Interpret a ratio as a comparison

Detailed Explanation: Interpret a ratio as a comparison

A ratio compares quantities by telling how many of one quantity correspond to another. The order matters.

For example, suppose a basket has 6 apples and 4 oranges.

Step 1: Identify the two quantities

• Apples: $6$
• Oranges: $4$

Step 2: Match the order in the question

Suppose the question asks for the ratio of apples to oranges.

Write apples first and oranges second:

This can also be written as:

• $6$ to $4$
• $\frac{6}{4}$

Step 3: Interpret the ratio

The ratio $6:4$ means:

For every $6$ apples, there are $4$ oranges.

This is a part-to-part comparison because it compares one part of the basket with another part.

It does not mean there are $6-4=2$ more apples. A ratio describes how the amounts compare, not their difference.

Step 4: Notice that changing the order changes the meaning

The ratio of oranges to apples is:

This means:

For every $4$ oranges, there are $6$ apples.

It is different from $6:4$ because the quantities are in the opposite order.

Step 5: Compare a part with the whole

There are $6+4=10$ pieces of fruit altogether. The ratio of apples to all the fruit is:

This is a part-to-whole comparison because apples are compared with the total number of fruits.

When interpreting any ratio:

1. Identify the two quantities.
2. Write them in the order named.
3. Explain what the ratio means using “for every.”
4. Decide whether it compares part to part or part to whole.