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Adding Fractions
Get ready to become an expert at adding fractions & mixed
numbers!
Adding with the same denominator.
Adding fractions that have the same denominator is simple. You add the numerators and write the sum over the common denominator. If your answer is an improper fraction, re-
write it as a mixed number.
Example:
35
45
+
75
= 125 Solve on your
own. Click for the
answer!
Adding fractions with different denominators.
Adding fractions with different denominators is impossible. In order for fractions to be added, they must have the same number of parts. The denominator represents the number of parts. Therefore, you must find a
common denominator.
Why?
You have two pies. One cut in 4 slices and the other cut in three slices. You at 1/4 of one pie and 1/3 of
the other pie. How much pie did you eat all together?
A common denominator is necessary so that each piece of pie is the same size and can be added
with the others. What is a common denominator for 3 and 4?
12
+ =
What are the steps?
To add fractions:
1. Find a common denominator if there isn’t one already. 2. Convert each of your fractions into an equivalent
fraction using the common denominator. 3. Add the numerators.4. Write the sum as the numerator in your answer. The
denominator will be your common denominator.5. If your answer is an improper fraction, convert to a
mixed number. Simplify if necessary.
35
47
+
35
Click for the answer!
What is the least common denominator?
3547+
Click for the answer!
How do you re-write the fractions using the common denominator?
35
35
=
=x 5
x 5
x 7
x 721
20
Solve:
35
47
+
4135
= 635
Rewrite using the least common
denominator, then solve on your own.
Click for the answer!
2135
2035
+ = 1
What is the least common denominator?
78
13
+
24
Click for the answer!
Solve:
78
13
+
2924
=
Rewrite using the least common
denominator, then solve on your own.
Click for the answer!
2124
824
+ 524
= 1
Solve:
56
34
+
1912
= 712
Rewrite using the least common
denominator, then solve on your own.
Click for the answer!
1012
912
+ = 1
When you add multi-digit numbers, do you add from:
Right to left? Left to right?
Right to Left!
For example: 485123
You add 5+3 first!+
When we add mixed numbers, we do the same
thing!
Right to Left!Add the fractions before the whole
numbers
For example: 4 ¼ 1 ¼5
You add ¼ + ¼ first!+
24
But Why?
We add the fractions before the whole numbers in order to make as many
“wholes” as possible.
Example:
+14
1 56
2
+
1456
=+
3121012
Click to move through the
problem visually.
1 112
We add the fractions before the whole numbers in order to make as many
“wholes” as possible.
Example:
+14
1 56
2Click to move through the
problem visually.
1 112
You already figured out that
+ is 1
14
56
112
Next, add the whole numbers
1 + 2 = 3
3 + 1 = 4
112
112
What are the steps?
To add mixed numbers:
1. Find a common denominator if there isn’t one already. 2. Convert each of your fractions into an equivalent fraction
using the common denominator. 3. Add the numerators.4. Write the sum as the numerator in your answer. The
denominator will be your common denominator.5. If your answer is an improper fraction, convert to a mixed
number. Simplify if necessary.6. Add the whole numbers.7. Combine with the fraction sum if necessary.
Solve:
15
78
2 + 4
4340
= 340
Rewrite using the least common
denominator, then solve on your own.
Click for the answer!
840
3540
+ =12 + 4 = 6
340
6 + 1 = 7
340
Solve:
56
23
5 + 3
96
=
Rewrite using the least common
denominator, then solve on your own.
Click for the answer!
56
46
+5 + 3 = 8
12
8 +1 = 912
12
= 1
Solve:
34
13
1 + 1
1312
= 112
Rewrite using the least common
denominator, then solve on your own.
Click for the answer!
912
412
+ =11 + 1 = 2
112
2 + 1 = 3
112
