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The ideas in this fraction lesson are taken from the ebooks that are sold on this website. Only a few examples of each problem type are shown; you should make more problems of each kind for the student. Dividing fractions by fractions
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As we saw in the last lesson, dividing something (fraction for example) by
a whole number
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1. Divide. Use the thinking pattern "how many times does this (divisor) go into this (dividend)? Use pictures to help.
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Did you notice anything especial in the last exercise? There is
a shortcut to these problems:
The same works if you are dividing by a fraction, too! Instead of dividing by a fraction, multiply by its reciprocal number.
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2. Fill in the dividend from the picture. Then divide by multiplying by the reciprocal number. When you get the answer, look at the picture and think if your answer is reasonabe.
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Instead of dividing by a fraction, multiply by its reciprocal number.This rule works ALWAYS - even when the divisor is a
more complex looking fraction.
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3. Practice time! Divide by multiplying by the reciprocal number of the divisor. Note: change mixed numbers first to fractions. As usual, give your answer as a mixed number and in lowest terms, if possible.
a. 5
8
÷ 2
5
=
f. 4
÷ 2
5
=
b. 8
5
÷ 3
4
=
g. 2
9
÷ 1
7
=
4. Find reciprocal numbers!
a. 5
8
b. 7
9
c. 1 7
8
d. 32
e. 100
f. 3
1000
g. 1 1
23
h. 3 12
13
i. 10 3
10
Next lesson: Dividing mixed numbers
The ideas in this fraction lesson are taken from the Fractions 2 ebook. Only a few examples of each problem type are shown; you should make more problems of each kind for the student.
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Understanding fractions
Part of whole group Mixed numbers Mixed number to fraction Fraction to mixed number Adding like fractions Equivalent fractions |
Adding unlike fractions
Adding mixed numbers Subtracting mixed numbers Subtracting mixed numbers 2 Part of whole group 2 Measuring in inches Comparing fractions |
Simplifying fractions
Whole number times a fraction Fraction times a fraction Multiplication as an area Simplify before multiplying Divide fractions by whole number Dividing fractions by fractions Dividing mixed numbers |
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