Math in Focus

Go through the Math in Focus Grade 6 Workbook Answer Key Chapter 3 Multiplying and Dividing Fractions and Decimals to finish your assignments.

Math in Focus Grade 6 Course 1 A Chapter 3 Answer Key Multiplying and Dividing Fractions and Decimals

Math in Focus Grade 6 Chapter 3 Quick Check Answer Key

Add or subtract.

Question 1.
5.3 + 6.49
Answer:
5.3 + 6.49 = 11.79.

Explanation:
The addition of 5.3 and 6.49 is 11.79.

Question 2.
6.51 – 2.03
Answer:
6.51 – 2.03 = 4.48.

Explanation:
The subtraction of 6.51 and 2.03 is 4.48.

Question 3.
9.62 + 7.08
Answer:
9.62 + 7.08 = 16.7.

Explanation:
The addition of 9.62 and 7.08 is 16.7.

Question 4.
8.4 – 7.52
Answer:
8.4 – 7.52 = 0.88.

Explanation:
The subtraction of 8.4 and 7.52 is 0.88.

Express each improper fraction as a mixed number in simplest form.

Question 5.
\(\frac{19}{3}\)
Answer:
6\(\frac{1}{3}\).

Explanation:
Here, improper fraction is a fraction in which the numerator is greater than the denominator. So the mixed fraction will be 6\(\frac{1}{3}\).

Question 6.
\(\frac{26}{4}\)
Answer:
6\(\frac{1}{2}\).

Explanation:
Here, improper fraction is a fraction in which the numerator is greater than the denominator. So the mixed fraction will be 6\(\frac{1}{2}\).

Question 7.
\(\frac{30}{7}\)
Answer:
4\(\frac{2}{7}\).

Explanation:
Here, improper fraction is a fraction in which the numerator is greater than the denominator. So the mixed fraction will be 4\(\frac{2}{7}\).

Question 8.
\(\frac{38}{5}\)
Answer:
7\(\frac{3}{5}\).

Explanation:
Here, improper fraction is a fraction in which the numerator is greater than the denominator. So the mixed fraction will be 7\(\frac{3}{5}\).

Question 9.
\(\frac{50}{8}\)
Answer:
6\(\frac{1}{4}\).

Explanation:
Here, improper fraction is a fraction in which the numerator is greater than the denominator. So the mixed fraction will be 6\(\frac{1}{4}\).

Question 10.
\(\frac{69}{9}\)
Answer:
7\(\frac{2}{3}\).

Explanation:
Here, improper fraction is a fraction in which the numerator is greater than the denominator. So the mixed fraction will be 7\(\frac{2}{3}\).

Express each mixed number as an improper fraction.

Question 11.
3\(\frac{1}{4}\)
Answer:
\(\frac{13}{4}\).

Explanation:
Here, a mixed fraction is a whole number and a proper fraction represented fraction. So 3\(\frac{1}{4}\) is \(\frac{13}{4}\).

Question 12.
4\(\frac{3}{7}\)
Answer:
\(\frac{31}{7}\).

Explanation:
Here, a mixed fraction is a whole number and a proper fraction represented fraction. So 4\(\frac{3}{7}\) is \(\frac{31}{7}\).

Question 13.
8\(\frac{5}{9}\)
Answer:
\(\frac{77}{9}\).

Explanation:
Here, a mixed fraction is a whole number and a proper fraction represented fraction. So 8\(\frac{5}{9}\) is \(\frac{77}{9}\).

Find each product in simplest form.

Question 14.
\(\frac{2}{5}\) × \(\frac{7}{8}\)
Answer:
\(\frac{2}{5}\) × \(\frac{7}{8}\) = \(\frac{7}{20}\).

Explanation:
The product of \(\frac{2}{5}\) × \(\frac{7}{8}\) is \(\frac{7}{20}\).

Question 15.
\(\frac{10}{11}\) × \(\frac{33}{5}\)
Answer:
\(\frac{10}{11}\) × \(\frac{33}{5}\) = 6.

Explanation:
The product of \(\frac{10}{11}\) × \(\frac{33}{5}\) is 2×3 = 6.

Question 16.
\(\frac{8}{7}\) × \(\frac{35}{12}\)
Answer:
\(\frac{8}{7}\) × \(\frac{35}{12}\) = 2\(\frac{1}{2}\).

Explanation:
The product of \(\frac{8}{7}\) × \(\frac{35}{12}\) which is \(\frac{10}{4}\) = 2\(\frac{1}{2}\).

Go through the Math in Focus Grade 6 Workbook Answer Key Chapter 2 Negative Numbers and the Number Line to finish your assignments.

Math in Focus Grade 6 Course 1 A Chapter 2 Answer Key Negative Numbers and the Number Line

Math in Focus Grade 6 Chapter 2 Quick Check Answer Key

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

Question 1.
Odd numbers from 20 to 30
Answer:
Odd numbers from 20 to 30 are 21, 23, 25, 27, 29.

Explanation:
Odd numbers from 20 to 30 are 21, 23, 25, 27, 29 are represented in the above horizontal number line. On a horizontal number line, the numbers become greater as you move to the right, and less as you move to the left.

Question 2.
Mixed numbers from 3 to 5, with an interval of \(\frac{1}{6}\) between each pair of mixed numbers
Answer:
Mixed numbers from 3 to 5, with an interval of \(\frac{1}{6}\) between each pair of mixed numbers are 3, 3(1/6), 3(2/6), 3(3/6), 3(4/6), 3(5/6), 4, 4(1/6), 4(2/6), 4(3/6), 4(4/6), 4(5/6), 5.

Question 3.
Decimals between 8.0 and 10.0, with an interval of 0.25 between each pair of decimals
Answer:

Explanation:
Decimals between 8.0 and 10.0, with an interval of 0.25 between each pair of decimals8.25, 8.5, 8.75, 9, 9.25, 9.5, 9.75 are represented in the above horizontal number line. On a horizontal number line, the numbers become greater as you move to the right, and less as you move to the left.

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

Question 4.

Answer:


Explanation:
The given numbers are 3/8 and 5/6. Here we have to compare the pair of numbers. On a horizontal number line, the numbers become greater as you move to the right, and less as you move to the left as we can observe in the above image. After comparing numbers on the number line 3/8 is less than 5/6.

Question 5.

Answer:


Explanation:
The given decimal numbers are 2.14 and 2.104. Here we have to compare the pair of numbers. On a horizontal number line, the numbers become greater as you move to the right, and less as you move to the left as we can observe in the above image. After comparing decimal numbers on the number line 2.14 is greater than 2.104.

Question 6.

Answer:


Explanation:
The given numbers are 0.72 and 7/12. Here we have to compare the pair of numbers. On a horizontal number line, the numbers become greater as you move to the right, and less as you move to the left as we can observe in the above image. After comparing numbers on the number line 0.72 is greater than 7/12.

Go through the Math in Focus Grade 6 Workbook Answer Key Chapter 1 Review Test to finish your assignments.

Math in Focus Grade 6 Course 1 A Chapter 1 Review Test Answer Key

Concepts and Skills

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

Question 1.
Positive whole numbers less than 8
Answer:
0, 1, 2, 3, 4, 5, 6 and 7.

Explanation:
The positive whole numbers less than 8 are 0, 1, 2, 3, 4, 5, 6 and 7.

Question 2.
Whole numbers greater than 25 but less than 33
Answer:
26, 27, 28, 29, 30, 31 and 32.

Explanation:
The whole numbers greater than 25 and less than 33 are 26, 27, 28, 29, 30, 31 and 32.

Question 3.
Mixed numbers from 4 to 6, with an interval of \(\frac{1}{4}\) between each pair of mixed numbers
Answer:
4\(\frac{1}{4}\) , 4\(\frac{2}{4}\) , 4\(\frac{3}{4}\) ,  5\(\frac{1}{4}\) , 5\(\frac{2}{4}\) and 5\(\frac{3}{4}\) .

Explanation:
The mixed numbers numbers from 4 to 6 are 4\(\frac{1}{4}\) , 4\(\frac{2}{4}\) , 4\(\frac{3}{4}\) ,  5\(\frac{1}{4}\) , 5\(\frac{2}{4}\) and 5\(\frac{3}{4}\) .

Question 4.
Decimals between 3.0 and 3.8, with an interval of 0.2 between each pair of decimals
Answer:
3.2, 3.4 and 3.6.

Explanation:
Decimals between 3.0 and 3.8 with 0.2 interval are 3.2, 3.4 and 3.6.

Express each number as a product of its prime factors.

Question 5.
42
Answer:
2 x 3 x 7

Explanation:
Prime factors of 42 are 2, 3 and 7
The product of prime factors of 42 is 2 x 3 x 7.

