A ratio describes the relationship between different amounts. A ratio can describe the relationship between two parts of a group, or between one part and the whole group.

**To better understand ratios…**

## LET’S BREAK IT DOWN!

### A ratio shows a relationship between two amounts.

A bunny has 2 eyes and 1 nose. That’s a ratio of 2 to 1. You can also write it as 2 : 1. If there are two bunnies, the ratio of eyes to noses becomes 4 to 2, or 4 : 2. For three bunnies, the ratio is 6 to 3, or 6 : 3, and for four bunnies, the ratio is 8 to 4, or 8 : 4. Like with equivalent fractions, you can multiply both numbers in a ratio to get another, equivalent ratio. Multiply 2 : 1 by 3 to get 6 : 3, or 6 eyes on 3 bunnies. Try this one yourself: **A sign has 5 parts red for every 1 part white. With the same color ratio, a larger sign has 20 parts red. How many parts white does the larger sign have? **

### Part-to-whole ratios are related to fractions.

A pack of 5 markers contains 1 blue marker. This is a part-to-whole ratio. We can represent part-to-whole ratios with fractions. Write this ratio as [ggfrac]1/5[/ggfrac]. We can use equivalent fractions to represent the number of blue markers in more packs. Two packs of markers have 2 blue markers out of 10 total, or [ggfrac]2/10[/ggfrac]. This is the same as multiplying the original numerator, 1, by 2 and multiplying the original denominator, 5, by 2. Try this one yourself: ** Find the part-to-whole ratio that describes the number of blue markers in 10 packs of markers. **

### Part-to-part ratios don’t show the whole.

A fish tank contains 20 fish: 14 blue and 6 yellow. The ratio [ggfrac]14/20[/ggfrac] describes the number of blue fish out of the total. The ratio [ggfrac]6/20[/ggfrac] describes the number of yellow fish out of the total. These are both part-to-whole ratios. You can also use 'part-to-part' ratios to show this information. The ratio 14 : 6 compares the number of blue fish to the number of yellow fish. Similarly, the ratio 6 : 14 compares the number of yellow fish to the number of blue fish. Try this one yourself: **A bag of marbles has 8 red marbles out of 15 total. The marbles that aren’t red are purple. Find the part-to-part ratio that compares the number of red marbles to the number of purple marbles. Then find the part-to-part ratio that compares the number of purple marbles to the number of red marbles.**

### You can simplify ratios by scaling them down.

Simplifying ratios can make the comparisons easier to understand. Let’s say a local animal shelter has 24 dogs and 16 cats, or 24 : 16.

You can divide both numbers by the same divisor to find an equivalent ratio. Divide by 2 to get 12 : 8. Divide by 2 again to get 6 : 4. Divide by 2 one more time to get 3 : 2. You could also divide 24 : 16 by 8 to get 3 : 2. Try this one yourself:

**Simplify the ratio “100 parakeets to 75 hamsters.”**

### Ratios can help you find the best deal.

Emily saw a deal online, where 4 t-shirts cost $20. Amari saw another deal advertising the same t-shirts, where 8 t-shirts cost $32. You can use ratios to decide which deal is better. Emily can describe her ratio as “$20 to 4 shirts.” Dividing each of these numbers by 4, that is equivalent to $5 : 1 shirt. Amari can describe his deal as “$32 to 8 shirts.” Dividing each of these numbers by 8, that is equivalent to $4 : 1 shirt. Buying shirts with Amari’s deal saves $1 for each shirt, so it is the better deal. Try this one yourself:**Which is the better deal: 5 pairs of socks for $15, or 2 pairs of socks for $12?**

### Graphing ratios shows patterns more visually.

A carnival game involves a basketball hoop. For each basket you make, you win 3 tickets. This is a ratio of 3 : 1. You can use multiplication to make a set of equivalent ratios: 6 : 2, 9 : 3, 12 : 4, 15 : 5. These ratios can be displayed on a coordinate grid. The number of baskets goes on the x-axis, and the number of tickets goes on the y-axis. Then the ratios also represent coordinate pairs: (3, 1), (6, 2), (9, 3), (12, 4), (15, 5). Each point is 3 right and 1 up from the previous point. To predict the number of tickets more easily, draw a straight line through these points and keep going up and to the right. Try this one yourself:**To get into a carnival, each child admission ticket is $5. Graph the cost of 1, 2, 3, 4, and 5 admission tickets on a coordinate grid. Draw a line through these points to find the cost of 8 admission tickets.**