If the numerator and denominator of either fraction have common
factors, you can simplify before multiplying.Simplify Before Multiplying
Find _^27 × _^38. Write in simplest form.
1
_^2 /
7 ×_^3
8 =_^2
7 ×_^3
8 Divide 2 and 8 by their GCF, 2.
4/= ^17 × ×^34 or 283 Multiply.
Multiply. Write in simplest form.d. - 31 × (^) (- 73 ) e. 94 × ^18 f. 65 × ^35
Multiply Mixed Numbers
Find ^12 × 4 ^25. Write in simplest form. Estimate ^12 × 4 = 2
Method 2 Use mental math.
The mixed number 4 ^25 is equal to 4 + ^25.
So, 21 × 4 52 = 21 ( 4 + 52 ). Use the Distributive Property to multiply,
then add mentally.
^12 ( 4 + 52 ) = 2 + 51 Think Half of 4 is 2 and half of 2 fifths is 1 fifth.
(^) = 2 (^1)
5 Rewrite the sum as a mixed number.
Method 1 Rename the mixed number.
11
^1 /
2 ×^4
^2
5 =
^1
2 ×
^22
5
Rename 4 52 as an improper fraction, 22 5.
1 Divide 2 and 22 by their GCF, 2.
/
= ^11 × ×^115 Multiply.
= ^115 or 2 ^15 Simplify.
So, ^12 × 4 52 = 2 51. Check for Reasonableness 2 ^15 ≈ 2 ✓
Multiply. Write in simplest form.
g. ^14 × 8 ^49 h. 5 ^13 × 3 i. - 1 ^78 × (^) (- 2 _^25 )
Simplifying Simplifying If you forget
to simplify before
multiplying, you can always
simplify the final answer.
However, it is usually
easier to simplify before
multiplying.
GCF
GCF stands for the
greatest of the common
factors of two or more
numbers.
Example: The GCF of 8
and 2 is 2.
Lesson 3B Multiply and Divide Fractions 161
158_165_C3L3_895130.indd 161 12/31/09 12:41 PM