Comparing Fractions Methods

Overview

This lecture explains two main methods for comparing fractions: cross multiplying and converting fractions to decimals, highlighting when each method is useful.

Why Comparing Fractions Is Tricky

• Fractions cannot always be compared just by looking at the numbers.
• The value of a fraction depends on both its numerator (top number) and denominator (bottom number).
• For example, 1/3 is greater than 1/10 even though 10 is larger than 3.

Method 1: Cross Multiplying

• If fractions share the same denominator, compare the numerators directly.
• For unlike denominators, multiply the numerator of each fraction by the denominator of the other.
• The larger resulting product shows which fraction is greater.
• Example: Compare 7/8 and 4/5 — cross multiply to get 35 (7×5) and 32 (4×8); since 35 > 32, 7/8 > 4/5.
• Example: Compare 6/11 and 9/15 — 15×6=90, 11×9=99; since 99 > 90, 9/15 > 6/11.

Method 2: Converting Fractions to Decimals

• Divide the numerator by the denominator for each fraction to get the decimal value.
• Compare decimal values directly; the higher decimal is the greater fraction.
• Example: 5/12 ≈ 0.42 and 7/15 ≈ 0.47, so 7/15 > 5/12.
• If two fractions have the same decimal value, they are equivalent fractions (e.g., 3/8 = 0.375 and 15/40 = 0.375).

Key Terms & Definitions

• Numerator — The top number of a fraction, indicating how many parts are being considered.
• Denominator — The bottom number of a fraction, indicating the total number of equal parts.
• Cross Multiply — Multiply the numerator of each fraction by the denominator of the other to compare values.
• Equivalent Fractions — Different fractions with the same numeric value.

Action Items / Next Steps

• Practice comparing fractions using both cross multiplying and decimal conversion methods.
• Complete exercises for this section to reinforce the concepts.