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4.6: Mental Math to Evaluate Products

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Have you ever had to use mental math to solve a problem? Well, sometimes it doesn't make sense to use paper and a pencil. It is easier to use mental math.

At the Science Museum, three groups of students went into an exhibit show on lightening. Given the structure of the seating, each group was able to sit together. There are eight students in each group, but right before the exhibit show started three more students joined. An additional person joined each group of eight.

Here is an expression to show the groupings. What is the total?

3(8 + 1)

We could use the distributive property to solve this, but mental math is probably just as simple.

This Concept will help you to practice this skill. Then you can come back to this problem at the end of the Concept.

Guidance

Some of you may have found that while the Distributive Property is useful, that sometimes it is easier to simply find the products by using mental math.

Some of you may have found that you did not need to write out the distribution of the number outside of the parentheses with the number inside of the parentheses to find the sum of the products.

The Distributive Property is a useful property, especially as you get into higher levels of mathematics like Algebra. There it is essential, but sometimes, you can use mental math to evaluate expressions.

2(1 + 4)

Now this is a problem where you could probably add and multiply in your head.

You know that you can add what is in parentheses first, so you add one and four and get five. Then you can multiply five times two and get a product of 10.

Our answer is 10.

When you have larger numbers, you can always use the Distributive Property to evaluate an expression. When you have smaller numbers, you can use mental math.

Now let's practice.

Example A

4(2 + 3)

Solution: 20

Example B

6(2 + 7)

Solution: 54

Example C

5(2 + 6)

Solution: 40

Ready to use mental math? Here is the original problem once again.

At the Science Museum, three groups of students went into an exhibit show on lightening. Given the structure of the seating, each group was able to sit together. There are eight students in each group, but right before the exhibit show started three more students joined. An additional person joined each group of eight.

Here is an expression to show the groupings. What is the total?

3(8 + 1)

We could use the distributive property to solve this, but mental math is probably just as simple.

Using mental math, our answer is 27.

Guided Practice

Here is one for you to try on your own.

Use mental math to solve this problem.

12(8 + 1)

Using mental math, our solution is 108 .

Video Review

Khan Academy The Distributive Property

Explore More

Directions: Use mental math to evaluate the following expressions.

1. 2(1 + 3)

2. 3(2 + 3)

3. 3(2 + 2)

4. 4(5 + 1)

5. 5(3 + 4)

6. 2(9 + 1)

7. 3(8 + 2)

8. 4(3 + 2)

9. 5(6 + 2)

10. 7(3 + 5)

11. 8(2 + 4)

12. 9(3 + 5)

13. 8(3 + 2)

14. 9(10 + 2)

15. 7(9 + 2)

16. 9(7 + 1)

17. 12(8 + 2)

18. 12(9 + 3)

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Difficulty Level:

At Grade

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Date Created:

Oct 29, 2012

Last Modified:

Feb 12, 2015
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