Download 3-12 Solving Equations Containing Fractions

3-12 Solving Equations Containing Fractions
Warm Up
Solve.
1. x – 16 = 8
2. 7a = 35
3. x = 11
12
4. y + 21 = 31
3-12 Solving Equations Containing Fractions
The goal when solving equations that
contain fractions is the same as when
working with other kinds of numbers—to
isolate the variable on one side of the
equation.
3-12 Solving Equations Containing Fractions
Additional Example 1A: Solving Equations by Adding
or Subtracting
Solve. Write the answer in simplest form.
x – 3= 5
7
7
3-12 Solving Equations Containing Fractions
Additional Example 1B: Solving Equations by Adding
or Subtracting
Solve. Write the answer in simplest form.
4
-1
+r=
9
2
–
4 , – 4 , to both sides.
9
9
3-12 Solving Equations Containing Fractions
Check It Out: Example 1A
x – 3= 7
8 8
3-12 Solving Equations Containing Fractions
Check It Out: Example 1B
x– 3=5
8
6
3-12 Solving Equations Containing Fractions
Recall that the product of a nonzero number and
its reciprocal is 1.This is called the Multiplicative
Inverse Property.
You can use the Multiplicative Inverse Property to
solve multiplication equations that contain
fractions and whole numbers.
3-12 Solving Equations Containing Fractions
Additional Example 2A: Solving Equations by
Multiplying
Solve. Write the answer in simplest terms.
3x
1
=
8
4
.
3-12 Solving Equations Containing Fractions
Additional Example 2B: Solving Equations by
Multiplying
Solve. Write the answer in simplest terms.
4y = 8
9
3-12 Solving Equations Containing Fractions
Check It Out: Example 2A
– 1x = 5
2
8
3-12 Solving Equations Containing Fractions
Check It Out: Example 2B
6y =
3
7
3-12 Solving Equations Containing Fractions
Check It Out: Example 2C
– 2z = 3
3
4
3-12 Solving Equations Containing Fractions
Check It Out: Example 2D
– 4p = 8
9
3-12 Solving Equations Containing Fractions
Additional Example 3: Food Application
Melissa made a fruit salad using a total of 5 1 pounds
4
of various fruits. She used 1 1 pounds of grapes, and
2
she used equal portions of 5 other fruits in her salad.
What weight of each of these fruits did she use?
3-12 Solving Equations Containing Fractions
Check It Out: Example 3
A salad bar in a restaurant contains 105
6
pounds of vegetables. There are 31 pounds of
3
greens, and there are equal amounts of
onions, bell peppers, celery, carrots, and
cucumbers. How much of each of these
vegetables does the salad bar contain?