
Explanation:
28% of a number is 168
28% of x = 168
\(\frac{28}{100}\)x = 168
\(\frac{28x}{100}\) = 168
28x = 168 x 100
28x = 16800
x = 16800 ÷ 28
x = 600

Question 41.
140% of a number is 364. Find the number. (Chapter 6)
Answer:
number is 260
Explanation:
140% of a number is 364
140% of x = 364
\(\frac{140}{100}\)x = 364
\(\frac{140x}{100}\) = 364
140x = 364 x 100
140x = 36400
x = 36400 ÷ 140
x = 260

Question 42.
Of the 90 students who sat for a test, 24 students passed. Find the ratio of the number of students who passed the test to the number of students who did not. Give your answer in simplest form. (Chapter 4)
Answer:
4 : 11
Explanation:
Of the 90 students who sat for a test, 24 students passed.
passed = 90 – 24 = 66
So, the ratio of the number of students who passed the test to the number of students who did not.
24 : 66 = 4 : 11
Question 43.
On Saturday, Aaron spent $108. On Sunday, he spent $54 more than what he spent on Saturday. Find the ratio of Aaron’s spending on Saturday to his spending on both Saturday and Sunday. Give your answer in simplest form. (Chapter 4)
Answer:
2 : 3
Explanation:
On Saturday, Aaron spent $108.
On Sunday, he spent $54 more than what he spent on Saturday.
$108 + $54 = $162
So, the ratio of Aaron’s spending on Saturday to his spending on both Saturday and Sunday.
108 : 162 = 2 : 3

Question 44.
A dalmatian weighs 72 pounds. A bullmastiff is 24 pounds heavier than the dalmatian. A bulldog is 12 pounds lighter than the bullmastiff. Find the ratio of the bulldog’s weight to the dalmatian’s weight. Give your answer in simplest form. (Chapter 4)
Answer:
7 : 6
Explanation:
A dalmatian weighs 72 pounds.
A bullmastiff is 24 pounds heavier than the dalmatian.
72 pounds + 24 pounds = 96 pounds
A bulldog is 12 pounds lighter than the bullmastiff.
96 pounds – 12 pounds = 84
The ratio of the bulldog’s weight to the dalmatian’s weight.
84 : 72 = 7 : 6

Question 45.
The ratio of the number of left-handers to the number of right-handers in a middle school is 6 : 15. If there are 120 left-handers, how many right-handers are there? (Chapter 4)
Answer:
300 right-handers
Explanation:
The ratio of the number of left-handers to the number of right-handers in a middle school is 6 : 15.
If there are 120 left-handers,
then how many right-handers are there
6 : 15 :: 120 : x
product of extremes = product of means
a:b = c:d
\(\frac{a}{b}\) = \(\frac{c}{d}\)
ad = bc
a = 6, b = 15, c = 120, d = x
6x = 15 x 120
4x = 1800
x = \(\frac{1800}{6}\)
x = 300

Question 46.
Mrs. Jackson gave a sum of money to her son and daughter in the ratio 8 : 9. Her daughter received $3,060. How much did Mrs. Jackson give to her two children in all? (Chapter 4)
Answer:
$5,780
Explanation:
Mrs. Jackson gave a sum of money to her son and daughter in the ratio 8 : 9.
Her daughter received $3,060.
Her son received
8 : 9 = 3060 : x
\(\frac{8}{9}\) = 3060
9x = 3060 x 8
x = 24480 ÷  9
x = 2720
Total amount Mrs. Jackson give to her two children in all
= 3060 + 2720
= 5780

Question 47.
The ratio of the number of boys to the number of girls in a school is 7 : 9. If there are 1,248 students in the school, how many girls are there? (Chapter 4)
Answer:
702 girls
The ratio of the number of boys to the number of girls in a school is 7 : 9.
If there are 1,248 students in the school,
Let the number of boys be 7x and girls be 9x
Total number of students = 7x + 9x = 1248
=> 16x = 1248
x = 1248 ÷ 16
x = 78
Number of girls = 9x
= 9 x 78 = 702