Question 6.
150
Answer:
2 x 3 x 5 x 5

Explanation:
Prime factors of 150 are 2, 3 and 5
The product of prime factors of 150 is 2 x 3 x 5 x 5.

Find the common factors of each pair of numbers.

Question 7.
21 and 63
Answer:
1, 3, 7, 21.

Explanation:
Factors of 21 – 1, 3, 7, 21
Factors of 63 – 1, 3, 7, 9, 21, 63.
Common factors of 21 and 63 are 1, 3, 7, and 21.

Question 8.
35 and 70
Answer:
1, 5, 7, 35.

Explanation:
Factors of 35 are 1, 5, 7, 35
Factors of 70 are 1, 2, 5, 7, 10, 14,  35, 70.
Common factors of 35 and 70 are 1, 5, 7 and 35.

Find the greatest common factor of each pair of numbers.

Question 9.
8 and 12
Answer:
4

Explanation:
Factors of 8 are 1, 2, 4, 8
Factors of 12 are 1, 2, 3, 4, 6, 12
The greatest common factor of 8 and 12 is 4.

Question 10.
42 and 32
Answer:
2

Explanation:
Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
Factors of 32 are 1, 2, 4, 8, 16, 32
The greatest common factor of 42 and 32 is 2.

Find the first three common multiples of each pair of numbers.

Question 11.
4 and 5
Answer:
20, 40, 60.

Explanation:
Multiples of 4 -4,8,12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60
Multiples of 5 – 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60
First three common multiples of 4 and 5 are 20, 40, 60.

Question 12.
9 and 21
Answer:
63, 126 and 189.

Explanation:
Multiples of 9 -9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126.
Multiples of 21 -21, 42, 63, 84, 105, 126, 147, 168, 189
First three common multiples of 9 and 21 are 63, 126, 189.

Find the least common multiple of each pair of numbers.

Question 13.
6 and 15
Answer:
30

Explanation:
Multiples of 6 -6, 12, 18, 24, 30
Multiples of 15 – 15, 30, 45.
Least common multiple of 6 and 15 is 30.

Question 14.
8 and 11
Answer:
88

Explanation:
Multiples of 8 – 8, 16, 24, 36, 40, 48, 56, 64, 72, 80, 88.
Multiples of 11 – 11, 22, 33, 44, 55, 66, 77, 88, 99,
Least common multiple of 8 and 11 is 88.

Find the square of each number.

Question 15.
14
Answer:

196

Explanation:
14² = 14 x 14
=196
The square of 14 is 196.

Question 16.
30
Answer:

900

Explanation:
30² = 30 x 30
= 900
The square of 30 is 900.

Find the square root of each number.

Question 17.
169
Answer:
13

Explanation:
Recalling the multiplication facts of 169, you know that
169 = 13 x 13
= 13²
So, \(\sqrt{169}\) = 13

Question 18.
484
Answer:
22

Explanation:
Recalling the multiplication facts of 484, you know that
484 = 22 x 22
= 22²
So, \(\sqrt{484}\) = 22

Find the cube of each number.

Question 19.
4
Answer:
64

Explanation:
4³ = 4 x 4 x 4
= 16 x 4
= 64
The cube of the number 4 is 64.

Question 20.
20
Answer:
8000

Explanation:
20³ = 20 x 20 x 20
= 400 x 20
= 8000
The cube of the number 20 is 8000.

Find the cube root of each number.

Question 21.
1,331
Answer:
11

Explanation:
Finding the cube root of a number is the inverse of finding the cube of a number
prime factorization of 1331 = 11 x 11 x 11
=11³
so, cube root of 1331 is 11.

Question 22.
9,261
Answer:
21

Explanation:
Finding the cube root of a number is the inverse of finding the cube of a number
prime factorization of 9261 = 21 x 21 x 21
=21³
so, cube root of 9621 is 21.

Find the value of each of the following.

Question 23.
4³ + 6²
Answer:
100

Explanation:
4³ = 4 x 4 x 4 = 64
6² = 6 x 6 = 36
4³ + 6² = 64 + 36 = 100
4³ + 6²  = 100

Question 24.
8³ – 5²
Answer:
487

Explanation:
8³ = 8 x 8 x 8 = 512
5² = 5 x 5 = 25
8³ – 5² = 512 – 25 = 487
8³ – 5² = 487

Question 25.
5³ × 4³ – 13²
Answer:
7381

Explanation:
5³ = 5 x 5 x 5 = 125
4³ = 4 x 4 x 4= 64
13² = 169
5³ x 4³ – 13² =125 x 64 – 169 = 7381
5³ x 4³ – 13² = 7381

Question 26.
8² + 10³ ÷ 5²
Answer:
104

Explanation:
8² = 8 x 8 = 64
10³ = 10 x 10 x 10 = 1000
5² = 5 x 5 = 25
8² + 10³ ÷  5² = 64 + (1000 ÷ 25)
= 64 + 40
= 104
8² + 10³ ÷  5² = 104.

Solve.

Question 27.
Given that 63² = 3,969, find the square of 630.
Answer:
396900

Explanation:
If 63² = 3,969 then square of 630 will be 396900.

Question 28.
Given that \(\sqrt{1,225}\) = 35, evaluate 350²
Answer:
122500

Explanation:
If \(\sqrt{1,225}\) = 35 then 350² will be 122500.

Question 29.
Given that 16³ = 4,096, find the cube root of 4,096,000.
Answer:
160

Explanation:
If 16³ = 4,096 then cube root of 4,096,000will be 160.

Question 30.
Given that = 24, evaluate 240³.
Answer:
13824000

If = 24 then 240³ will be 13824000.

Problem Solving

Solve. Show your work.

Question 31.
Find two consecutive numbers whose squares differ by 25.
Answer:
12 and 13

Explanation:
Square of 12 is 144, square of 13 is 169
169 – 144 = 25
SO, 12 and 13 are the two consecutive numbers whose squares differ by 25.

Question 32.
Riley is packing 144 pencils, 120 files, and 108 notebooks equally into as many boxes as possible.
a) Find the greatest number of boxes that Riley could pack the items into.
Answer:
9 boxes

Explanation:
Riley is packing 144 pencils, 120 files, and 108 notebooks equally into as many boxes as possible.
He needs 12 of each thing and he can pack 9 boxes.(12 x 9 = 108).

b) Find the number of pencils, files, and notebooks in each box.
Answer:
12 pencils, 12 files and 12 notebooks.

Question 33.
Imelda, Susan, and Clara are driving go-carts around a track. Imelda takes 14 minutes, Susan takes 18 minutes, and Clara takes 10 minutes to drive one lap. Suppose all three of them start together at a point and drive at their same speeds. After how many minutes would all three meet again?
Answer:

Question 34.
How many squares with sides that are 6 inches long are needed to cover a square with a side length of 30 inches without overlapping?
Answer:
5

Explanation:
A  square with a side 6 inches long,
6 x 5 = 30
So, to cover a square with a side length of 30 inches 5 squares with side of 6 inches are needed.

Question 35.
A wooden crate is a cube with edge lengths of 18 inches. The crate contains tiny plastic cubes with edge lengths of 3 inches. How many plastic cubes can fit inside the wooden crate?
Answer:
6

Explanation:
A wooden crate is a cube with edge lengths of 18 inches.
The crate contains tiny plastic cubes with edge lengths of 3 inches
3 x 6 = 18
So, 6 plastic cubes can fit inside the wooden crate.

Go through the Math in Focus Grade 6 Workbook Answer Key Chapter 1 Lesson 1.3 Common Factors and Multiples to finish your assignments.

Math in Focus Grade 6 Course 1 A Chapter 1 Lesson 1.3 Answer Key Common Factors and Multiples

Math in Focus Grade 6 Chapter 1 Lesson 1.3 Guided Practice Answer Key

Complete.

Use the lists of factors on the right to find the common factors of 10 and 28.

Question 1.
The factors of 1o are , , , and .
The factors of 28 are , , , , and .
The common factors of 10 and 28 are and .

Answer:
The factors of 10are 1, 2, 5, 10
The factors of 28 are 1, 2, 4, 7, 4, 28
The common factors are 1 and 2.

Find the common factors of each pair of numbers.

Question 2.
16 and 24
Answer:
1, 2 and 4.

Explanation:
The factors of 16 are 1, 2, 4, 8, 16
The factors of 24 are 1, 2, 3, 4, 6, 12, 24
The common factors of 16 and 24 are 1, 2 and 4.

Question 3.
27 and 35
Answer:
1

Explanation:
The factors of 27 are 1, 3, 9, 27
The factors of 35 are 1, 5, 7, 35
The common factors of 27 and 35 is 1.

Question 4.
36 and 50
Answer:
1 and 2.

Explanation:
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 50 are 1, 2, 5, 10, 25, 50
The common factors of 36 and 50 are 1 and 2.

