Fraction Coefficients
Solve _^3
4
x = _^12
20. Check your solution.
_^3
4
x = _^12
20
Write the equation.(^) ( ^4
3
(^) ) · ^3
4
x = (^) ( ^4
3
(^) ) · ^12
20
Multiply each side by the reciprocal of ^34 , ^43.
1
/
1
/
1
/
4
^4 /
3 ·
^3
4 x =^
^4
3 ·
^12
20 Divide by common factors.
1
/
1
/
1
/
5
/
x = ^45 Simplify.
Check ^34 x = ^1220 Write the original equation.
43 ( (^45) ) 2012 Replace x with ^45.
2012 = 2012 ✓ This sentence is true.
i. 21 x = 8 j. - ^34 x = 9 k. - ^78 x = - ^2164
SCHOOL PLAY Valerie needs ^23 yard of fabric to make each hat
for the school play. Write and solve an equation to find how
many hats can she make with 6 yards of fabric.
Each hat needs 32 yard of fabric. So, 32 of some number n is 6. Draw
a bar diagram.
n
6
Write and solve a multiplication equation.
^23 n = 6 Write the equation.
(^) ( (^32) ) · ^23 n = (^) ( ^32 ) · 6 Multiply each side by ^32.
n = 9 Simplify.
Valerie can make 9 hats.
l. TRAIL MIX Wilson has 9 pounds of trail mix. How many ^34 -pound
bags of trail mix can he make?
Fractions as Coefficients Fractions as Coefficients
The expression ^34 x can
be read as ^34 of x, 43
multiplied by x, 3x divided
by 4, or 4 x multiplied by 3.
Lesson 2D Multiplication and Division Equations 223
214_226_C04L2_895130.indd 223 12/31/09 3:57 PM