Estimate Sums and Differences
of Fractions and Mixed
Numbers
Jen Kershaw
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Printed: November 19, 2014
AUTHOR
Jen Kershaw
www.ck12.org
C HAPTER
Chapter 1. Estimate Sums and Differences of Fractions and Mixed Numbers
1
Estimate Sums and
Differences of Fractions and Mixed
Numbers
Here you’ll learn to estimate sums and differences of fractions and mixed numbers.
Have you ever tried to estimate using fractions? Take a look at this dilemma.
3
Harriet and Matt have two identical jars. Harriet’s jar is 10
full of pennies. Matt’s jar is
and Harriet combine their pennies into one jar, how full will the jar be?
1
4
full of pennies. If Matt
Do you know how to figure this out? We can use estimation to help us. Pay attention to this Concept and you will
be able to figure out the fullness of the jar.
Guidance
When you estimate fraction sums and differences you will need to work with rounding fractions. You can work with
rounding fractions in a couple of different ways. One way is to look at the relationship between the fraction and a
whole.
Here are some guiding questions:
1. Is this fraction close to one-half or one-whole?
2. If I simplify the fractions that I am adding or subtracting, will they have a common denominator?
3. Is this fraction so close to one-whole that it would make sense to round up to a whole?
1
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Take a few minutes and write these guiding questions down in your notebook.
Now apply this information and estimate the following sum.
4
25
+ 11
20
The first fraction is close to
5
25 ,
The second fraction is close to
or 15 .
12
20 ,
or 35 .
Now you can easily add the rounded fractions.
1
5
+ 53 =
4
5
A good estimate for the sum is 45 .
With this problem, it made sense to round the fractions so that we could simplify them. The simplified fractions had
a common denominator. This makes our work easier.
Here is another one.
Estimate the difference:
24
49
7
− 31
This first fraction is about 12 .
The second fraction is about 14 .
1
2
− 41 = 24 − 14 =
1
4
A good estimate for the difference is 41 .
2
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Chapter 1. Estimate Sums and Differences of Fractions and Mixed Numbers
It seems tricky because there is not one set way of estimating sums and differences of fractions. You need to
use your thinking skills and powers of reason to look at the relationship between the fraction and a whole or
a half and so on. As you move into higher levels of mathematics, this will become necessary for many of your
assignments. It is a good skill to begin practicing now.
Find a reasonable estimate for each sum or difference.
Example A
1
4
+ 76
Solution: 1 14
Example B
8
9
− 21
Solution:
1
2
Example C
4
5
9
+ 10
Solution: 2
Now let’s go back to the dilemma from the beginning of the Concept.
To find the how full the jar will be, write a simple equation to represent the problem. Let x represent the amount of
the jar that has been filled.
3
1
+
10 4 3 2
1 5
=
·
+
·
10 2
4 5
6
5
=
+
20 20
11
=
20
x=
11
The jar will be 20
full. Now let’s think about this logically. What information does this fraction tell you? Well,
we can think in terms of halves or wholes. Since 10 is half of 20, we can say that this jar is a little more than
half full.
This is our estimate of the sum of the jar.
Vocabulary
Fraction
represents a part of a whole.
Improper fraction
a fraction where the numerator is greater than the denominator. It means that we have more than one whole
represented.
3
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Mixed Number
a whole number and a fraction written together.
Denominator
the bottom number in a fraction tells you how many parts the whole has been divided into.
Numerator
the top number in a fraction. It tells you how many parts you have out of the whole.
Guided Practice
Here is one for you to try on your own.
Estimate the following difference.
5 11
12 − 2
Solution
To estimate this difference, first look at the mixed number.
5 11
12 is close to 6.
We can use 6 − 2.
6−2 = 4
Our estimate is 4.
Video Review
MEDIA
Click image to the left or use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/65512
Explore More
Directions: Estimate each sum or difference.
1.
2.
6
7
1
2
1
+ 22
9
+ 10
1
3. 2 67 + 4 12
4.
8
9
5.
16
1
17 − 22
1
1
2+9
6.
7.
8.
4
+ 21
22
11
21
12 − 22
8
1
7 10
− 3 22
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9.
4
6
Chapter 1. Estimate Sums and Differences of Fractions and Mixed Numbers
+ 23
1
10. 11 76 + 14 22
1
11. 9 71 + 14 22
12.
18
20
13.
16
1
32 − 2
5 21 − 2 12
1
6
+ 15 22
12 12
14.
15.
− 12
5