Select all ratios equivalent to 16:4. 56:14 112:28 28:7
The correct answer and explanation is:
The correct ratios equivalent to 16:4 are:
- 56:14
- 112:28
- 28:7
Explanation:
To determine whether two ratios are equivalent, you need to check if the fraction formed by simplifying each ratio is the same.
Step 1: Simplify 16:4.
- Divide both terms of the ratio by their greatest common divisor (GCD), which is 4.
- 16 ÷ 4 = 4 and 4 ÷ 4 = 1, so 16:4 simplifies to 4:1.
Step 2: Simplify 56:14.
- The GCD of 56 and 14 is 14.
- 56 ÷ 14 = 4 and 14 ÷ 14 = 1, so 56:14 simplifies to 4:1.
Step 3: Simplify 112:28.
- The GCD of 112 and 28 is 28.
- 112 ÷ 28 = 4 and 28 ÷ 28 = 1, so 112:28 simplifies to 4:1.
Step 4: Simplify 28:7.
- The GCD of 28 and 7 is 7.
- 28 ÷ 7 = 4 and 7 ÷ 7 = 1, so 28:7 simplifies to 4:1.
Since all the ratios simplify to 4:1, they are equivalent to the original ratio of 16:4.
In general, to check for equivalent ratios, divide both terms of each ratio by their GCD and compare the simplified results.