Adding Fractions with Different Denominators

Show your work for each problem.

1.
What is the LCD (Least Common Denominator) of and ?
1. a)6
2. b)5
3. c)3
4. d)2
Answer: 6
The LCD of 2 and 3 is 6 because 6 is the smallest number that both 2 and 3 divide into evenly (6 ÷ 2 = 3 and 6 ÷ 3 = 2).
2.
What is as an equivalent fraction with denominator 6?
1. a)
2. b)
3. c)
4. d)
Answer:
. We multiply both top and bottom by 3 because .
3.
Calculate: . Write your answer as a simplified fraction (e.g., 3/4).
Answer: 3/4
, so
4.
Calculate: . Write your answer as a simplified fraction.
Answer: 1/2
, so
5.
Which is the first step when adding ?
1. a)Simplify both fractions
2. b)Multiply the fractions
3. c)Find a common denominator
4. d)Add the numerators
Answer: Find a common denominator
Before adding fractions with unlike denominators, you must find a common denominator so the pieces are the same size.
6.
Add
Answer: 5/6
1. What is the LCD of 2 and 3? 6
2. Convert to sixths. Enter as a fraction (e.g., 3/6) 3/6
3. Convert to sixths. Enter as a fraction 2/6
4. Add the numerators: . Enter the final answer. 5/6
7.
Calculate: . Write your answer as a simplified fraction.
Answer: 11/12
and . Sum:
8.
What is ?
1. a)
2. b)
3. c)
4. d)
Answer:
and . Sum:
9.
Add
Answer: 11/15
1. What is the LCD of 5 and 3? 15
2. Convert to fifteenths 6/15
3. Convert to fifteenths 5/15
4. Add the fractions: 11/15
10.
Calculate: . Write your answer as a simplified fraction.
Answer: 5/8
, so
11.
Add and simplify if needed
Answer: 13/12
1. What is the LCD of 6 and 4? 12
2. Convert to twelfths 10/12
3. Convert to twelfths 3/12
4. Add: 13/12
12.
A recipe calls for cup of oil and cup of vinegar. How much liquid is that in total?
1. a) cup
2. b) cup
3. c) cup
4. d) cup
Answer: cup
and . Sum: cup
13.
Calculate: . Write as a mixed number (e.g., 1 5/12).
Answer: 1 5/12
and . Sum:
14.
Add and write as a mixed number
Answer: 1 7/24
1. What is the LCD of 8 and 3? 24
2. Convert to twenty-fourths 15/24
3. Convert to twenty-fourths 16/24
4. Add: 31/24
5. Convert to a mixed number 1 7/24
15.
Calculate: . Write as a mixed number.
Answer: 1 11/20
, . Sum:
16.
Add and simplify
Answer: 1 9/20
1. What is the LCD of 10 and 4? 20
2. Convert to twentieths 14/20
3. Convert to twentieths 15/20
4. Add: 29/20
5. Convert to mixed number 1 9/20
17.
You walk km to school and then km to the library. How far did you walk in total?
1. a) km
2. b) km
3. c) km
4. d) km
Answer: km
, . Sum: km
18.
Add and write as a mixed number
Answer: 1 17/24
1. What is the LCD of 6 and 8? 24
2. Convert to twenty-fourths 20/24
3. Convert to twenty-fourths 21/24
4. Add: 41/24
5. Convert to mixed number 1 17/24