Estimate Products and
Quotients of Fractions and
Mixed Numbers
Jen Kershaw
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Printed: December 14, 2014
AUTHOR
Jen Kershaw
www.ck12.org
Chapter 1. Estimate Products and Quotients of Fractions and Mixed Numbers
C HAPTER
1
Estimate Products and
Quotients of Fractions and Mixed
Numbers
Here you’ll estimate products and quotients of fractions and mixed numbers.
Have you ever tried to estimate a product or a quotient? Take a look at this dilemma with fractions and mixed
numbers.
1
4 12
× 12 32
To figure this out, you need to know how to estimate a product. You will know how to do this by the end of the
Concept.
Guidance
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 21 , round down. If the fraction is greater than 12 , round up.
4
Estimate the product: 8 11
× 7 11
12
Round the first number.
Since
4
11
4
is less than 12 , 8 11
rounds down to 8.
Round the second number.
Since
11
12
is greater than 12 , 7 11
12 rounds up to 8.
Now multiply to find the estimated product.
8 × 8 = 64
A reasonable estimate is 64.
Here is another one.
3
9
Estimate the quotient: 22 10
÷ 6 13
Round the first number.
Since
3
10
3
is less than 12 , 22 10
rounds down to 22.
Round the second number.
Since
9
13
9
is greater than 12 , 6 13
rounds up to 7.
Now divide to find the estimated product. Since 22 is not divisible by 7, round it down to 21 to make compatible
numbers that are easier to divide.
21 ÷ 7 = 3
A good estimate for the quotient is 3.
Notice that you have to use some common sense and thinking to figure out that you had to round 22 down to
21 to find a good estimate.
Estimate each product or quotient.
1
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Example A
6 12 × 4 18
Solution: 7 × 4 = 28
Example B
1
11 43 ÷ 2 10
Solution: 12 ÷ 2 = 6
Example C
3
4
× 98
Solution: 1 × 1 = 1
Now let’s go back to the dilemma from the beginning of the Concept.
3
1
× 12 12
4 12
First, round each value.
1
4 12
becomes 4
3
becomes 12
12 12
Now we can write a new problem.
4 × 12 = 48
Our reasonable estimate is 48.
Vocabulary
Greatest Common Factor
a number that will divide evenly into both the numerator and the denominator of a fraction.
Product
the answer in a multiplication problem.
Quotient
the answer in a division problem.
Fraction
a part of a whole
Mixed Number
a number with a whole number and a fraction.
Improper Fraction
a number that is greater than a whole with a larger top number and a smaller bottom number.
Estimation
a reasonable answer
2
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Chapter 1. Estimate Products and Quotients of Fractions and Mixed Numbers
Guided Practice
Here is one for you to try on your own.
Estimate the following quotient.
11
14 12
÷ 2 78
Solution
Begin by rounding each value. Here is the new equation.
15 ÷ 3 = x
Now solve for x.
x=5
This is our estimate.
Video Review
MEDIA
Click image to the left or use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/65515
Explore More
Directions: Estimate each product or quotient.
1.
7
8
× 78
2. 3 12 × 34
3. 6 23 × 45
1
4. 8 12
× 3 81
5. 9 45 × 6 91
6. 12 31 × 4 56
7. 6 47 × 3 83
8. 12 81 ÷ 3 13
2
9. 24 10
÷ 3 13
1
10. 28 91 ÷ 7 10
11. 9 32 ÷ 1 45
1
12. 14 12 ÷ 3 10
3
13. 9 10
÷ 3 19
4
14. 16 15
÷ 2 15
4
1
15. 30 12
÷ 3 18
3