Adding And Subtracting Fractions Worksheet With Answer Key - Unit 3: Linear Equations Page 5
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How to
• • • • • • • • • • • • • • • • • Subtract Fractions
Facts to Know
Subtracting Fractions with the Same Denominators
When fractions have the same denominators, subtract the numerators only and place the total over the
denominator.
Sample: From a bag that contained 7 –
pound of birdseed, Margery poured 3 –
of a pound into the bird
8
8
feeder. How much birdseed is left?
Step 1
Subtract the numerators.
7 – 3 = 4
4 –
Step 2
Write the answer over the denominator.
8
4 –
pound = 1 –
Step 3
Reduce the final answer.
pound
8
2
More on Finding Common Denominators
Sometimes you must change more than one denominator to add or subtract. For example, how would
you solve this problem:
Sample: 1 –
– 1 –
= ?
2
3
These fractions have different denominators. You cannot subtract them, nor can only one
denominator be changed because 2 won’t divide into 3 evenly, and 3 won’t divide into 2 evenly.
Therefore, you must find a common denominator, a number that both 2 and 3 will divide into evenly.
There are three methods for finding a common denominator.
Method 1— Check the largest denominator in the problem to find out whether it can be divided evenly
by the other denominator(s) in the problem.
1 –
= 2 –
–
Sample: 1 –
– 1 –
3
6
= ?
3
6
– 1 –
= 1 –
6 can be evenly divided by 3, so there’s no need to look for another number.
6
6
1 –
Method 2—Multiply the denominators together to find a common denominator.
6
Sample: 3 –
– 2 –
= ?
4
3
Step 1
Multiply the denominators. The number 12
3 –
= 9 —
–
4
12
is the common denominator.
– 2 –
= 8 —
Step 2
Raise each fraction to 12ths.
3
12
1 —
Step 3
Subtract the new fractions.
12
Method 3—Go through the multiplication table of the largest denominator.
Sample: 5 –
– 1 –
= ?
9
6
Step 1
Go through the multiplication table of the largest
5 –
= 10 —
9
18
denominator, 9.
– 1 –
= 3 —
Step 1
9 x 1 = 9 which cannot be divided evenly by 6.
6
18
25 —
7 —
Step 1
9 x 2 = 18 which can be divided evenly by 6 and 9.
= 1
18
18
Step 2
Raise each fraction to 18ths.
Step 3
Subtract the new fractions.
9
.
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