Sections:

# Comparing Fractions

In this section, we learn how to compare the relative size of two or more fractions. We will learn two different methods:
1. Convert each Fraction into an Equivalent Fraction with the LCD as the Denominator
2. Cross Multiply
Convert each Fraction into an Equivalent Fraction with the LCD as the Denominator
1. Identify the LCD for the denominators of the fractions involved
2. Convert each fraction into an equivalent fraction with the LCD as the Denominator
3. Compare numerators, the larger numerator belongs to the larger fraction
Example 1: Determine which fraction is larger: $$\frac{3}{8}\hspace{.25em}or\hspace{.25em}\frac{2}{7}$$ • What is the LCD? 56
• Convert each fraction into an equivalent fraction with the LCD (56) as the Denominator $$\frac{21}{56}\hspace{.25em}or\hspace{.25em}\frac{16}{56}$$ • 21 is larger than 16 $$\frac{3}{8}> \frac{2}{7}$$ Cross Multiply
1. Multiply the denominator of one fraction by the numerator of the other
2. The numerator from the larger product belongs to the larger fraction
Example 2: Determine which fraction is larger: $$\frac{7}{11}\hspace{.25em}or\hspace{.25em}\frac{6}{7}$$ • Multiply: 11 x 6 = 66
• Multiply: 7 x 7 = 49
• 66 is the larger product, the numerator 6 belongs to the larger fraction $$\frac{7}{11}< \frac{6}{7}$$