Question 48.
A sum of money was shared among Daniel, Elliot, and Frank in the ratio 5 : 7 : 8. If Frank’s share was $2,781 more than Daniel’s share, what was the original sum of money shared among the three men? (Chapter 4)
Answer:
$18540
Explanation:
Let 5x = Daniel’s share
7x = Elliot’s share
8x = Frank’s share
8x = 5x + 2781
3x = 2781
x = 927
Daniel’s share = 5x
= 5 × 927 = $4635
Elliot’s share = 7x
= 7 × 927 = $6489
Frank’s share = 8x
= 8 × 927 = $7416
Amount shared among all = 4635 + 6489 + 7416 = $18540

Question 49.
A tank is filled with water at a rate of 2.4 liters per minute. At this rate, how long will it take to fill the tank with 84 liters of water? (Chapter 5)
Answer:
35 minutes
Explanation:
A tank is filled with water at a rate of 2.4 liters per minute.
At this rate, how long will it take to fill the tank with 84 liters of water
1 min = 2.4 L
84 L = x
x = 84 ÷ 2.4
x = 35min

Question 50.
A farmer uses 920 grams of grains to feed 8 chickens. (Chapter 5)
a) At this rate, how many grams of grains does he use to feed 100 chickens?
Answer:
11500 grams
Explanation:
number of grams used to feed 8 chickens = 920g
number of grams used to feed 1 chicken = 920 ÷ 8 = 115g
number of grams used to feed 100 chickens = 100 × grams used for 1 chicken
= 100 × 115 = 11500g

b) At this rate, how many chickens can he feed using 48.3 kilograms of grains?
Answer:
420 chickens
Explanation:
Grams used = 48.3 × 1000 = 48300g
1kg = 1000g
number of grams used to feed 1 chicken = 115g
number of chickens = grams used ÷ number of grams used to feed 1 chicken
= 48300 ÷ 115
= 420 chickens

Question 51.
The distance between School A and School B is 360 kilometers. (Chapter 5)
a) If a bus leaves School A at 9:30 A.M. and reaches School B at 2:30 P.M., what is its speed in kilometers per hour?
Answer:
A to B = 360Km
Explanation:
start time at  A 9:30 AM
reaching time at B 2:30 PM
the difference = 5Hours
Speed = \(\frac{Distance}{Time}\)
= \(\frac{360}{5}\)
= 72 kilometers per hour

b) If a car travels at a speed of 80 kilometers per hour, how long will it take to travel from School A to School B?
Answer:
400 kilometer
Explanation:
start time at  A 9:30 AM
reaching time at B 2:30 PM
speed of car is 80kilometer per hour
Speed = \(\frac{Distance}{Time}\)
80 = \(\frac{Distance}{5}\)
80 × 5 = Distance
Distance travels by a car = 400 kilometers

Question 52.
A truck traveled from Town A to Town B, and then to Town C. The truck took 3 hours to travel from Town A to Town B at an average speed of 42 kilometers per hour. It then traveled from Town B to Town C at an average speed of 68 kilometers per hour. The truck took a total of 5 hours to travel from Town A to Town C. (Chapter 5)
a) What is the distance between Town A and Town B?
Answer:
126km
Explanation:
Town A to Town B
time = 3hours and (speed = 42 kmph)
the distance between Town A and Town B
Distance = Speed x time
= 42 × 3
= 126 kilometers
the distance between Town A and Town B is 126 km

b) What was average speed of the truck for the whole journey?
Answer:
55 kilometers per hour
Explanation:
(42 + 68)/2
= 110/2
= 55 kilometers per hour

Question 53.
Russell bought a CD player that cost $120 before it went on sale for a 15% discount. If he paid 5% sales tax on the sale price, how much did Russell pay for the CD player? (Chapter 6)

