Evaluating Expressions Using Mental Math

8.8.1 Evaluating Expressions Using Mental Math

8.8.1 • Evaluating Expressions Using Mental Math

Warm Up

Finding a product mentally can be done by changing the way you look at a multiplication problem.

For example, $9 \cdot 39$ can be thought of as $9 \cdot (40 - 1)$ . For some people, this might be easier to calculate mentally since you can imagine the solution as $360 - 9$ , or 351. This method leverages the distributive property of multiplication over addition.

For the following questions, find each product mentally. Then, explain how you changed the way you looked at each multiplication problem to use the distributive property.

$9 \cdot 11$

Compare your answer:

For example, $9 \cdot 11$ can be thought of as $9 \cdot (10 + 1)$ . This simplifies to $90 + 9$ , or 99.

$19 \cdot 21$

Compare your answer:

399

For example, $19 \cdot 21$ can be thought of as $19 \cdot (20 + 1)$ . This simplifies to $380 + 19$ , or 399.

$99 \cdot 101$

Compare your answer:

9999

For example, $99 \cdot 101$ can be thought of as $99 \cdot (100 + 1)$ . This simplifies to $9900 + 99$ , or 9999.

$109 \cdot 101$

Compare your answer:

11,009

For example, $109 \cdot 101$ can be thought of as $109 \cdot (100 + 1)$ . This simplifies to $10, 900 + 109$ , or 11,009.