do the ratios form a proportion: word problems

Key Notes :

Understanding Ratios and Proportions

• Ratio: A comparison of two quantities using division. For example, the ratio of 4 to 8 is written as 4:8 or 4/8.
• Proportion: An equation stating that two ratios are equal. For example, 4/8=1/2.

Steps to Check if Ratios Form a Proportion

1. Simplify Ratios: Reduce each ratio to its simplest form by dividing both terms by their greatest common factor (GCF).
   • Example: 6:9 simplifies to 2:3.
2. Cross-Multiply: Compare two ratios by cross-multiplying.
   • If a/b=c/d, then a⋅d=b⋅ca .
   • Example: Are 3:4 and 6:8 proportional? 3×8=24 and 4×6=24. Since the products are equal, the ratios are proportional.

Word Problems Involving Ratios and Proportions

1. Identify the Ratios: Extract the two ratios from the problem statement.
2. Simplify or Cross-Multiply: Use either simplification or cross-multiplication to determine if the ratios form a proportion.
3. Interpret the Result:
   • If the products of cross-multiplication are equal, the ratios form a proportion.
   • If they are not equal, the ratios do not form a proportion.

Learn with an example