Dividing Fractions

Show your work for each problem.

1.
What is the reciprocal of ?
1. a)
2. b)
3. c)
4. d)
Answer:
The reciprocal of is . We flip the fraction by swapping the numerator (3) and denominator (4). Note: the reciprocal is NOT the opposite (negative).
2.
Calculate
Answer: 2
. Two quarters fit in one half!
3.
Calculate using Keep-Change-Flip
Answer: 2
1. Keep: What is the first fraction? 2/3
2. Change: What operation replaces division? multiplication
3. Flip: What is the reciprocal of ? 3/1
4. Calculate 2
4.
Which step comes FIRST in Keep-Change-Flip?
1. a)Simplify the answer
2. b)Keep the first fraction the same
3. c)Flip the second fraction
4. d)Change division to multiplication
Answer: Keep the first fraction the same
The first step is to KEEP the first fraction exactly as it is. Then CHANGE division to multiplication. Finally, FLIP the second fraction.
5.
Calculate
Answer: 3
. Three quarters contain three one-quarters!
6.
Calculate and simplify your answer
Answer: 5/4
1. Apply Keep-Change-Flip: what? 3/2
2. Multiply the numerators: 15
3. Multiply the denominators: 12
4. Simplify to lowest terms 5/4
7.
Calculate
1. a)
2. b)
3. c)
4. d)
Answer:
. There are 8 halves in 4 wholes! Dividing by doubles the number.
8.
Calculate and give your answer as a simplified fraction
Answer: 3/2
. Or cross-cancel:
9.
A recipe needs cup of sugar. If you want to make of the recipe, how much sugar do you need?
Answer: 3/8
1. What operation should we use? (multiply/divide) multiply
2. Set up the expression: 1/2
3. Multiply numerators: 3
4. Multiply denominators: 8
5. What is the final answer? 3/8
10.
You have of a pizza. Each serving is of a pizza. How many servings do you have?
Answer: 6
servings. Six eighths fit in three quarters!
11.
Calculate
1. a)
2. b)
3. c)
4. d)
Answer:
simplifies to , so we have . Any number divided by itself equals 1!
12.
A board is meter long. You need pieces that are meter each. How many complete pieces can you cut?
Answer: 3
1. Set up the division: . Apply Keep-Change-Flip to get: 9/2
2. Multiply numerators: 45
3. Multiply denominators: 12
4. Simplify . What is the mixed number? 15/4
5. How many COMPLETE pieces? (Round down) 3
13.
Calculate and give your answer as a simplified fraction
Answer: 3/2
. Cross-cancel: or
14.
Calculate and express as a mixed number
Answer: 3
1. Convert to an improper fraction 5/2
2. Apply Keep-Change-Flip: 6/5
3. Multiply: 30/10
4. Simplify 3
15.
If , what must be true?
1. a) (the fractions are equal)
2. b) (sums are equal)
3. c) (only denominators equal)
4. d) (only numerators equal)
Answer: (the fractions are equal)
For any division to equal 1, the dividend and divisor must be equal. So . Example: because the fractions are identical.