Adding Decimals, Subtracting Decimals, Multiplying Decimals, Dividing Decimals

The decimal grid in each model represents 1 whole. Shade each model to show the decimal number below the model. Complete the comparison statements. 0.05 is _______ of 0.5. 0.5 is _______ times the value of 0.05.

• 0.05 is 1/10 of 0.5. 0.5 is 10 times the value of 0.05.

• 0.05 is 1/5 of 0.5. 0.5 is 5 times the value of 0.05.

• 0.05 is 1/20 of 0.5. 0.5 is 20 times the value of 0.05.

• 0.05 is 1/2 of 0.5. 0.5 is 2 times the value of 0.05.

Answer explanation

0.05 is 1/10 of 0.5 because 0.5 divided by 0.05 equals 10. Therefore, 0.5 is 10 times the value of 0.05, confirming the correct choice.

Complete the equations. 0.5 ÷ _______ = 0.05 0.05 × _______ = 0.5

• 0.5 ÷ 10 = 0.05 and 0.05 × 10 = 0.5

• 0.5 ÷ 5 = 0.05 and 0.05 × 5 = 0.5

• 0.5 ÷ 0.1 = 0.05 and 0.05 × 0.1 = 0.5

• 0.5 ÷ 2 = 0.05 and 0.05 × 2 = 0.5

Answer explanation

To find the missing numbers, divide 0.5 by 10 to get 0.05, and multiply 0.05 by 10 to return to 0.5. Thus, the correct choice is 0.5 ÷ 10 = 0.05 and 0.05 × 10 = 0.5.

Draw a number line from 0 to 2. Then draw and label points at 2 and 0.2. Use the number line to explain why 2 is 10 times the value of 0.2.

• 2 is 10 times the value of 0.2 because it is 10 times further from 0 on the number line.

• 2 is 10 times the value of 0.2 because it is 10 times closer to 0 on the number line.

• 2 is 10 times the value of 0.2 because it is 10 times larger in size.

• 2 is 10 times the value of 0.2 because it is 10 times smaller in size.

Answer explanation

2 is 10 times the value of 0.2 because on the number line, 2 is located at 2 units from 0, while 0.2 is at 0.2 units. The distance from 0 to 2 is 10 times greater than the distance from 0 to 0.2.

Complete the equations to show the relationship between 2 and 0.2. 0.2 × _______ = 2 2 ÷ _______ = 0.2

• 0.2 × 10 = 2 and 2 ÷ 10 = 0.2

• 0.2 × 5 = 2 and 2 ÷ 5 = 0.2

• 0.2 × 20 = 2 and 2 ÷ 20 = 0.2

• 0.2 × 0.1 = 2 and 2 ÷ 0.1 = 0.2

Answer explanation

To find the missing numbers, we can use multiplication and division. 0.2 × 10 = 2 shows that multiplying 0.2 by 10 gives 2. Similarly, 2 ÷ 10 = 0.2 confirms that dividing 2 by 10 results in 0.2. Thus, the correct choice is 0.2 × 10 = 2 and 2 ÷ 10 = 0.2.

Multiply or divide. 6 ÷ 10 = _______

• 0.6

• 0.06

• 1.6

• 6

Answer explanation

To solve 6 ÷ 10, divide 6 by 10, which equals 0.6. This is the correct answer, as it represents the fraction of 6 out of 10.

Multiply or divide. 0.6 ÷ 10 = _______

• 0.06

• 0.6

• 0.006

• 6

Answer explanation

To divide 0.6 by 10, move the decimal point one place to the left, resulting in 0.06. Therefore, 0.6 ÷ 10 = 0.06.

Multiply or divide. 0.6 ÷ 10² = _______

• 0.006

• 0.06

• 0.6

• 6

Answer explanation

To solve 0.6 ÷ 10², first calculate 10² which is 100. Then divide 0.6 by 100: 0.6 ÷ 100 = 0.006. Therefore, the correct answer is 0.006.

Multiply or divide. 0.3 × 10 = _______

• 3

• 0.3

• 30

• 0.03

Answer explanation

To multiply 0.3 by 10, you move the decimal point one place to the right, resulting in 3. Therefore, 0.3 × 10 = 3.

Multiply or divide. 0.3 × 10² = _______

• 3

• 30

• 0.03

• 300

Answer explanation

To solve 0.3 × 10², first calculate 10² which is 100. Then multiply 0.3 by 100: 0.3 × 100 = 30. Therefore, the correct answer is 30.

Multiply or divide. 0.3 × 10³ = _______

• 0.3 × 10³

• 3

• 30

• 300

Answer explanation

To solve 0.3 × 10³, multiply 0.3 by 1000. This equals 300. Therefore, the correct answer is 300.