Answer:
$107.10
Explanation:
Russell bought a CD player that cost $120,
before it went on sale for a 15% discount.
If he paid 5% sales tax on the sale price, how much did Russell pay for the CD player
(120 × 15)/100
= 18
= 120 – 18
= 102
= (102 × 5)/100
= 510/100
= 5.1
Russell pay for the CD player
= $102 + $5.1
= $107.10

Question 54.
Last year, Jane had $2,800 in her bank account. This year, her savings increased by 4.5%. $he plans to increase her savings by 5% next year. How much will Jane have in her account after the two-year period? (Chapter 6)
Answer:
$3,072.30
Explanation:
Jane had $2,800 in her bank account.
(2,800 × 4.5)/100
=12,600/100
=126
2,800 + 126 = 2,926
= (2,926 × 5 )/100
= 14,630/100
= 146.3
2926 + 146.3
= 3,072.3

Question 55.
Two jackets were on sale. The first jacket cost $239 and was marked down 40%. The second jacket cost $159 and was given a 20% discount. Which of the two jackets cost less during the sale? Justify your reasoning. (Chapter 6)
Answer:
Second jacket
Explanation:
The first jacket cost $239 and was marked down 40%.
100 – 40 = 60%
60% of 239
(60 ÷ 100) × 239 = 143.40
The second jacket cost $159 and was given a 20% discount
100 – 20 = 80%
80% of 159
(80 ÷ 100) × 159 = 127.20
By compare the price of both the jackets,
second jacket price is less than the first one.

Question 56.
One year, the price of a motorcycle was $3,000. It increased to $3,550 another year. What is the percent increase in its price? Round your answer to 2 decimal places. (Chapter 6)
Answer:
18.33 or 18%
Explanation:
the price of a motorcycle was $3,000.
It increased to $3,550 another year.
the price in second year increased = 3550 – 3000 = 550
the percent increase in its price
1 – (3550 ÷ 3000)
= 1 – 1.1833
= 1833 ÷ 100 = 18.33

Question 57.
Leonard has 5 times as many stamps as Alison. Melissa has 7 more stamps than Leonard. If Alison has q stamps, how many stamps does Melissa have? (Chapter 7)
Answer:
5q + 7 stamps
Explanation:
A ⇒ q
L ⇒ 5q
M ⇒5q + 7
Melissa have 5q + 7 stamps

Question 58.
Tim is k years old and Jennifer is 4 years younger than Tim. Find their average age in 3k years’ time, in terms of k. (Chapter 7)
Answer:
(4k – 2) years
Explanation:
Tim k years
Jennifer is k – 4
average age in 3k years
= (k + 3k +k – 4 + 3k)/2
= 8k – 4/2
= 2(4k – 2)/2
= 4k – 2

Question 59.
The length of a rectangular garden is 7 meters longer than its width. If its perimeter is (12x + 14) meters, find its length in terms of x. (Chapter 7)
Answer:
(3x + 7)m
Explanation:
Perimeter of rectangle = 2 (length +width)
12x + 14 = 2 (x + 7 + x)
Perimeter = 2 width + 2 length
12x + 14  = 2 length + 2x
12x – 2x + 14 = 2 length
10x + 14 = 2 length
length = 2(5x+ 7)/2
= 5x+7

Question 60.
A cupboard weighs (5y + 6) pounds more than a table. 3 cupboards and 4 tables weigh (29y + 18) pounds in all. (Chapter 7)
a) Find the weight of the table in terms of y.
Answer:
2y lb
Explanation:
29y + 18 = 3 cupboards + 4 tables
29y + 18 = 3[( 5y + 6 ) + table] + 4 tables
29y + 18 =15y + 18 + 3 tables + 4 tables
29y – 15y +18 – 18 = 7 tables
14y = 7 tables
table = 2y

b) If y = 15, find the total weight of 2 cupboards and 3 tables.
Answer:
312 lb
Explanation:
y = 15
2[( 5y + 6 ) + table] + 3 tables
2[( 5y + 6 ) + 2y] + 3 × 2y
for y = 15
10y + 12 + 4y + 6y
20y +12
= 20(15) + 12
= 300 + 12
= 312 lbs