Question 5.
40 and 54
Answer:
1 and 2.

Explanation:
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54.
The common factors of 40 and 54 are 1 and 2.

Complete.

Question 6.
Find the greatest common factor of 20 and 32.
Answer:
Method 1

The factors of 20 are , , , , , and .
The factors of 32 are , , , , , and
The common factors of 20 and 32 are , , and .
The greatest common factor of 20 and 32 is .

Method 2
By prime factorization,
20 = 2 • •
32 = 2 • • • •
Greatest common factor = 2 •
=
The greatest common factor of 20 and 32 is .

Method 3

The greatest common factor of 20 and 32 is .

Find the greatest common factor of each pair of numbers.

Question 7.
15 and 27
Answer:
3

Explanation:
The factors of 15 = 1, 3, 5, 15
The factors of 27 = 1, 3, 9, 27
The common factors of 15 and  27 are 1 and 3
The greatest common factor of 15 and 27 is 3.

Question 8.
36 and 54
Answer:
18

Explanation:
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 54 are  1, 2, 3, 6, 9, 18, 27, 54
The common factors of 36 and 54 are 1, 3, 6, 9, 18
The greatest common factor of 36 and 54 is 18.

Question 9.
48 and 72
Answer:
24

Explanation:
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The factors of 72 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 36, 72
The common factors of 48 and 72 are 1, 2, 3, 4, 6, 8, 12, 16, 24
The greatest common factor of 48 and 72 is 24.

Question 10.
40 and 100
Answer:
20

Explanation:
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100
The common factors of 40 and 100 are 1, 2, 4, 5, 10, 20.
The greatest common factors of 40 and 100 is 20.

Hands-On Activity

Find The Common Factors And The Greatest Common Factor Of Two Numbers

Materials:

• number cards (from 10 to 100)
• factor cards (2s, 3s, 5s, and 7s)

Work in pairs.

Step 1.
Shuffle the number cards and place them face down on a flat surface. Give half the factor cards to each player.

Step 2.
Each player turns over a number card and uses his or her factor cards to show the prime factorization of the number.

Step 3.
The first player states the greatest common factor (GCF) of the two numbers. If the player is correct, the player keeps the two number cards. Players reuse the factor cards on each turn.
Example

Step 4.
Two new number cards are turned over and the process repeats. This time the second player gets to state the GCF.
Step 5.
Play continues until all number cards have been used. The player with more number cards is the winner.

Use the greatest common factor with the distributive property.

Express 12 + 20 as a product of the greatest common factor of the numbers and another sum.

First find the greatest common factor of the two numbers.

Greatest common factor of 12 and 20 = 2 • 2
= 4
Then write the sum a different way. You know that
12 = 4 • 3 20 = 4 • 5
So, 12 + 20 = 4 • 3 + 4 • 5
= 4(3 + 5)
The distributive property says that:
4(3 + 5) = 4 • 3 + 4 • 5

The number lines below show you that 12 + 20 and 4(3 + 5) represent the same number.
Notice that either way, you “end up” at the same place on the number line.
12 + 20 is a jump of 12 plus a jump of 20.

Complete.

Question 11.
Express 18 + 45 as a product of the greatest common factor of the numbers and another sum.
By prime factorization,
18 = 2 • • 45 = 3 • •
Greatest common factor of 18 and 45 = •
=
18 + 45 = • + •
= ( + )
Answer:

Express the sum of each pair of numbers as a product of the greatest common factor of the numbers and another sum.

Question 12.
35 + 91
Answer:
7( 5 + 13 )

Explanation:
By prime factorization,
35 = 5 x 7, 91 = 7 x 13
Greatest common factor of 35 and 91 = 7
35 + 91 = 5 . 7 + 13 . 7
= 7(5+ 13)
35 + 91 = 7(5 + 13).

Question 13.
60 + 85
Answer:
5 ( 12 + 17 )

Explanation:
By prime factorization,
60 = 2 x 2 x 3 x 5, 85 = 5 x 17
Greatest common factor of 60and 85 = 5
60 + 85 = 5 . 12 + 5 . 17
= 5( 12 + 17 )
60 + 85 = 5( 12 + 17 ).

Question 14.
24 + 64
Answer:
8( 3 + 8 )

Explanation:
By prime factorization,
24 = 2 x 2 x 2 x 3, 64 = 2 x 2 x 2 x 2 x 2 x 2
Greatest common factor of 2 4and 64 = 2 . 2 . 2 = 8
24 + 64 = 8 . 3 + 8 . 8
= 8( 3 + 8)
24 + 64 = 8( 3 + 8 )

Complete.

Question 15.

Answer:
15, 30 and 45

Explanation:
The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45
The multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45
The first three common multiples of 3 and 5 are 15, 30, 45.

List the first ten multiples of each pair of numbers. Then find the common multiples of each pair of numbers from the first ten multiples.

Question 16.
6 and 12
Answer:
12, 24, 36 and 48.

Explanation:
The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
The multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120
The common multiples of 6 and 12 from first ten multiples are 12, 24, 36, 48.

Question 17.
7 and 11
Answer:
11

Explanation:
The multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77
The multiples of 11 are 11, 22, 33, 44, 55, 66, 77, 88, 99, 110.
The common multiples of 7 and 11 from first ten multiples is 77.

Complete.

Question 18.
Find the least common multiple of 8 and 10.
Method 1

Method 2
By prime factorization,
8 = 2 • • 10 = 2 •
Least common multiple = 2 • • •
=
The least common multiple of 8 and 10 is .

Method 3

The least common multiple of 8 and 10 is .

Find the least common multiple of each pair of numbers.

Question 19.
3 and 7
Answer:
21

Explanation:
By prime factorization,
3 = 3, 7= 7
The least common multiple = 3 . 7 = 21
The least common multiple of 3 and 7 is 21.

Question 20.
5 and 12
Answer:
60

Explanation:
By prime factorization,
5 = 5, 12 = 2 x 2 x 3
The least common multiple = 2 . 2 . 2. 3 . 5 = 60
The least common multiple of 5 and 12 is 60

Question 21.
4 and 9
Answer:
36

Explanation:
By prime factorization,
4 = 2 x 2, 9 = 3 x 3
The least common multiple = 2 . 2 . 3 . 3 = 36
The least common multiple of 4 and 9 is 36

Question 22.
6 and 11
Answer:
66

Explanation:
By prime factorization,
6 = 2 x 3, 11 = 11
The least common multiple = 2 . 3 . 11 = 66
The least common multiple of 6 and 11 is 66.

Math in Focus Course 1A Practice 1.3 Answer Key

Find the common factors of each pair of numbers.

Question 1.
18 and 63
Answer:
1, 3 and 9

Explanation:
The factors of 18 are 1, 2, 3, 6, 9, 18
The factors of 63 are 1, 3, 7, 9, 21, 63
The common factors of 18 and 63 are 1, 3, 9.

Question 2.
15 and 75
Answer:
1, 3, 5 and 15.

Explanation:
The factors of 15 are 1, 3, 5, 15
The factors of 75 are 1, 3, 5, 15, 25, 75
The common factors of 15 and 75 are 1, 3, 5, 15.

Question 3.
30 and 50
Answer:
1, 2, 5 and 10

Explanation:
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 50 are 1, 2, 5, 10, 25, 50
The common factors of 30 and 500 are 1, 2, 5, 10.

Question 4.
64 and 92
Answer:
1, 2 and 4.

Explanation:
The factors of 64 are 1, 2, 4, 8, 16, 32, 64
The factors of 92 are 1, 2, 4, 23, 46, 92
The common factors of 44 and 92 are 1, 2, 4.

Question 5.
26 and 78
Answer:
1, 2, 13 and 26.

Explanation:
The factors of 26 are 1, 2, 13, 26
The factors of 78 are 1, 2, 6, 13, 26, 39, 78
The common factors of 26 and 78 are 1, 2, 13, 26.

Question 6.
55 and 88
Answer:
1 and 11.

Explanation:
The factors of 55 are 1, 5, 11, 55
The factors of 88 are 1, 2, 4, 8, 11, 22, 44, 88
The common factors of 55 and 88 are 1, 11.

Find the greatest common factor of each pair of numbers.

Question 7.
24 and 36
Answer:
12

Explanation:
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
The common factors are 1, 2, 3, 4, 6, 12
The greatest common factors of 24 and 36 is 12.

Question 8.
30 and 54
Answer:
6

Explanation:
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
The common factors are 1, 2, 3, 6
The greatest common factors of 30 and 54 is 6.

Question 9.
42 and 98
Answer:
14

Explanation:
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 98 are 1, 2, 7, 14, 49, 98
The common factors are 1, 2, 7, 14
The greatest common factors of 42 and 98 is 14.

