Setting Up & Setting Proportions

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal.

Front

How do you set up a proportion?

Back

To set up a proportion, you can use the formula \( \frac{a}{b} = \frac{c}{d} \), where a and b are part of one ratio, and c and d are part of another.

Front

If a car travels 420 miles in 8 hours, what is its speed in miles per hour?

Back

The speed is \( \frac{420}{8} = 52.5 \) miles per hour.

Front

How far will a car travel in 12 hours at the same speed of 52.5 miles per hour?

Back

The car will travel \( 52.5 \times 12 = 630 \) miles.

Front

What is the relationship between the amount of cocoa and the amount of hot chocolate made?

Back

The relationship can be expressed as a proportion: \( \frac{6 \text{ tablespoons}}{24 \text{ ounces}} = \frac{x \text{ tablespoons}}{y \text{ ounces}} \).

Front

If 6 tablespoons of cocoa make 24 ounces of hot chocolate, how many ounces can be made with 144 tablespoons?

Back

Using the proportion, \( \frac{24}{?} = \frac{x}{144} \), the answer is 6.

Front

How do you find the expected duration of a product based on its size?

Back

You can set up a proportion based on the size and duration of a similar product.

Front

If a 12-ounce shampoo bottle lasts 16 weeks, how long will an 18-ounce bottle last?

Back

Using the proportion \( \frac{12}{16} = \frac{18}{x} \), the answer is 24 weeks.

Front

What is the formula to find the number of presents wrapped based on tape used?

Back

Set up a proportion: \( \frac{8 ext{ cm}}{4 ext{ presents}} = \frac{30 ext{ cm}}{x ext{ presents}} \).

Front

If Danielle used 8 cm of tape for 4 presents, how much tape does she use per present?

Back

She uses \( \frac{8}{4} = 2 \) cm of tape per present.