Exercise Rename the fraction in lowest terms. 6 10 3 5 =

Exercise Rename the fraction in lowest terms. 9 15 3 5 =

Exercise Rename the fraction in lowest terms. 21 35 3 5 =

Equivalent Fractions Equivalent fractions are fractions representing the same rational number; thus they are reducible to the same fraction.

1 2 2 4 3 6

To convert one equivalent fraction to another, multiply it by where n is an integer. nn

13 44 33 22 , • , • , • . . .

Example 1 Find a fraction equivalent to by multiplying the numerator and denominator by 3. 5 8 5 8 5(3) 8(3) = 15 24 =

Example 1 Find a fraction equivalent to by dividing the numerator and denominator by 5. 15 20 15 20 15 ÷ 5 20 ÷ 5 = 3 4 =

To compare fractions, convert them into equivalent fractions having the same denominator.

Example 2 Determine the relative size of and . 5 6 7 8 LCM = 2 • 2 • 2 • 3 = 24 24 ÷ 6 = 4 and 24 ÷ 8 = 3

Example 2 Determine the relative size of and . 5 6 7 8 5 6 5(4) 6(4) = 5 6 5(4) 6(4) = 20 24 = 20 24 21 24 < 7 8 7(3) 8(3) = 21 24 = 7 8 < 5 6

Example 3 Compare and . 5 8 7 12 8 = 23 and 12 = 22 • 3 LCM = 23 • 3 = 24

Example 3 Compare and . 5 8 7 12 5 8 5(3) 8(3) = 15 24 = 15 24 14 24 5 8 5(3) 8(3) = 15 24 = 15 24 14 24 > 7 12 7(2) 12(2) = 14 24 = 7 12 > 5 8

Example 7 12 11 18 Compare and . 21 36 22 36 < 11 18 < 7 12

Cross Multiplication Cross multiplication is multiplying the numerator of the first fraction times the denominator of the second and multiplying the denominator of the first times the numerator of the second.

a b c d a b c d ad bc

Example 4 5 8 4 7 Compare and using cross multiplication. 5 8 4 7 4 7 4 7 > 5 8 5 • 7 8 • 4 35 32 >

Example 5 13 16 Are the fractions and equivalent? 33 40 13 16 33 40 = ≠ 13 • 40 16 • 33 = ? 520 528 ≠

Example 6 6 7 Are the fractions and equivalent? 78 91 6 7 78 91 = ? 6 • 91 7 • 78 = ? 546 =

Example 120 210 140250 Compare and using cross multiplication. 4 7 14 25 > 120 210 140250 100 98 >

Example 130 210 150250 Compare and reducing to lowest terms first. 13 21 3 5 > 130 210 150250 65 63 >

Example 7 Graph the following rational numbers on a single number line. 1 4 3 4 – 3 4 1 9 4 – • 3 4 – • 1 4 • 3 4 1 • 9 4 – –3 –2 –1 1 2 3

Example 8 Graph the following rational numbers on a single number line. 1 4 – 4 1 3 2 4 5 – • 1 4 – 4 4 5 – • • 1 3 2 • –5 –4 –3 –2 1 2 3 –1