Question

for every 2 books beckett reads robin reads 3 the table shows the ratio 2:3 and two equivalent ratios

Answer 1

The student's question involves the mathematical concept of ratios, specifically the 2:3 ratio between the number of books read by Beckett and Robin. Equivalent ratios are found by multiplicative scaling of both terms in the original ratio. Examples include 4:6 and 6:9, obtained by multiplying the original ratio by 2 and 3, respectively.

Step-by-step explanation:

For every 2 books Beckett reads, Robin reads 3. This relationship is described by the ratio 2:3, which is a mathematical expression that shows how quantities are related to each other. To find equivalent ratios, you multiply or divide both terms of the ratio by the same number.

For example, if you multiply both terms by 2, you get 4:6, which means for every 4 books Beckett reads, Robin reads 6. In terms of fractional representations, the ratio can also be seen as ⅓ (two-thirds) or 0.666... – showing the part of the whole that Beckett reads in comparison to Robin.

Equivalent Ratios Examples

1. 2:3 can be scaled up to 4:6 by multiplying both sides by 2.
2. 2:3 can be scaled up to 6:9 by multiplying both sides by 3.
3. 2:3 can be scaled down to 1:1.5 by dividing both sides by 2.

The concept of equivalent ratios is crucial for solving problems involving comparisons of different quantities, often found in the real world and mathematics problems alike.