Question 10.
48 and 72
Answer:
24

Explanation:
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The common factors are 1, 2, 3, 4, 6, 8, 12, 24
The greatest common factors of 48 and 72 is 24.

Question 11.
65 and 91
Answer:
13

Explanation:
The factors of 65 are 1, 5, 13, 65
The factors of 91 are 1, 7, 13, 91
The common factors are 1, 13
The greatest common factors of 65 and 91 is 13.

Question 12.
84 and 100
Answer:
4

Explanation:
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100
The common factors are 1, 2, 4
The greatest common factors of 84 and 100 is 4.

Find the first five common multiples of each pair of numbers.

Question 13.
5 and 6
Answer:
30, 60, 90, 120 and 150

Explanation:
The multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65…..
The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60….
First five common multiples of 5 and 6 are 30, 60, 90, 120, 150.

Question 14.
4 and 7
Answer:
28, 56, 84, 112, 140

Explanation:
The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60….
The multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70…..
First five common multiples of 4 and 7 are 28, 56, 84, 112 and 140

Question 15.
9 and 10
Answer:
90, 180, 270, 360 and 450.

Explanation:
The multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90…..
The multiples of 10 are 10, 20, 30, 40, 50, 60, 70, 80 , 90…..
First five common multiples of 10 and 9 are 90, 180, 270, 360, 450.

Question 16.
8 and 11
Answer:
88, 176, 264, 352 and 440.

Explanation:
The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88…
The multiples of 11 are 11, 22, 33, 44, 55, 66, 77, 88, 99, 110
First five common multiples of 8 and 11 are 88, 176, 264, 352 and 440.

Question 17.
15 and 25
Answer:
75, 150 and 225.

Explanation:
The multiples of 15 are 15, 30, 45, 60, 75, 90, 105, 120, 135, 150….
The multiples of 25 are 25, 50, 75, 100, 125, 150, 175, 200, 225….
First five common multiples of 15 and 25 are 75, 150 and 225.

Question 18.
7 and 20
Answer:
140, 280, 420, 560 and 700

Explanation:
The multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70…..
The multiples of 20 are 20, 40, 60, 80, 100, 120, 140,160…
First five common multiples of 7 and 20 are 140, 280, 420, 560 and 700.

Find the least common multiple of each pair of numbers.

Question 19.
3 and 10
Answer:
30

Explanation:
By prime factorization,
3 = 3, 10 = 2 x 5
The least common multiple = 3 . 2 . 5 = 30
The least common multiple of 3 and 10 is 30.

Question 20.
7 and 12
Answer:
84

Explanation:
By prime factorization,
7 = 7, 12 = 2 x 2 x 3
The least common multiple = 7 . 2 . 2 . 3
The least common multiple of 7 and 12 is 84.

Question 21.
5 and 8
Answer:
40

Explanation:
By prime factorization,
5 = 5, 8= 2 x 2 x 2
The least common multiple = 5 . 2 . 2 . 2 = 40
The least common multiple of 5 and 8 is 40.

Question 22.
9 and 11
Answer:
99

Explanation:
By prime factorization,
9 = 3 x 3, 11 = 11
The least common multiple = 3 . 3 .11 = 99
The least common multiple of 9 and 11 is 99.

Question 23.
10 and 14
Answer:
70

Explanation:
By prime factorization,
10 = 2 x 5, 14 = 2. 7
The least common multiple = 2 . 5 . 7
The least common multiple of 10 and 14 is 70.

Question 24.
18 and 24
Answer:
72

Explanation:
By prime factorization,
18 = 2 x 3 x 3, 24 = 2 x 2 x 2 x 3
The least common multiple = 2 . 2 . 2 . 3 . 3 = 72
The least common multiple of 18 and 24 is 72.

Find the greatest common factor of each set of numbers.

Question 25.
24, 26, and 84
Answer:
2

Explanation:
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.
The factors of 26 are 1, 2, 13, 26
The factors of 84 are 1, 2, 4, 6, 7, 12, 14, 21, 28, 42, 84
The greatest common factor of 24, 26 and 84 is 2.

Question 26.
30, 48, and 72
Answer:
6

Explanation:
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The greatest common factor of 30, 48 and 72 is 6.

Question 27.
36, 24, and 96
Answer:
12

Explanation:
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The greatest common factor of 36, 24 and 96 is 12.

Question 28.
42, 90, and 81
Answer:
3

Explanation:
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
The factors of 81 are 1, 3, 9, 27, 81
The greatest common factor of 42, 90 and 81 is 3

Question 29.
60, 75, and 102
Answer:
3

Explanation:
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12,15, 20, 30, 60
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102
The greatest common factor of 60, 75 and 102 is 3.

Question 30.
63, 105, and 294
Answer:
7

Explanation:
The factors of 63 are 1, 3, 7, 9, 21, 63
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294
The greatest common factor of 63, 105 and 294 is 7.

Find the least common multiple of each set of numbers.

Question 31.
18, 24, and 42
Answer:

Explanation:
The least common multiple of 18, 24 and 42 is 2 x 3 x 3 x 4 x 7 = 504.

Question 32.
21, 33, and 57
Answer:

Explanation:
The least common multiple of 21, 33 and 57 is 3 x 7 x 11 x 19 = 4389.

Question 33.
14, 30, and 70
Answer:

Explanation:
The least common multiple of 14, 30 and 70 is 2 x 5 x 7 x 3 = 210.

Question 34.
27, 48, and 66
Answer:

Explanation:
The least common multiple of 27, 48 and 66 is 2 x 3 x 9 x 8 x 11 = 4752.

Question 35.
55, 75, and 115
Answer:

Explanation:
The least common multiple of 55, 75 and 115 is 5 x 11 x 15 x 23 = 18975.

Question 36.
78, 90, and 140
Answer:

Explanation:
The least common multiple of 78, 90 and 140 is 2 x 3 x 3 x 5 x 13 x 14 = 16380.

Find the greatest common factor and the least common multiple of each set of numbers.

Question 37.
10, 20, and 25
Answer:
5, 100

Explanation:
By prime factorization,
10 = 2 x 5, 20 = 2 x 2 x 5, 25 = 5 x 5
The least common multiple = 2 . 5 . 2 . 5 = 100
The least common multiple of 10 , 20 and 25 is 100.
The greatest common factor is 5.

Question 38.
16, 28, and 40
Answer:

Greatest common factor is 4.

Explanation:
The least common multiple of 16, 28 and 135 is 560.
By prime factorization:
16 = 2 x 2 x 2 x 2, 28 = 2 x 2 x 7, 40 = 2 x 2 x 2 x 5
common factors are 2 x 2
The greatest common factor is 4.

Question 39.
54, 81, and 135
Answer:
27, 810

Explanation:
By prime factorization,
54 = 2 x 3 x 3 x 3, 81= 3 x 3 x 3 x 3, 135 = 3 x 3 x 3 x 5
The least common multiple =2 . 3 . 3 . 3 . 3  . 5
The least common multiple of 84 , 81 and 135 is 810
The greatest common factor is 3 x 3 x 3 = 27.

Question 40.
72, 144, and 216
Answer:
72, 432

Explanation:
By prime factorization,
72 = 2 x 2 x 2 x 3 x 3, 144 = 2 x 2 x 2 x 2 x 3 x 3, 216 = 2 x 2 x 2 x 3 x 3 x 3
The least common multiple = 2 . 2 . 2 . 2 . 3 . 3 . 3
The least common multiple of 72 , 114 and 216 is 432.
The greatest common factor is 2 x 2 x 2 x 3 x 3 = 72

Solve.

Question 41.
Makayla has two types of ropes. She wants to cut the ropes into pieces of the same length for butterfly knots,

a) Find the greatest possible length that she can cut for each piece, so that no rope will be left unused.
Answer:

b) Write the sum of the two lengths and factor out the number you found in part a). What does the number inside the parentheses represent?
Answer:

Question 42.
Giselle buys two types of flowers, 48 pink roses and 56 white lilies. She combines the flowers to make identical bouquets, with no flowers left over.
a) Find the greatest number of bouquets that Giselle can make.
Answer:
Giselle can make 8 bouquets

Explanation:
By prime factorization,
48 = 2 x 2 x 2 x 2 x 3, 56 = 2 x 2 x 2 x 7
common multiple is 2 x 2 x 2 = 8
Greatest common multiple of 48  and 56 is 8

b) Find the number of pink roses and white lilies in each bouquet.
Answer:
6 pink roses and 7 white lilies

Explanation:
pink roses = 48 = 8 x 6
white lilies = 56 = 8 x 7
So, Each bouquet has 6 pink roses and 7 white lilies.

