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Example 1: Add fractions with like (same)
denominators
| |
1 |
|
2 |
| Add the fractions |
____ |
+ |
____ |
| |
4 |
|
4 |
Solution to example 1:
When the fractions have the same denominator, we add the
numerators and keep the same denominator
| 1 |
|
2 |
|
3 |
| ____ |
+ |
____ |
= |
____ |
| 4 |
|
4 |
|
4 |
Example 2: Add fractions with unlike
(different) denominators.
| |
4 |
|
2 |
| Add the fractions |
____ |
+ |
____ |
| |
7 |
|
5 |
Solution to example 2:
step 1: Find the lowest
common multiple (LCM) of the two denominators.
The LCM of 7 and 5 is 35.
step 2: Write equivalent
fractions with a lowest common denominator (LCD) equal to the LCM.
| 4 |
|
4 x 5 |
|
20 |
| ____ |
= |
____ |
= |
____ |
| 7 |
|
7 x 5 |
|
35 |
and
| 2 |
|
2 x 7 |
|
14 |
| ____ |
= |
____ |
= |
____ |
| 5 |
|
5 x 7 |
|
35 |
step 3: Replace the given
fractions by their equivalent and add the fractions with like denominator.
| 4 |
|
2 |
|
20 |
|
14 |
|
34 |
| ____ |
+ |
____ |
= |
____ |
+ |
____ |
= |
____ |
| 7 |
|
5 |
|
35 |
|
35 |
|
35 |
step 3: Reduce the fraction
if possible.
The fraction obtained above cannot be further reduced.
Example 3: Add fractions mixed numbers.
| |
|
2 |
|
|
5 |
| Add the mixed
numbers |
3 |
____ |
+ |
2 |
____ |
| |
|
3 |
|
|
7 |
Solution to example 3:
step 1: Add the whole numbers
3 + 2 = 5
step 2: Find the LCD, equivalent fractions with common denominator and add the
fractions.
| 2 |
|
5 |
|
14 |
|
15 |
|
29 |
| ____ |
+ |
____ |
= |
____ |
+ |
____ |
= |
____ |
| 3 |
|
7 |
|
21 |
|
21 |
|
21 |
step 3: Reduce and write the
fraction as a mixed number if possible.
step 4: Add the
whole number obtained in step 1 and the mixed number obtained in step 3
| |
|
|
8 |
|
|
8 |
| 5 |
+ |
1 |
____ |
= |
6 |
____ |
| |
|
|
21 |
|
|
21 |
Questions with answers: Add and reduce if possible the following
fractions and mixed numbers.
1.
2.
3.
4.
|
2 |
|
|
9 |
| 4 |
______ |
+ |
2 |
______ |
|
3 |
|
|
11 |
|