Understanding Ratios and Fractions

This page introduces fundamental concepts of ratio comparison and fraction analysis through detailed mathematical examples and problem-solving techniques.

The content explores three main methods for comparing and analyzing ratios:

1. Using common denominators to compare fractions
2. Applying cross multiplication to verify ratios
3. Solving for unknown values in given ratios

Example: Comparing 35/55 with the ratio 5:8 using cross multiplication:

• First step: 5 × 11 = 55
• Second step: 7 × 8 = 56
• Since 55 ≠ 56, the numbers are not in the ratio 5:8

Definition: Cross multiplication is a method where you multiply the numerator of one fraction by the denominator of another to compare ratios.

Highlight: When comparing fractions, you can either convert them to the same denominator or use cross multiplication - both methods are equally valid.

Example: Finding N in the ratio N:24 = 5:8 Solution process:

• Set up the equation: 8 × N = 5 × 24
• Solve for N: N = (5 × 24) ÷ 8 = 15

Vocabulary:

• Ratio: A comparison between two or more related quantities
• Cross Product: The result of multiplying the numerator of one fraction by the denominator of another
• Equivalent Ratios: Ratios that represent the same relationship between numbers