Question 43.
A red light flashes every 14 minutes. A blue light flashes every 24 minutes. When will the two lights flash together again, if they last flashed together at 8 A.M.?
Answer:

Question 44.
a) Find the product of 84 and 90.
Answer:

Explanation:
The product of 84 and 90 is 7560.

b) Find the product of the greatest common factor and the least common multiple of 84 and 90.
Answer:

Explanation:
Least common multiple of 84 and 90 is 1260,
Greatest common factor of 84 and 90 is 6
Product of the greatest common factor and the least common multiple of 84 and 90 is
1260 x 6 = 7560.

c) What do you observe about your answers to parts a) and b)?
Answer:
The answers of both parts a and b are same.

d) Choose two other numbers and repeat parts a) and b). Do you get the same results?
Answer:
I chose the numbers 6 and 12
Yes, the results are same

Explanation:

The product of the two numbers is equal to the product of the least common multiple and greatest common factor of the numbers.

Go through the Math in Focus Grade 6 Workbook Answer Key Chapter 1 Lesson 1.2 Prime Factorization to finish your assignments.

Math in Focus Grade 6 Course 1 A Chapter 1 Lesson 1.2 Answer Key Prime Factorization

Math in Focus Grade 6 Chapter 1 Lesson 1.2 Guided Practice Answer Key

Complete.

Question 1.
Express 48 as a product of its prime factors.
Answer:
Method 1

Method 2

Math in Focus Course 1A Practice 1.2 Answer Key

Question 1.
Copy the array of numbers. Circle all the prime numbers.

Answer:

Explanation:
I circled all the prime numbers between 1 and 30.

Express each number as a product of its prime factors.

Question 2.
6
Answer:

6 = 2 x 3

Explanation:
2 and 3 are the prime factors of 6.

Question 3.
15
Answer:

15 = 3 x 5

Explanation:
3 and 5 are the prime factors of 15.

Question 4.
36
Answer:

36 = 2 x 2 x 3 x 3

Explanation:
2 and 3 are the prime factors of 36.

Question 5.
78
Answer:

78 = 2 x 3 x 13

Explanation:
2, 3 and 13 are the prime factors of 78.

Question 6.
184
Answer:

184 = 2 x 2 x 2 x 23

Explanation:
2 and 23 are the prime factors of 184.

Question 7.
360
Answer:

360 = 2 x 2 x 2 x 3 x 3 x 5

Explanation:
2, 3 and 5 are the prime factors of 360.

Question 8.
24
Answer:

24 = 2 x 2 x 2 x 3

Explanation:
2 and 3 are the prime factors of 24.

Question 9.
49
Answer:

49 = 7 x 7

Explanation:
7 is the only prime factor of 49.

Question 10.
81
Answer:

81 = 3 x 3 x 3 x 3

Explanation:
3 is the prime factor of 81.

Question 11.
144
Answer:

144 = 2 x 2 x 2 x 2 x 3 x 3

Explanation:
2 and 3 are the prime factors of 144.

Question 12.
245
Answer:

245 = 5 x 7 x 7

Explanation:
5 and 7 are the prime factors of 245.

Question 13.
510
Answer:

510 = 2 x 3 x 5 x 17

Explanation:
2, 3, 5 and 17 are the prime factors of 510.

Question 14.
250
Answer:

250 = 2 x 5 x 5 x 5

Explanation:
2 and 5 are the prime factors of 250.

Question 15.
1,089
Answer:

1089 = 3 x 3 x 11 x 11

Explanation:
3 and 11 are the prime factors of 1089.

Question 16.
4,725
Answer:

4725 = 3 x 3 x 3 x 5 x 5 x 7.

Explanation:
3, 5 and 7 are the prime factors of 4725.

Question 17.
900
Answer:

900 = 2x 2 x 3 x 3 x 5 x 5

Explanation:
2, 3 and 5 are the prime factors of 900.

Question 18.
27,000
Answer:

27000 = 2x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5.

Explanation:
2, 3 and 5 are the prime factors of 27000.

Solve.

Question 19.
Math Journal Describe the steps for finding the prime factors of 42.
Answer:

Question 20.
400 written as a product of its prime factors is 2 × 2 × 2 × 2 × 5 × 5. Write 800 as a product of its prime factors.
Answer:
2 x 2 × 2 × 2 × 2 × 5 × 5 = 800

Explanation:
800 written as a product of its prime factors is 2 x 2 × 2 × 2 × 2 × 5 × 5.

Question 21.
Given that 320 written as a product of its prime factors is 2 × 2 × 2 × 2 × 2 × 2 × 5, write 3,200 as a product of its prime factors.
Answer:
2 x 2 × 2 × 2 × 2 × 2 × 2 × 5 x 5 = 3200

Explanation:
3200 written as a product of its prime factors is 2 x 2 × 2 × 2 × 2 × 2 × 2 × 5 x 5 .

Question 22.
2,700 written as a product of its prime factors is 2 × 2 × 3 × 3 × 3 × 5 × 5. Write 270 as a product of its prime factors.
Answer:
2 × 3 × 3 × 3 × 5 = 270

Explanation:
270 written as a product of its prime factors is 2 ×  3 × 3 × 3 × 5.

Question 23.
It is given that 4,800 can be expressed in terms of its prime factors as 2 × 2 × 2 × 2 × 2 × 2 × 3 × 5 × 5.

a) Write 1,200 as a product of its prime factors.
Answer:
2 x 2 x 2 x 2 x 3 x 5 x 5 = 1200

Explanation:
1200 can be expressed in terms of its prime factors as 2 x 2 x 2 x 2 x 3 x 5 x 5.

b) Now, write 120 as a product of its prime factors.
Answer:
2 x 2 x 2 x 3 x 5 = 120

Explanation:
120 can be expressed in terms of its prime factors as 2 x 2 x 2 x 3 x 5 .

Go through the Math in Focus Grade 6 Workbook Answer Key Chapter 5 Lesson 5.2 Real-World Problems: Rates and Unit Rates to finish your assignments.

Math in Focus Grade 6 Course 1 A Chapter 5 Lesson 5.2 Answer Key Real-World Problems: Rates and Unit Rates

Math in Focus Grade 6 Chapter 5 Lesson 5.2 Guided Practice Answer Key

Solve.

Question 1.
A unicycle wheel makes 196 revolutions in 7 minutes.
a) At this rate, how many revolutions does it make in 1 minute?
The unicycle wheel makes the same number of revolutions every minute.

Answer:
28 revolutions
Explanation:

b) At this rate, how many revolutions does the unicycle wheel make in 15 minutes?

min → × = revolutions
The unicycle makes revolutions in 15 minutes.
Answer:
420 revolutions
Explanation:

15 min → 28 × 15 = 420 revolutions
The unicycle makes 420 revolutions in 15 minutes.

Question 2.
Megan babysits for 5 hours and earns $60.
a) At this rate, how much does she earn in 1 hour?
hours → $
1 hour → $ ÷ = $
She earns $ in 1 hour.
Answer:
$ 12 in 1 hour.
Explanation:
5 hours → $ 60
1 hour → $ 60 ÷ 5 = $12
She earns $ 12 in 1 hour.

b) At this rate, how much will Megan earn if she babysits for 14 hours?
14 hours → × = $
Megan will earn $ if she babysits for 14 hours.
Answer:
$168 for 14 hours
Explanation:
14 hours → 14 × 12 = $168
Megan will earn $ 168 if she babysits for 14 hours.

Question 3.
The table shows the charges for renting a bicycle.
Tom rented a bicycle from 10 A.M. to 2 P.M. ON the same day. How much did he pay for renting the bicycle?

Total number of hours = h
Charge for first hour = $
Charge for each additional 1 hour = 2 × Cost for each additional \(\frac{1}{2}\) hour
= 2 × $
= $
Charge for last three hours = × $
= $
Total charge = $ + $
= $
Tom paid $ for renting the bicycle.
Answer:
$18
Explanation:
Total number of hours = 4 h
Charge for first hour = $3.00
Charge for each additional 1 hour = 2 × Cost for each additional \(\frac{1}{2}\) hour
= 2 × $2.5
= $5.0
Charge for last three hours = 3 × $5
= $15.00
Total charge = $3.00 + $15.00
= $18.00
Tom paid $18.00 for renting the bicycle.

Question 4.
Chloe scored 87 points in 5 basketball games, and Fiona scored 45 points in 2 basketball games. Which of the two players scored more points per game? Explain.
Chloe: .
5 games → points
1 game → ÷ 5 = points
Chloe scored points per game.

Fiona: .
2 games → points
1 game → ÷ = points
Fiona scored points per game.

Comparing the number of points each player scored per game, scored a higher number of points per game.
So, scored more points per game.
Answer:
5.1 scored more points per game
Explanation:
Chloe: .
5 games → 87 points
1 game → 87 ÷ 5 = 17.4 points
Chloe scored 17.4 points per game.

