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.

4^{3} + 6^{2}

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.

8^{3} – 5^{2}

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.

5^{3} × 4^{3} – 13^{2}

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.

8^{2} + 10^{3} ÷ 5^{2}

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 63^{2} = 3,969, find the square of 630.

Answer:

396900

Explanation:

If 63^{2} = 3,969 then square of 630 will be 396900.

Question 28.

Given that \(\sqrt{1,225}\) = 35, evaluate 350^{2}

Answer:

122500

Explanation:

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

Question 29.

Given that 16^{3} = 4,096, find the cube root of 4,096,000.

Answer:

160

Explanation:

If 16^{3} = 4,096 then cube root of 4,096,000will be 160.

Question 30.

Given that = 24, evaluate 240^{3}.

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.