Question

Consider each ratio situation:
In one classroom, the ratio of the number of boys to the number of girls is 4:3.
The ratio of the lengths of the 2 sides of a right triangle that form the right angle is 8:6.
At the time of birth, the ratio of the number of boys born to the number of girls born is 107 to 100.
The ratio of the length of the diagonal of a rectangle to a side length is 15:12.
A shade of green paint is created by mixing 2 cans of blue paint with 1.5 cans of yellow paint.

Choose one of the ratio situations above. Create 3 equivalent ratios. Show or explain how you know they are equivalent.

Answer 1

Answer:

Chosen ratio situation: In one classroom, the ratio of the number of boys to the number of girls is 4:3.

Equivalent ratios:  8:6  12:9  16:12

The new ratios are equivalent because they are all 4:3 when simplified.

Step-by-step explanation:

Let's choose the first ratio situation:

In one classroom, the ratio of the number of boys to the number of girls is 4:3.

To find equivalent ratios, we can just multiply both sides of the ratio by the same number.

Original ratio:  4:3

Multiply both sides by 2:  4 * 2 = 8   3 * 2 = 6

New ratio:  8:6

Original ratio:  4:3

Multiply both sides by 3:  4 * 3 = 12   3 * 3 = 9

New ratio:  12:9

Original ratio:  4:3

Multiply both sides by 4:  4 * 4 = 16   3 * 4 = 12

New ratio:  16:12

You know that the new ratios are equivalent because they are all 4:3 when simplified.