Fiona: .
2 games → 45 points
1 game → 45 ÷ 2 = 22.5 points
Fiona scored 22.5 points per game.

Comparing the number of points each player scored per game, Fiona scored a higher number of points per game.
22.5 – 17.4 = 5.1
So, 5.1 scored more points per game.

Question 5.
A high-speed train can travel at a speed of 65 meters per second. How far can the train travel in 2 seconds?

Answer:
130 M
Explanation:

Question 6.
The distance between City X and City Y is 216 kilometers. Mr. Thomas rides his motorcycle at a speed of 54 kilometers per hour. How long does he take to travel from City X to City Y?
Method 1
km → h
km → \(\frac{?}{?}\) = h
Mr. Thomas takes hours to travel from City X to City Y.

Method 2
Time = Distance ÷ Speed
= ÷
= h
Mr. Thomas takes hours to travel from City X to City Y.
Answer:
4 hours
Explanation:
Method 1
216 km → h
216 km → \(\frac{216}{54?}\) = 4 h
Mr. Thomas takes 4 hours to travel from City X to City Y.

Method 2
Time = Distance ÷ Speed
= 216 ÷ 54
= 4 h
Mr. Thomas takes 4 hours to travel from City X to City Y.

Question 7.
The distance between Town P and Town Q is 80 miles, and the distance between Town Q and Town R is 320 miles. A van takes 2\(\frac{1}{2}\) hours to travel from Town P to Town Q. It takes another 5 hours to travel from Town Q to Town R. Find the average speed of the van for the whole journey.

Total distance from Town P to Town R = 80 +
= mi
Total time taken to travel from Town P to Town R = 2\(\frac{1}{2}\) +
= h

= \(\frac{?}{?}\)
= ÷
= mi/h or mph
The average speed of the van is miles per hour.
Answer:
53.33 min/hr or 53 mph
Explanation:

Total distance from Town P to Town R = 80 + 320 = 400 mi
Total time taken to travel from Town P to Town R = 2\(\frac{1}{2}\) + 5
= \(\frac{15}{2}\) h
=7\(\frac{1}{2}\) h

= \(\frac{?}{?}\)
= 400 ÷7 \(\frac{1}{2}\)
= 53.33 min/hr or 53 mph
The average speed of the van is 53.33 miles per hour.

Question 8.
Celia ran around a 400-meter track two times. It took her 4 minutes to run around the track once, and 6 minutes to run around it again. Find Celia’s average speed.
Total distance Celia ran = 2 ×
= m
Total time taken to run around the track twice = +
= min

= \(\frac{?}{?}\)
= m/min
Celia’s average speed was meters per minute.
Answer:
80 meters per minute.
Explanation:
Total distance Celia ran = 2 × 400 = 800 m
Total time taken to run around the track twice = 4 + 6 = 10 min

= \(\frac{800}{10}\)
= 80 m/min
Celia’s average speed was 80 meters per minute.

Math in Focus Course 1A Practice 5.2 Answer Key

Solve. Show your work.

Question 1.
A tennis ball machine can launch 60 tennis balls in 12 minutes. At this rate, how many tennis balls can it launch in 2 hours?
Answer:
600 Tennis balls
Explanation:
There are 120 minutes in 2 hours
10 sets of 12 minutes in 120 minutes.
\(\frac{120}{12}\) x 60 = 600
Therefore, 10 sets of 60 balls launched.

Question 2.
Water flows from a faucet at a rate of 5 liters every 25 seconds.
a) At this rate, how much water will flow from the faucet in 45 seconds?
Answer:
9 liters
Explanation:
The rate per 5 seconds, given in the first question is 45 seconds.
\(\frac{5}{25}\) = \(\frac{11}{5}\)
The x amount of liters in 45 seconds.
\(\frac{x}{45}\) = \(\frac{11}{5}\)
5x = 45
x = 9 liters

b) At this rate, how long will it take to collect 60 liters of water?
Answer:
300 seconds or 5 hours
Explanation:
9 liters for every 45 seconds.
60 liters in x amount of seconds.
\(\frac{60}{x}\) = \(\frac{11}{5}\)
x = 60 x 5
x = 300 sec

Question 3.
There are 1,600 kilocalories in the 5 cups of dog food that Mike gives his adult dog. Mike gives his puppy 2 cups of the same dog food. How many kilocalories are there in this 2-cup serving?
Answer:
640 kilocalories
Explanation:
There are 1,600 kilocalories in the 5 cups of dog food that Mike gives his adult dog.
Kilocalories = \(\frac{1,600}{5}\)
Mike gives his puppy 2 cups of the same dog food.
Total kilocalories are there in this 2-cup serving
Kilocalories = 320 per cup
Kilocalories for 2 cups = 320 x 2 = 640 for 2 cups

Question 4.
The table shows the postal charges for sending letters to Country Y. How much does it cost to send a letter weighing 60 grams to Country Y?

Answer:
$1.70
Explanation:
Cost of a letter weighing 60 grams to Country
first 20 g = 50 cents
next 40 g = 30 cents x 4 = 120 cents
weighing 60 grams to Country Y total  = 120 + 50
= 170 cents or $1.70

Question 5.
A vehicle traveled at a speed of 54 kilometers per hour for 3 hours. Find the distance traveled.
Answer:
162 kilometers
Explanation:
A vehicle traveled at a speed of 54 kilometers per hour
The distance traveled for 3 hours
1 hour = 54 kilometers
3 hours = 54 x 3 = 162 kmph.

Question 6.
A pigeon can fly at a speed of 84 kilometers per hour. How long does it take the pigeon to fly 7 kilometers?
Answer:
\(\frac{1}{12}\)minutes
Explanation:
A pigeon can fly at a speed of 84 kilometers per hour.
\(\frac{84}{1}\) = \(\frac{7}{x}\)
84x = 7
x = \(\frac{7}{84}\)
The distance taken by pigeon to fly 7 kilometers
= \(\frac{1}{12}\)

Question 7.
Karen walks home from school at a speed of 5 kilometers per hour. She takes 12 minutes to reach home. What is the distance between her school and her home? (Hint: Convert the time from minutes to hours.)
Answer:
1 kilometer
Explanation:
Distance = speed x time
= 5 x 12
=5 x 12/60 km
=60/60
=1 km

Question 8.
Kayla ran from her home to a beach at a speed of 6 meters per second. The distance from her home and the beach was 756 meters.
a) How long did she take to run from her home to the beach?
Answer:
126 seconds
Explanation:
Time = Distance ÷ Speed
Kayla ran from her home to a beach at a speed of 6 meters per second.
The distance from her home and the beach was 756 meters.
Distance = 756m
Speed= 6 meters per second
756m ÷ 6m/s = 126s

b) If Kayla wants to take 18 fewer seconds to reach the beach, at what speed must she run?

Answer:
7 meter per second
Explanation:
speed = Distance /time
= 756 / 108    (126 – 18 = 108sec)
= 7 m/s

Question 9.
Car A travels 702 miles on 12 gallons of gasoline. Car B travels 873 miles on 15 gallons of gasoline. David wants to buy a car with the lowest fuel consumption. Find out the distance traveled by each car per gallon of gasoline. Then tell which of the two cars, A, or B, David should buy.
Answer:
Car A
Explanation:
Car A travels 702 miles on 12 gallons of gasoline
= \(\frac{702}{12}\)
= 58.5 miles per gallon

Car B travels 873 miles on 15 gallons of gasoline
= \(\frac{873}{15}\)
= 58.2 miles of gallon
Car A,  David should buy.

Question 10.
Post A and Post B are 120 meters apart. Post B and Post C are 300 meters apart. Ben cycled from Post A to Post B in 15 seconds. Then he cycled from Post B to Post C in 55 seconds. Find Ben’s average speed for the distance from Post A to Post C.
Answer:
6 meters per second
Explanation:
Post A to B
= \(\frac{120}{15}\)
= 8m/s
Post B to C
= \(\frac{300}{55}\)
= 5.45 m/s
average speed for the distance from Post A to Post C.
\(\frac{8 + 5.45}{2}\)
= 6.72m/s

Question 11.
Mr. Alan drove for 2\(\frac{1}{5}\) hours at a speed of 70 kilometers per hour. He then drove another 224 kilometers. He took 5 hours for the whole journey. What was Mr. Alan’s average speed for the whole journey?
Answer:
57.4 KMPH
Explanation:
Mr. Alan drove for 2\(\frac{1}{5}\) hours at a speed of 70 kilometers per hour
Distance = speed x time
Speed = Distance /Time
= \(\frac{224}{5}\)
= 44.5 KMPH
Mr. Alan’s average speed for the whole journey
= (70 + 44.5)/2
= 57.4 KMPH

Question 12.
A family took 2 hours to drive from City A to City B at a speed of 55 miles per hour. On the return trip, due to a snowstorm, the family took 3 hours to travel back to City A.
a) How many miles did the family travel in all?
Answer:
220 miles
Explanation:
City A to B
Distance = Speed x time
= 55 x 2 = 110 km
Return journey from city B to A distance 110 km
Distance = Speed x time
110 = Speed x 3
Speed = 36.66 miles per hour

b) What was the average speed for the entire trip?
Answer:
44 miles per hour
Explanation:
Return journey from city B to A distance 110 km
Distance = Speed x time
110 = Speed x 3
Speed = 36.66 miles per hour
the average speed for the entire trip
(55 + 36.66)/2 = 45.83 miles per hour

Brain @ Work

Question 1.
The distance between Point A and Point B is 3,120 meters. Caroline leaves Point A and Laura leaves Point B at the same time. The two girls cycle toward each other until they meet at Point C. Caroline’s speed is 7.2 meters per second, and Laura’s speed is 8.4 meters per second.
a) How long does Laura take to reach Point C?
Answer:
1,680 minutes
Explanation:
7.2 + 8.4 = 15.6 m/s
Time = Distance / Speed
= 3120/15.6
= 200 s
Laura take to reach Point C
Distance = Time x speed
= 200 x 8.4 = 1680 min

b) What is the distance between Point A and Point C?