Question 61.
A factory can produce 45 containers of yogurt in t minutes. 950 grams of fruit are used for every 25 containers of yogurt. (Chapters 5, 7)
a) Find, in terms of t, the number of containers of yogurt that the factory can produce in 5 minutes.
Answer:
\(\frac{225}{t}\) containers
Explanation:
45 containers in t minutes,
950 grams of fruit are used for every 25 containers of yogurt.
(45 × 5) ÷  t
= \(\frac{225}{t}\)min

b) Find, in terms of t, the time taken by the factory to produce 100 containers of yogurt.
Answer:
\(\frac{20}{9}\)min or 2.22min
Explanation:
45 containers in t minutes,
time taken for 100 containers
Time = (100 containers ÷ 45 containers) × t
= \(\frac{20}{9}\)min or 2.22min

c) If t = 6, find the amount of fruit used in producing containers of yogurt in 8 minutes.
Answer:
2,280 grams
Explanation:
If t = 6min
45 containers in 6min
In 8 min number of containers produced
(45/6min) × 8min = 60 Containers.
the amount of fruit used in producing containers of yogurt in 8 minutes
=(950grams/25cont) × 60 = 2280 Grams

Practice the problems of Math in Focus Grade 6 Workbook Answer Key Chapter 7 Lesson 7.4 Expanding and Factoring Algebraic Expressions to score better marks in the exam.

Math in Focus Grade 6 Course 1 A Chapter 7 Lesson 7.4 Answer Key Expanding and Factoring Algebraic Expressions

Math in Focus Grade 6 Chapter 7 Lesson 7.4 Guided Practice Answer Key

Expand each expression.

Question 1.
3(x + 4)
Answer:
3x+12
Explanation:
3(x + 4)
= 3x + 3 x 4
= 3x + 12

Question 2.
6(2x + 3)
Answer:
12x + 18
Explanation:
6(2x + 3)
= 6 X 2x  +  6 x 3
= 12x + 18

Question 3.
2(7 + 6x)
Answer: 14+ 12x
Explanation:
2(7 + 6x)
= 2 x 7 + 6x X 2
= 14 + 12x

Question 4.
5(y – 3)
Answer:
5y – 15
Explanation:
5(y – 3)
= 5y-15

Question 5.
4(4y – 1)
Answer:
16y – 4
Explanation:
4(4y – 1)
= 16y – 4

Question 6.
9(5x – 2)
Answer:
45x – 18
Explanation:
9(5x – 2)
= 9 x 5x – 2 x 9
= 45x – 18

State whether each pair of expressions are equivalent.

Question 7.
6(x + 5) and 6x + 30
Answer:
Yes, pair of expressions are equivalent
Explanation:
6(x + 5) and 6x + 30
6(x + 5) = 6x + 30
6(x + 5) and 6x + 30 are equal.

Question 8.
7(x + 3) and 21 + 7x
Answer:
Yes, pair of expressions are equivalent
Explanation:
7(x + 3) and 21 + 7x
7(x + 3) = 7x + 21
7x + 21 and 21 + 7x are equal.

Question 9.
4(y – 4) and 4y – 4
Answer:
NO, pair of expressions are not equivalent
Explanation:
4(y – 4) and 4y – 4
4(y – 4) = 4y – 16
4y – 16 is not equal to 4y – 4

Question 10.
3(y – 6) and 18 – 3y
Answer:
NO, pair of expressions are not equivalent
Explanation:
3(y – 6) and 18 – 3y
3(y – 6) = 3y – 18
3y – 18 is not equal to 18 – 3y

Hands-On Activity

Materials

• paper
• ruler
• scissors

RECOGNIZE THAT EXPANDED EXPRESSIONS ARE EQUIVALENT

STEP 1: Draw a rectangle that is 8 centimeters wide and more than 3 centimeters long on a piece of paper. Then cut out the rectangle.
Answer:

STEP 2: Find the area of the rectangle in terms of p.
Answer:
8p + 24 cm
Explanation:
Area of rectangle = Length x Breadth
= (p+3) x 8
= 8p + 24 cm
STEP 3: Then cut the rectangle into two rectangles A and B as shown.

