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Dividing Fractions
Get ready to become an expert at dividing fractions & mixed
numbers!
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Division without division?
When you divide fractions, you don’t actually have to divide! So if
division isn’t your thing, that’s OK!
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So if I don’t divide, what do I do?
When you divide by a fraction, you can actually multiply.
Why?
First let’s look at a problem using division.
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34
112÷
Click through to see how you solve
this type of problem.
Dividing by a fraction using division
1. Divide straight across. 3 ÷ 1
4 ÷ 122. You may be left with a fraction in the numerator and/or denominator. 3. What happens then?3
1/3
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Click through to see how you solve
this type of problem.
Dividing by a fraction using division
4. We need to get rid of the fraction in the denominator. 3 x 3
1/3 x 3 5. Since 1 is the identity, we will multiply both the numerator and denominator by 3. 3. Simplify if necessary.
31/3
91
= 9
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34
112÷
Is there an easier way?
1. Re-write the division problem as a multiplication problem, but use the inverse of the second fraction.
2. Cross reduce if possible.
3. Multiply straight across.
91
Dealing with fractions inside of a
fraction can be complicated and
confusing.
Luckily – you can avoid that all
together!
Click through to see how you can use multiplication
to divide by a fraction!
34
121x
4. Simplify if necessary.
3 x 31 x 1
= 9
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What are the steps?
To divide by a fraction using multiplication:
1. Re-write the problem using multiplication and the inverse of the fraction after the operational symbol.
2. Cross reduce if possible.3. Multiply straight across.
4. Simplify if necessary.
numerator x numeratordenominator x denominator
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78
34÷
Try it!
1. Re-write the division problem as a multiplication problem, but use the inverse of the second fraction.
2. Cross reduce if possible.
3. Multiply straight across.
76
Solve the problem on your own. Click through to see the steps and correct
answer. 78
43x
4. Simplify if necessary.
7 x 12 x 3
= 116
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37
35÷
Practice
1. Re-write the division problem as a multiplication problem, but use the inverse of the second fraction.
2. Cross reduce if possible.
3. Multiply straight across.
57
Solve the problem on your own.
Click to see the answer. 3
753x
4. Simplify if necessary.
1 x 57 x 1
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18
23÷
Practice
1. Re-write the division problem as a multiplication problem, but use the inverse of the second fraction.
2. Cross reduce if possible.
3. Multiply straight across.
316
Solve the problem on your own.
Click to see the answer. 1
832x
4. Simplify if necessary.
1 x 38 x 2
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59
13÷
Practice
1. Re-write the division problem as a multiplication problem, but use the inverse of the second fraction.
2. Cross reduce if possible.
3. Multiply straight across.
53
Solve the problem on your own.
Click to see the answer. 5
931x
4. Simplify if necessary.
5 x 13 x 1
= 123
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How about mixed numbers?
To divide by a fractions or mixed numbers using multiplication:
1. Convert all mixed numbers to improper fractions. 2. Re-write the problem using multiplication and the
inverse of the fraction after the operational symbol.3. Cross reduce if possible.4. Multiply straight across.
5. Simplify if necessary.
numerator x numeratordenominator x denominator
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45
124 ÷ 2
Practice
2. Re-write the division problem as a multiplication problem, but use the inverse of the second fraction.
3. Cross reduce if possible.
4. Multiply straight across.
4825
Solve the problem on your own.
Click to see the answer.
245
25
x
5. Simplify if necessary.
24 x 25 x 5
1. Change mixed numbers to improper fractions.
= 12325
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34
136 ÷ 3
Practice
2. Re-write the division problem as a multiplication problem, but use the inverse of the second fraction.
3. Cross reduce if possible.
4. Multiply straight across.
8140
Solve the problem on your own.
Click to see the answer.
274
310
x
5. Simplify if necessary.
27 x 34 x 10
1. Change mixed numbers to improper fractions.
= 2 140
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310
147 ÷ 1
Practice
2. Re-write the division problem as a multiplication problem, but use the inverse of the second fraction.
3. Cross reduce if possible.
4. Multiply straight across.
14625
Solve the problem on your own.
Click to see the answer.
7310
45
x
5. Simplify if necessary.
73 x 25 x 5
1. Change mixed numbers to improper fractions.
= 52125