Download adding and subtracting fractions and mixed numbers

ADDING AND SUBTRACTING FRACTIONS AND MIXED NUMBERS
When adding or subtracting fractions with different denominators:
1) Make the denominators the same by finding the lowest common multiple for both
denominators.
2) Create equivalent fractions: Whatever you multiplied the denominator by to get the
lowest multiple, you multiply the numerator by the same amount.
3) Write your new equivalent fractions (with the same denominator)
4) Add or subtract the numerators as required. The denominators remain the same.
5) Write your answer in lowest terms (or as a mixed number if needed).
3
4
↓
↓
+ 2
The lowest common multiple of 4 and 3 is 12.
3
4 x 3 = 12 and 3 x 4 = 12.
↓
↓
Create equivalent fractions.
9 + 8
4(denominator) x 3 is 12, so then multiply 3(numerator) also by 3 to get 9.
12
12
3(denominator) x 4 is 12, so then multiply 2 (numerator) also by 4 to get 8.
9 + 8
12
12
= 17
12
=
1 5/12
When adding or subtracting mixed numbers it can be done in 3 ways:
1) Add or subtract the whole numbers and fractions as needed. If denominators are same.
If denominators are NOT the same.
1) First convert to improper, then find equivalent fraction (LCD), then add or subtract as
needed. **(this is the easiest way)**
1 3/5
+
2 2/3
↓ Change to ↓
↓ improper fractions ↓
8
5
↓
↓
Find equivalent
fractions
24
15
8
3
↓
↓
40
+
15
64
=
15 → → →
4
4
/15
Change to a mixed number
2) Leave whole numbers, find LCD for fractions and then rewrite them with the LCD (equivalent
fraction), then add or subtract as needed.
1 3/5
↓
+
2 2/3
Leave whole numbers and
change fraction part to
↓
equivalent fractions
1 9/15
+
↓
↓
2 10/15
OR
STEPS
1) *Change mixed numbers to improper fractions
(This step can be done first, or it can be done after creating equivalent fractions)
2) Find a Common denominator.
3) Create equivalent fractions.
4) Add or subtract as instructed.
5) Reduce to lowest terms and change improper fractions into mixed numbers
When subtracting fractions or mixed numbers from whole numbers only, borrow one from the
whole number and create a fraction (make it with the same denominator as is being subtracted)
then subtract as normal.
5 – 2/3
5 ¼ - 2 2 /3