Lesson 3D Multiply and Divide Fractions 169Divide by Fractions
Find _^3
4
÷ (- _^1
2(^) ). Write in simplest form.
Estimate 1 ÷ (- ^12 ) =
Think How many groups of 21 are in 1? 1 ÷ ^12 = 2, so 1 ÷ (^) (- 12 (^) ) = -2.
^3
4
÷ (- ^1
2
(^) ) = ^3
4
· (- ^2
1
(^) ) Multiply by the reciprocal of - 21 , which is - ^21.
1
= ^3 /
4
· (- ^2
1
(^) ) Divide 4 and 2 by their GCF, 2.
2
/
= - ^32 or - 1 ^12 Multiply.
Check for Reasonableness - 1 ^12 ≈ - 2 ✓
Divide. Write in simplest form.
a. ^34 ÷ ^14 b. - ^45 ÷ 98 c. - 65 ÷ (- ^23 )
To divide by a mixed number, first rename the mixed number as a
fraction greater than one. Then multiply the first fraction by the
reciprocal, or multiplicative inverse, of the second fraction.
Divide by Mixed Numbers
Find ^23 ÷ 3 ^13. Write in simplest form.
Estimate 21 ÷ 3 = ^12 · 31 or ^16
32 ÷ 3 31 = 32 ÷ ^103 Rename 3 ^13 a fraction greater than one.
= ^2
3
· ^3
10
Multiply by the reciprocal of ^103 , which is 103.
1
/
1
= ^2 /
3 ·
^3
10 Divide out common factors.
1
/
5
/
= ^15 Multiply.
Check for Reasonableness ^15 is close to^16 . ✓
Divide. Write in simplest form.
d. 5 ÷ 1 ^13 e. - ^34 ÷ 1 21 f. 2 ^13 ÷ 5
g. NUTS In planning for a party, 5 ^14 pounds of cashews will
be divided into ^34 -pound bags. How many such bags can
be made?
Dividing by a Whole
Number Number Remember that
a whole number can be
written as a fraction with
a 1 in the denominator.
So, 2 3 1 ÷ 5 can be
rewritten as 2 31 ÷ ^51.
Reciprocal
The reciprocal of a number
is its multiplicative inverse.
For example, the
reciprocal of ^59 is ^95. The
reciprocal of 8 is _^18.
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