EQUIVALENT RATIOS
Definition Of Equivalent Ratios
If two ratios have the same value when simplified, then they are called Equivalent Ratios.
More About Equivalent Ratios
Equivalent ratios can be obtained by multiplying or dividing both sides by the same non-zero number.
Video Examples: Equivalent Ratios
Example of Equivalent Ratios
1/3 and 2/6 are equivalent ratios since they represent the same fraction.
The two ratios 8 : 24 and 4 : 12 are equivalent.
There are 10 dolls for every 40 children in a preschool. Then the ratio of the number of children to that of the dolls = 40:10 = 4:1
Solved Example on Equivalent Ratios
Ques: A carnival game has 3 winners for every 7 losers. Find two ratios equal to the ratio of winners to losers.
Choices:
A.14/6, 21/9
B.6/14, 10/21
C.7/14, 9/21
D.6/14, 9/21
Correct Answer: D
Solution:
Step 1: The ratio of winners to losers = 3/7
Step 2: 3/7= 
=6/14 [Multiply both the numerator and the denominator by 2.]
Step 3: 3/7 = = 9/21[Multiply both the numerator and the denominator by 3.]
Step 4: The two ratios equal to the ratio of winners to the losers are 6/14 and 9/21.
Quick Summary
- Equivalent ratios represent the same proportional relationship.
- They can be found by multiplying or dividing both parts of the ratio by the same non-zero number.
🍎 Teacher Insights
Use visual aids like fraction bars or diagrams to illustrate equivalent ratios. Emphasize the importance of simplifying ratios.🎓 Prerequisites
- Fractions
- Multiplication
- Division
Check Your Knowledge
Q1: Which of the following ratios is equivalent to 2:5?
Q2: Are the ratios 8:12 and 2:3 equivalent?
Frequently Asked Questions
Q: How do I determine if two ratios are equivalent?
A: Simplify both ratios. If they are the same after simplification, they are equivalent.
Q: Can equivalent ratios be found by adding or subtracting?
A: No, equivalent ratios are found by multiplying or dividing both parts of the ratio by the same non-zero number.