STEP 4: Find the areas of rectangle A and rectangle B.
Answer:
24cm
Explanation:
Area of rectangle A = Length x Breadth
= p x 8
= 8p cm
Area of rectangle B = Length x Breadth
= 3 x 8
= 24 cm

STEP 5: Using your answers found in STEP 2 and STEP 4, state how the three areas are related.
Answer:
8p + 24 cm
Explanation:
Area of rectangle = Area of rectangle A + Area of rectangle B
8p + 24 cm = 8p + 24 cm

STEP 6: You may repeat the activity using rectangles of other sizes.
can be done with different size of rectangles

Factor each expression.

Question 11.
3x + 3
Answer:
3,(x + 1)
Explanation:
In the above expression 3 is common factor.
3 and (x + 1) are the factors of 3x + 3

Question 12.
4x + 6
Answer:
2 and (2x + 3)
Explanation:
In the above expression 2 is common factor.
2,(2x + 3) are the factors of 4x + 6

Question 13.
8 + 6y
Answer:
2 and (4 + 3y)
Explanation:
8+6y
In the above expression 2 is common factor.
2 and (4 + 3y) are the factors of 8 + 6y

Question 14.
5y – 10
Answer:
5, (y-2)
Explanation:
In the above expression 5 is common factor.
5y – 10 = 5(y – 2)

Question 15.
4 – 10z
Answer:
2(2 – 5z)
Explanation:
In the above expression 2 is common factor.
4 – 10z = 2(2 – 5z)

Question 16.
12 – 8x
Answer:
4, (3-2x)
Explanation:
In the above expression 4 is common factor.
12 – 8x = 4(3 – 2x)

Question 17.
8f + 6
Answer:
2 ,(4f+3)
Explanation:
In the above expression 2 is common factor.
8f + 6 = 2(4f + 3)

Question 18.
12t – 8
Answer:
4,(3f – 2)
Explanation:
In the above expression 4 is common factor.
12t – 8 = 4(3f – 2)

Question 19.
15 + 5q
Answer:
5, (3+q)
Explanation:
In the above expression 5 is common factor.
15 + 5q = 5(3 + q)

Question 20.
32m – 40
Answer:
8 and (4m-5)
Explanation:
In the above expression 8 is common.
8 and (4m – 5)are the factors of 32m – 40

State whether each pair of expressions are equivalent.

Question 21.
8x + 6 and 2(4x + 3)
Answer:
Yes, pair of expressions are equivalent.
Explanation:
8x + 6 and 2(4x + 3)
8x + 6  = 2(4x + 3)
2(4x + 3) and 2(4x + 3) are equal.

Question 22.
3(y + 6) and 18 + 3y
Answer:
Yes, pair of expressions are equivalent.
Explanation:
3(y + 6) and 18 + 3y
3(y + 6) = 3y + 18
3y + 18 = 18 + 3y are equal.

Question 23.
5x – 10 and 5(x – 5)
Answer:
No, pair of expressions are not equivalent.
Explanation:
5x – 10 and 5(x – 5)
5x – 10 = 5(x – 2)
5(x – 2) and 5(x – 5) are not equal.

Question 24.
4(y – 4) and 16 – 4y
Answer:
No, pair of expressions are not equivalent.
Explanation:
4(y – 4) and 16 – 4y
4(y – 4) = 4y – 16
4y – 16 is not equivalent to 16 – 4y
4(y – 4) and 16 – 4y are not equivalent.

Question 25.
3(x + 5) and 15 + 3x
Answer:
Yes, pair of expressions are not equivalent.
Explanation:
3(x + 5) and 15 + 3x
3(x + 5) = 3x + 15
3x + 15 is equal to 15 + 3x
3(x + 5) and 15 + 3x are equivalent expressions.