Answer:
Caroline leaves Point A
Explanation:
Distance from Point A to C
A = 3,120 and C = 1,680
3,120 – 1,680 = 1,440m

Go through the Math in Focus Grade K Workbook Answer Key Chapter 19 Measurement to finish your assignments.

Math in Focus Kindergarten Chapter 19 Answer Key Measurement

Lesson 1 Comparing Weights Using Nonstandard Units

Circle the heavier thing.

Question 1.

Answer:

Explanation:
The watermelon is heavier than banana

Question 2.

Answer:

Explanation:
The rabbit is heavier than bird

Question 3

Answer:

Explanation:
The ball is heavier than a balloon

Circle the lighter thing.

Question 1.

Answer:

Explanation:
The Feather is lighter than the cap

Question 2.

Answer:

Explanation:
The Gloze is lighter than the bag

Question 3.

Answer:

Explanation:
The berry is lighter than the apple

Count and write.

Answer:

Explanation:
The owl weighs 9 blocks and the mouse weighs 2 blocks

Circle the heavier animal.

Answer:

Explanation:
The owl weighs more than the mouse

Count and write.

Answer:

Explanation:
The teddy bear weighs 8 blocks and  doll weighs 10 blocks

Circle the lighter thing.

Answer:

Explanation:
The teddy weighs lighter than the doll.

Lesson 2 Comparing Capacities

Circle the container that holds more.

Question 1.

Answer:

Explanation:
The yellow container can contains more than the pink

Question 2.

Answer:

Explanation:
The Brown container contains more than the purple.

Question 3.

Answer:

Explanation:
The bowl contains more than the glass

Circle the container that holds less.

Question 1.

Answer:

Explanation:
The bottle contains less than the bucket

Question 2.

Answer:

Explanation:
The jar contains less than the kettle

Question 3.

Answer:

Explanation:
The pack contains less than the can

Color the containers that hold the same amount.

Question 1.

Answer:

Explanation:
The 2 yellow jars contains the same quantity

Question 2.

Answer:

Explanation:
The 2 red jars contains the same quantity

Question 3.

Answer:

Explanation:
The 2 pink boxes contains the same quantity

Lesson 3 Comparing Events in Time

Which takes more time? Circle.

Question 1.

Answer:

Explanation:
Eating takes more time than drinking

Question 2.

Answer:

Explanation:
Cleaning takes more time than throwing the dust in dust bin

Which takes less time? Circle.

Question 1.

Answer:

Explanation:
Cleaning one cup takes less time than the more plates

Question 2.

Answer:

Explanation:
Buttoning the shirt takes more time than zipping a shirt.

Go through the Math in Focus Grade K Workbook Answer Key Chapter 18 Subtraction Stories to finish your assignments.

Math in Focus Kindergarten Chapter 18 Answer Key Subtraction Stories

Lesson 1 Writing Subtraction Sentences and Representing Subtraction Stories

Count and write.

Question 1.

Answer:

Explanation:
The difference of 5 and 2 is 3
5 – 2 = 3

Question 2.

Answer:

Explanation:
The difference of 7 and 3 is 4
7 – 3 = 4

Question 3.

Answer:

Explanation:
The difference of 9 and 4 is 5
9 – 4 = 5

Count and write.

Question 1.

Answer:

Explanation:
The difference of 4 and 2 is 2
There are 4 bowls of soup out of that 2 fell down
4 – 2 = 2

Question 2.

Answer:

Explanation:
The difference of 1 and 0
There is 1 girl and not going anywhere so, 1 – 0 = 1

Question 3.

Answer:

Explanation:
The difference of 5 and 3 is 2
There are 5 bananas 3 were eaten
so, 2 are remaining
5 – 3 = 2

Question 4.

Answer:

Explanation:
The difference of 6 and 1 is 5
There are 6 apples and 1 fell down from the tree
6 – 1 = 5

Question 5.

Answer:

Explanation:
The difference of 9 and 5 is 4
There are 9 spiders 5 fell down and 4 are still remaining on the tree
9 – 5 = 4

Lesson 2 Comparing Sets

How many more? Circle. Write the number sentence.

Question 1.

Answer:

Explanation:
The difference of 6 and 5 is 1
There are 6 cars and 5 teddy
6 – 5 = 1
so, there is 1 more car than teddy

Question 2.

Answer:

Explanation:
The difference of 7 and 3 is 4
There are 7 basket balls and 3 American footballs
so, there are 4 more basket balls

Question 3.

Answer:

Explanation:
The difference of 8 and 5 is 3
There 8 shirts out of it there are only 5 shorts
so there are 3 more shirts

Question 4.

Answer:

Explanation:
The difference of 9 and 4 is 5
There are 9 milk packets and 4 milk bottles
so there are 5 more milk packets

Question 5.

Answer:

Explanation:
The difference of 10 and 3 is 7
There are 10 shoes out of it only 3 pairs of socks are there
7 shoes are more

How many more? Write the number sentence.

Question 1.

Answer:

Explanation:
The difference of 5 and 2 is 3
5 – 2 = 3
There are 3 more books than pencils

Question 2.

Answer:

Explanation:
The difference of 6 and 4 is 2
There are 2 more bats than balls

Question 3.

Answer:

Explanation:
The difference of 8 and 3 is 5
There are 5 more mushrooms than carrots

Question 4.

Answer:

Explanation:
The difference of 9 and 3 is 6
There are 6 more orange fishes than black fishes

Lesson 3 Subtraction Facts to 5

Match.

Answer:

Explanation:
The difference between the numbers are matched with the answers
3 – 1 = 2
2 – 1 = 1
4 – 1 = 3
5 – 0 = 5
1 – 1 = 0
4 – 0 = 4

Complete the number sentence.

Question 1.

Answer:

Explanation:
The difference of 5 and 4 is 1
5 – 4 = 1

Question 2.

Answer:

Explanation:
The difference of 3 and 3 is 0
3 – 3 = 0

Question 3.

Answer:

Explanation:
The difference of 4 and 2 is 2
4 – 2 = 2

Question 4.

Answer:

Explanation:
The difference of 1 and 0 is 1
1 – 0 = 1

Go through the Math in Focus Grade K Workbook Answer Key Chapter 17 Addition Stories to finish your assignments.

Math in Focus Kindergarten Chapter 17 Answer Key Addition Stories

Lesson 1 Writing Addition Sentences and Representing Addition Stories

Count and write.

Question 1.

Answer:

Explanation:
The sum of  pears are 7
4 + 3 = 7

Question 2.

Answer:

Explanation:
The sum of  balls are 6
2 + 4 = 6

Count and write.

Question 3.

Answer:

Explanation:
The sum of  pencils are 9
5 + 4 = 9

Question 4.

Answer:

Explanation:
The sum of  cars are 8
6 + 2 = 8

Question 5.

Answer:

Explanation:
The sum of  ducks are 10
3 + 7 = 10

Count and write.

Question 1.

Answer:

Explanation:
The sum of animals drinking the water and not drinking the water
3 + 1 = 4

Question 2.

Answer:

Explanation:
The sum of brown dogs and grey dogs in the park are 5
3 + 2 = 5

Question 3.

Answer:

Explanation:
The sum of  birds on the tree and the birds on the sky are 6
4 + 2 = 6

Question 4.

Answer:

Explanation:
The sum of  brown cows and black cows are 7
5 + 2 = 7

Question 5.

Answer:

Explanation:
The sum of  sleeping sheep’s and standing sheep’s are 8
6 + 2 = 8

Lesson 2 Addition Facts to 5

Fill in the missing numbers.

