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Product Estimation with Mixed Numbers/Fractions

Use benchmarks of 0, 1/2 and 1 whole to estimate products of mixed numbers and fractions.

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Estimate Products and Quotients of Fractions and Mixed Numbers

License: CC BY-NC 3.0

Nisi and Jamie ordered pizza for lunch. They ate 23 of the pizza which was cut into 24 slices. How many slices did they eat altogether? If Ethan woke up in the morning and ate half of the remaining pizza, what fraction of the 24 slices did he eat?

In this concept, you will learn to estimate products and quotients of fractions and mixed numbers.

Estimating Products and Quotients of Fractions

Estimation is a useful strategy to use to check that your computation is reasonable. It is also a way to find an approximate answer to a solution.

To estimate products and quotients of mixed numbers, round the fractions to the nearest whole number. If the fraction is less than 12 round down and if it is more than 12 round up.

Let's look at an example.

Estimate the product:

8411×71112 

First, since 411 is less than 12,8411 rounds down to 8.

Next, since 1112 is greater than 12, 71112 rounds up to 8.

Then, multiply to find the estimated product.

8×8=64 

The answer is 64.

Here is another example.

Estimate the quotient:

22310÷6913

First, since 310 is less than 12, 22310 rounds down to 22.

Next, since 913 is greater than 12, 6913 rounds up to 7.

Then, divide to find the estimated product.

22÷7=3.14

The answer is approximately 3.

Examples

Example 1

Earlier, you were given a problem about Nisi and Jamie and their pizza.

Of the 24 slices, they had eaten 23 of the pizza.

Therefore, multiply 23×24 to find the number of slices they had eaten.

First, set up the expression to multiply: 23×241

Next, multiply the numerator and the denominators.

23×241=483

Then, simplify.

483=16

Therefore, Nisi and Jamie ate 16 of the 24 slices.

Now, since they ate 16 of the 24 slices, there were 8 of the 24 slices left. How many did Ethan eat when he got up?

First, remember that Ethan ate 12 of the remaining pizza.

Next, set up the expression to solve.

824×12

Then solve and simplify.

824×12848==84816

So, Ethan ate 16 of the original pizza, or 4 slices.

Example 2

Estimate the following quotient.

141112÷278

First, since 1112 is greater than 12, 141112 rounds up to 15.

Next, since 78 is greater than 12, 278 rounds up to 3.

Then, divide to find the estimated product.

15÷3=5

The answer is approximately 5.

Example 3

612×418

First, since the fraction is 12, 612 rounds up to 7.

Next, since 18 is less than 12, 418 rounds down to 4.

Then, multiply to find the estimated product.

7×4=28

The answer is 28.

Example 4

1134÷2110

First, since 34 is greater than 12,1134 rounds up to 12.

Next, since 110 is less than 12,2110 rounds down to 2.

Then, divide to find the estimated product.

12÷2=6

The answer is approximately 6.

Example 5

34×89

First, since 34 is greater than 12,34 rounds up to 1.

Next, since 89 is greater than 12,89 rounds up to 1.

Then, multiply to find the estimated product.

1×1=1

The answer is 1.

Review

Estimate each product or quotient. 

  1. 78×78=
  2. 312×34=
  3. 623×45= 
  4. 8112×318=
  5. 945×619=
  6. 1213×456=
  7. 647×338=
  8. 1218÷313=
  9. 24210÷313=
  10. 2819÷7110=
  11. 923÷145= 
  12. 1412÷3110=
  13. 9310÷319=
  14. 16415÷215=
  15. 30412÷3118=

Review (Answers)

To see the Review answers, open this PDF file and look for section 2.9.  

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Vocabulary

TermDefinition
Estimation Estimation is the process of finding an approximate answer to a problem.
fraction A fraction is a part of a whole. A fraction is written mathematically as one value on top of another, separated by a fraction bar. It is also called a rational number.
Greatest Common Factor The greatest common factor of two numbers is the greatest number that both of the original numbers can be divided by evenly.
improper fraction An improper fraction is a fraction in which the absolute value of the numerator is greater than the absolute value of the denominator.
Mixed Number A mixed number is a number made up of a whole number and a fraction, such as 4\frac{3}{5}.
Product The product is the result after two amounts have been multiplied.
Quotient The quotient is the result after two amounts have been divided.

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  1. [1]^ License: CC BY-NC 3.0

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