Question 26.
12 – 8y and 4(2y – 3)
Answer:
No, pair of expressions are not equivalent.
Explanation:
12 – 8y and 4(2y – 3)
12 – 8y = 4(3 – 2y)
12 – 8y and 4(2y – 3) are not equivalent.

Math in Focus Course 1A Practice 7.4 Answer Key

Expand each expression.

Question 1.
5(x + 2)
Answer:
5x + 10
Explanation:
5(x + 2)
= 5 X x + 5 X 2
= 5x + 10

Question 2.
7(2x – 3)
Answer:
14x – 21
Explanation:
7(2x – 3)
= 7 X 2x – 7 X 3
= 14x – 21

Question 3.
4(y – 3)
Answer:
4y – 12
Explanation:
4(y – 3)
= 4 X y – 4 X 3
= 4y – 12

Question 4.
8(3y – 4)
Answer:
24y – 32
Explanation:
8(3y – 4)
= 8 X 3y – 8 X 4
= 24y – 32

Question 5.
3(x+ 11)
Answer:
3x + 33
Explanation:
3(x+ 11)
= 3 X x + 3 X 11
= 3x + 33

Question 6.
9(4x – 7)
Answer:
36x – 63
Explanation:
9(4x – 7)
= 9 X 4x – 9 X 7
= 36 x – 63

Factor each expression.

Question 7.
6p + 6
Answer:
6 , (p + 1)
Explanation:
6p + 6
Take 6 as common factor
6 (p + 1)
6, (p + 1) are the factors of  6p + 6

Question 8.
3p + 18
Answer:
3, (p + 6)
Explanation:
3p + 18
Take 3 as common factor
3 (p + 6)
3, (p+6) are the factors of 3p + 18

Question 9.
12 + 3q
Answer:
3, (4 + q)
Explanation:
12 + 3q
Take 3 as common factor
3 (4 + q)
3, (4 + q) are the factors of 12 + 3q

Question 10.
4w – 16
Answer:
4, (w – 4)
Explanation:
4w – 16
take 4 as common factor,
4 (w – 4)
4, (w – 4) are the factors of 4w – 16

Question 11.
14r – 8
Answer:
2, (7r – 4)
Explanation:
14r – 8
take 2 as common factor,
2 (7r – 4)
2, (7r – 4) are the factors of 14r – 8

Question 12.
12r – 12
Answer:
12, (r – 1)
Explanation:
12r – 12
take 12 as common factor,
12 (r – 1)
12, (r – 1) are the factors of 12r – 12

State whether each pair of expressions are equivalent.

Question 13.
4x + 12 and 4(x + 3)
Answer:
YES, pair of expressions are equivalent
Explanation:
4x + 12 and 4(x + 3)
4x + 12 and 4x + 12
both are equal

Question 14.
5(x – 1) and 5x – 1
Answer:
NO, pair of expressions are not equivalent
Explanation:
5(x – 1) and 5x – 1
5x – 5 and 5x – 1
both are not equal

Question 15.
7(5 + y) and 7y + 35
Answer:
YES, pair of expressions are equivalent
Explanation:
7(5 + y) and 7y + 35
35 + 7y and 7y + 35
both are equal

Question 16.
9(y – 2) and 18 – 9y
Answer:
NO, pair of expressions are not equivalent
Explanation:
9(y – 2) and 18 – 9y
9y – 18 and 18 – 9y
both are not equal

Expand and simplify each expression.

Question 17.
3(m + 2) + 4(6 + m)
Answer:
7m + 30
Explanation:
3(m + 2) + 4(6 + m)
= 3m + 6 + 24 +4m
= 7m + 30

Question 18.
5(2p + 5) + 4(2p – 3)
Answer:
18p+13
Explanation:
5(2p + 5) + 4(2p – 3)
= 10p + 25 + 8p – 12
= 18p + 13

Question 19.
4(6k + 7)+ 9 – 14k
Answer:
10k + 37
Explanation:
4(6k + 7)+ 9 – 14k
= 24k + 28 + 9 – 14k
= 10k + 37

Simplify each expression. Then factor the expression.

