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This lesson focuses on solving fraction equations involving a variable as either a numerator or in multiplication. When a variable is the numerator, we can use multiplication to isolate it. For example, if ( y/8 = 20 ), multiplying both sides by 8 gives ( y = 160 ). If a variable is being multiplied by a fraction, we can use the reciprocal to isolate it. This lesson includes essential examples and a homework section to practice these techniques effectively.
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Solving Fraction Equations by Multiplying Lesson 5-5
If the variable is in the fraction… • When the variable is the numerator of the fraction, then it suggests a division problem. • To solve a division problem, the inverse operation is multiplying.
Example y 20 = 8 This equation reads “y divided by 8 equals 20.” The opposite of dividing by 8 is multiplying by 8. Multiply both sides by 8.
y 1 8 20 8 = · · 8 1 1 y 160 = 1 y = 160
Example 2 m 1 2 3 2 = · · 1 2 1 m = 6 1 m 6 =
Check answers in the original equation. m = 3 2 6 = 3 2 = 3 3
If the variable is being multiplied by a fraction… • To isolate a variable that is being multiplied by a fraction, multiply by the reciprocal. • Perform the same operation on the other side of the equation.
Example 5 3 2 1 1 3 10 r = · · 2 3 1 1 2 1 1 15 r 1 = 1 r 15 =