Section C: Practice Problems Multiply Decimals

Section Summary

Details

In this section, we learned to use place value relationships to multiply a whole number and and a decimal. For example,

$6 \times 0.14 = 0.84$

because 6 groups of 14 hundredths is $6 \times 14$ or 84 hundredths.

We also found products like $1.7 \times 0.3$ . We can use a diagram to see that this is $17 \times 3$ hundredths or $0.51$ .

Two diagrams. Each squares. Length and width, 1.

Problem 1 (Lesson 17)

Shade $5 \times 0.07$ on the diagram.
What is the value of $5 \times 0.07$ ? Explain or show your reasoning.
What is the value of $5 \times 0.2$ ? Use the diagram if it is helpful.

Problem 2 (Lesson 18)

Mai says that $7 \times 0.4$ and $7 \times 0.04$ both have the same value. She says that they are both 28. Do you agree with Mai? Explain or show your reasoning.
Explain why $8 \times 0.03 = (8 \times 3) \times 0.01$ .

Problem 3 (Lesson 19)

Explain why each expression is equivalent to $9 \times 0.45$ .

$(9 \times 0.4) + (9 \times 0.05)$

$(9 \times 45) \div 100$

$(10 \times 0.45) - (1 \times 0.45)$
Find the value of $9 \times 0.45$ using one of the expressions or your own strategy.

Problem 4 (Lesson 20)

Shade the diagram to represent $0.7 \times 0.4$ .
What is the value of $0.7 \times 0.4$ ?

Problem 5 (Lesson 21)

Explain or show why $5.6 \times 3.4 = (56 \times 34) \times 0.01$ .
Use this strategy to calculate $5.6 \times 3.4$ .

Problem 6 (Exploration)

Here is Diego’s strategy to find the value of $17.5 \times 3.3$ . I know $\frac{175}{10} \times \frac{33}{10} = \frac{175 \times 33}{100}$ so I just find $175 \times 33$ and then divide by 100.

Explain or show why Diego’s method works.
Use Diego’s method to find the value of $17.5 \times 3.3$ .

Problem 7 (Exploration)

Han says the picture shows $4 \times 0.5 = 2$ . Label the diagram to show Han’s thinking.
Mai says it shows $10 \times 0.2 = 2$ . Label the diagram to show Mai’s thinking.
What other products can the diagram represent? Explain or show your reasoning.