8.8.1 Evaluating Expressions Using Mental Math

Algebra 18.8.1 Evaluating Expressions Using Mental Math

Search for key terms or text.

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.

$9 \cdot 11$

Enter the product and your explanation.

Compare your answer:

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

$19 \cdot 21$

Enter the product and your explanation.

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.

$99 \cdot 101$

Enter the product and your explanation.

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.

$109 \cdot 101$

Enter the product and your explanation.

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.

Previous Next

Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution-NonCommercial-ShareAlike License and you must attribute OpenStax.

Attribution information

If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
Access for free at https://openstax.org/books/algebra-1/pages/about-this-course
If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

Citation information

Use the information below to generate a citation. We recommend using a citation tool such as this one.
- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, Jay Abramson, Sharon North, Amy Baldwin, Alyssa Howell
- Publisher/website: OpenStax
- Book title: Algebra 1
- Publication date: Jun 4, 2025
- Location: Houston, Texas
- Book URL: https://openstax.org/books/algebra-1/pages/about-this-course
- Section URL: https://openstax.org/books/algebra-1/pages/8-8-1-evaluating-expressions-using-mental-math

© May 21, 2025 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.