Lesson 11: Multiply Decimals: Properties and Hundredths

Property

The associative property of multiplication states that you can change the grouping of factors without changing the product.

Examples

• To solve $6 \times 0.5$, we can decompose $6$ into $3 \times 2$. Then, using the associative property: $3 \times (2 \times 0.5) = 3 \times 1 = 3$.
• To solve $12 \times 0.25$, we can decompose $12$ into $3 \times 4$. Then, we can regroup the factors: $3 \times (4 \times 0.25) = 3 \times 1 = 3$.

Explanation

The associative property is a powerful tool for simplifying multiplication problems involving decimals. By breaking a whole number into factors, you can regroup them with the decimal to create an easier product, such as the number 1. This strategy allows you to strategically rearrange the problem to make mental math easier. It highlights that changing the grouping of the numbers being multiplied does not affect the final answer.

Property

When you multiply a number in the tenths place by another number in the tenths place, the product will be in the hundredths place.

Examples

• $0.2 \times 0.4 = 0.08$
• $0.7 \times 0.3 = 0.21$
• $1.5 \times 0.2 = 0.30$ or $0.3$

Explanation

Multiplying tenths by tenths is similar to multiplying fractions. For example, $0.2 \times 0.4$ is the same as $\frac{2}{10} \times \frac{4}{10}$, which equals $\frac{8}{100}$, or $0.08$. A general rule is to multiply the numbers as if they were whole numbers, and then count the total number of decimal places in the factors to place the decimal in the product. This skill is foundational for understanding how place values shift during decimal multiplication.