Mental Math to Evaluate
Products
Jen Kershaw
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Printed: November 21, 2014
AUTHOR
Jen Kershaw
www.ck12.org
C HAPTER
Chapter 1. Mental Math to Evaluate Products
1
Mental Math to Evaluate
Products
Here you’ll use mental math to evaluate products.
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
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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.
Vocabulary
Numerical expression
a number sentence that has at least two different operations in it.
Product
the answer in a multiplication problem
Sum
the answer in an addition problem
Property
a rule that works for all numbers
Evaluate
to find the quantity of values in an expression
The Distributive Property
the property that involves taking the product of the sum of two numbers. Take the number outside the
parentheses and multiply it by each term in the parentheses.
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
2
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Chapter 1. Mental Math to Evaluate Products
MEDIA
Click image to the left or use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/5328
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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