Question 20.
14x + 13 – 8x – 1
Answer:
6, (x+2)
Explanation:
14x + 13 – 8x – 1
= 14x – 8x + 13 – 1
= 6x + 12
= 6(x + 2)
6, (x + 2) are the factors of 14x + 13 – 8x – 1

Question 21.
8(y + 3) + 6 – 3y
Answer:
5, (y+6)
Explanation:
8(y + 3) + 6 – 3y
= 8y + 24 + 6 – 3y
= 8y – 3y + 24 + 6
= 5y + 30
= 5(y + 6)
5, (y + 6) are the factors of the 8(y + 3) + 6 – 3y

Question 22.
4(3z + 7) + 5(8 + 6z)
Answer:
2 , (21z+34)
Explanation:
4(3z + 7) + 5(8 + 6z)
= 12z + 28 + 40 + 30z
= 12z + 30z + 40 + 28
= 42z + 68
= 2 (21z + 34)
2 , (21z + 34) are the factors of 4(3z + 7) + 5(8 + 6z)

Solve.

Question 23.
Expand and simplify the expression 3(x – 2) + 9(x + 1) + 5(1 + 2x) + 2(3x – 4).
Answer:
28x
Explanation:
3(x – 2) + 9(x + 1) + 5(1 + 2x) + 2(3x – 4).
= 3x – 6 + 9x + 9 + 5 + 10x + 6x – 8.
= 3x + 9x + 10x  + 6x – 6 +9 +5 – 8
= 28x + 0
= 28x

Question 24.
Are the two expressions equivalent? Justify your reasoning.
15(y + 6) + 10(y – 5) + 20(2y + 3)and 5(20 + 13y)
Answer:
Yes, the two expressions equivalent
Explanation:
15(y + 6) + 10(y – 5) + 20(2y + 3) and 5(20 + 13y)
= 15(y + 6) + 10(y – 5) + 20(2y + 3) and 5(20 + 13y)
= 15y + 90 + 10y – 50 +40y + 60  and 100 + 65y
= 65y + 100 and 100 + 65y
So, both are same.

Question 25.
A yard of lace costs w cents and a yard of fabric costs 40c more than the lace. Kimberly wants to buy one yard of lace and 2 yards of fabric. How much money will she need? Express your answer in terms of w.
Answer:
$80 w cents
Explanation:
cost of one yard of lace = w cents
cost of 2 yards of fabric = 2 × 40 = $80
Therefore, the total money needed is $80 + w cents
= $80 w cents

Question 26.
The average weight of 6 packages ¡s (9m + 8) pounds. 2 more packages, with weights of (12m + 1 2) pounds and (14m + 12) pounds, are added to the original 6 packages. Find the average weight of the 8 packages.
Answer:
10m + 9
Explanation:
9m + 8 is the average weight of the 6 packages = 54m + 48
12m + 12 and 14m + 12 is added
12m+12+14m+12 = 26m + 24
26m + 24 is added to the 54m + 48
= 54m + 26m + 48 + 24
= 80m + 72
the average weight of the 8 packages is = (80m + 72)/8 = 10m + 9

Question 27.
The figure shows two rectangles joined to form rectangle ABCD.

a) Write the length of \(\overline{B C}\) in terms of x. Then write an expression for the area of the rectangle ABCD in terms of x.
Answer:
Area =3x + 6 cm
Explanation:
the length of \(\overline{B C}\) in terms of x = x + 2
an expression for the area of the rectangle ABCD in terms of x
= x + 2 X 3
= (x + 2)3
= 3x + 6cm

b) Write an expression for the area of each of the two smaller rectangles.
Answer:
6 cm
Explanation:
the area of each of the two smaller rectangles
= 2 x 3 = 6cm

c) Math Journal Explain how you can use your answers in a) and b) to show that the following expressions are equivalent.  3x + 6 and 3(x + 2)
Answer:
Yes, both are equivalent
Explanation:
3x + 6 and 3(x + 2)
3(x + 2) can be written as 3x + 6
So, both are equal.