Question 1.

Answer:

Explanation:
When we add 0 to a number than the result is the same number.
Hence 0 is called the additive identity.
Adding zero means adding nothing in short.
The sum of 0 and 5 is 5

Question 2.

Answer:

Explanation:
The sum of 1 and 4 makes 5
1 + 4 = 5

Question 3.

Answer:

Explanation:
The sum of 2 and 3 makes 5
2 + 3 = 5

Question 4.

Answer:

Explanation:
The sum of 3 and 2 makes 5
3 + 2 = 5

Question 5.

Answer:

Explanation:
When we add 0 to a number than the result is the same number.
Hence 0 is called the additive identity.
Adding zero means adding nothing in short.
The sum of

Question 6.

Answer:

Explanation:
The sum of 5 and 0 is 5
5 + 0 = 5

Go through the Math in Focus Grade K Workbook Answer Key Chapter 12 Counting On and Counting Back to finish your assignments.

Math in Focus Kindergarten Chapter 12 Answer Key Counting On and Counting Back

Lesson 1 Counting On to 10

How many more to make 10? Count and write.

Question 1.

Answer: 4 more needed to make 10.
Explanation:
The counting on addition strategy is a great mental math strategy used to build number fact fluency.  To put it simply, counting involves adding 1, 2 or 3 to a number.
5 + 3, 6 + 2, 8 + 1 are all count on facts. So are 3 + 8, 2 + 14 and 1 + 7.
– Mental math strategy to add two numbers. We start with the biggest number of the numbers to add and count up to the second.
The above-given diagram has 6 boxes are there. To make 10 how many more boxes do we need to add. Assume it as X.
Now we need to find out the value of X.
X=10-6
X=4
therefore 4 more boxes are needed.
Or we can write as:
6+4=10.

Question 2.

Answer: 0 boxes
Explanation:
The counting on addition strategy is a great mental math strategy used to build number fact fluency.  To put it simply, counting involves adding 1, 2 or 3 to a number.
5 + 3, 6 + 2, 8 + 1 are all count on facts. So are 3 + 8, 2 + 14 and 1 + 7.
– Mental math strategy to add two numbers. We start with the biggest number of the numbers to add and count up to the second.
The above-given diagram has 5 boxes are there. To make 10 how many more boxes do we need to add. Assume it as X.
Now we need to find out the value of X.
X=10-10
X=0
therefore 0 boxes are needed.
Or we can write as:
10+0=10.

Question 3.

Answer: 7 more are needed to make 10.
Explanation:
The counting on addition strategy is a great mental math strategy used to build number fact fluency.  To put it simply, counting involves adding 1, 2 or 3 to a number.
5 + 3, 6 + 2, 8 + 1 are all count on facts. So are 3 + 8, 2 + 14 and 1 + 7.
– Mental math strategy to add two numbers. We start with the biggest number of the numbers to add and count up to the second.
The above-given diagram has 5 boxes are there. To make 10 how many more boxes do we need to add. Assume it as X.
Now we need to find out the value of X.
X=10-3
X=7
therefore 7 more boxes are needed.
Or we can write as:
3+7=10.

Question 4.

Answer: 1 more are needed to make 10.
Explanation:
The counting on addition strategy is a great mental math strategy used to build number fact fluency.  To put it simply, counting involves adding 1, 2 or 3 to a number.
5 + 3, 6 + 2, 8 + 1 are all count on facts. So are 3 + 8, 2 + 14 and 1 + 7.
– Mental math strategy to add two numbers. We start with the biggest number of the numbers to add and count up to the second.
The above-given diagram has 5 boxes are there. To make 10 how many more boxes do we need to add. Assume it as X.
Now we need to find out the value of X.
X=10-9
X=1
therefore 1 more box is needed.
Or we can write as:
9+1=10.

How many more to make 10? Count and write.

Question 5.

Answer: 6 more are needed to make 10.
Explanation:
The counting on addition strategy is a great mental math strategy used to build number fact fluency.  To put it simply, counting involves adding 1, 2 or 3 to a number.
5 + 3, 6 + 2, 8 + 1 are all count on facts. So are 3 + 8, 2 + 14 and 1 + 7.
– Mental math strategy to add two numbers. We start with the biggest number of the numbers to add and count up to the second.
The above-given diagram has 5 boxes are there. To make 10 how many more boxes do we need to add. Assume it as X.
Now we need to find out the value of X.
X=10-4
X=6
therefore 6 more boxes are needed.
Or we can write as:
6+4=10.

Question 6.

Answer: 3 more needed to make 10.
Explanation:
The counting on addition strategy is a great mental math strategy used to build number fact fluency.  To put it simply, counting involves adding 1, 2 or 3 to a number.
5 + 3, 6 + 2, 8 + 1 are all count on facts. So are 3 + 8, 2 + 14 and 1 + 7.
– Mental math strategy to add two numbers. We start with the biggest number of the numbers to add and count up to the second.
The above-given diagram has 5 boxes are there. To make 10 how many more boxes do we need to add. Assume it as X.
Now we need to find out the value of X.
X=10-7
X=3
therefore 3 more boxes are needed.
Or we can write as:
7+3=10.

Question 7.

Answer: 8 more needed to make 10.
Explanation:
The counting on addition strategy is a great mental math strategy used to build number fact fluency.  To put it simply, counting involves adding 1, 2 or 3 to a number.
5 + 3, 6 + 2, 8 + 1 are all count on facts. So are 3 + 8, 2 + 14 and 1 + 7.
– Mental math strategy to add two numbers. We start with the biggest number of the numbers to add and count up to the second.
The above-given diagram has 5 boxes are there. To make 10 how many more boxes do we need to add. Assume it as X.
Now we need to find out the value of X.
X=10-2
X=8
therefore 8 more boxes are needed.
Or we can write as:
2+8=10.

Question 8.

Answer: 9 more needed to make 10.
Explanation:
The counting on addition strategy is a great mental math strategy used to build number fact fluency.  To put it simply, counting involves adding 1, 2 or 3 to a number.
5 + 3, 6 + 2, 8 + 1 are all count on facts. So are 3 + 8, 2 + 14 and 1 + 7.
– Mental math strategy to add two numbers. We start with the biggest number of the numbers to add and count up to the second.
The above-given diagram has 5 boxes are there. To make 10 how many more boxes do we need to add. Assume it as X.
Now we need to find out the value of X.
X=10-1
X=9
therefore 9 more boxes are needed.
Or we can write as:
9+1=10.

Question 9.

Answer: 5 more needed to make 10.
Explanation:
The counting on addition strategy is a great mental math strategy used to build number fact fluency.  To put it simply, counting involves adding 1, 2 or 3 to a number.
5 + 3, 6 + 2, 8 + 1 are all count on facts. So are 3 + 8, 2 + 14 and 1 + 7.
– Mental math strategy to add two numbers. We start with the biggest number of the numbers to add and count up to the second.
The above-given diagram has 5 boxes are there. To make 10 how many more boxes do we need to add. Assume it as X.
Now we need to find out the value of X.
X=10-5
X=5
therefore 5 more boxes are needed.
Or we can write as:
5+5=10.

Lesson 2 Counting Back Using Fingers

Color, count and write.

Question 1.

Answer:

Explanation:
Above-given 10 flowers and 10 leaves.
But in the box 5 flowers and 5 leaves are there.
5 flowers are given so I coloured 5 circles and counted the remaining circles.
The remaining circles are 5.
Now count the leaves present in the box=5.

Question 2.

Answer:

Explanation:
Above-given 10 spoons and 10 forks.
But in the box 6 spoons and 4 forks are there.
6 spoons are given so I coloured 6 circles and counted the remaining circles.
The remaining circles are 4.
Now count the forks present in the box=4.

Color, count and write.

Question 3.

Answer:

Above-given 10 apples and 10 bananas.
But in the box 3 apples and 4 bananas are there.
3 apples are given so I coloured 3 circles and counted the remaining circles.
The remaining circles are 7.
Now count the bananas present in the box=4.

Question 4.

Answer:

Explanation:
The above-given: 10 shoes and 10 umbrellas.
There are 8 shoes and we need to colour the 8 circles. And we need to count the remaining circles which are not coloured.
The umbrellas present in the box=2.

Lesson 3 Finding Differences Using Fingers

Count, write and circle.

Question 1.

How many more? ____________

How many fewer? ____________
Answer:

The total number of caps=9
The total number of hats=6
The caps are more than hats.
There are 3 caps more than hats
There are 3 hats less than caps.

Count, write and circle.

Question 2.

How many more? ____________

How many fewer? ____________
Answer:

The tortoise are more.
The total number of star fish=4
The total number of tortoise=8
The tortoise is 4 more than starfish

Starfish are fewer.
The starfish are 4 fewer than tortoise.