Writing and Solving Proportions

Front

What is a proportion?

Back

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

Front

How do you write a proportion?

Back

A proportion can be written as \( \frac{a}{b} = \frac{c}{d} \), where a, b, c, and d are numbers.

Front

What does it mean for two quantities to vary directly?

Back

Two quantities vary directly if they increase or decrease together at the same rate.

Front

If a car travels 280 miles in 7 hours, what is its speed in miles per hour?

Back

Speed = Distance / Time = 280 miles / 7 hours = 40 miles per hour.

Front

How do you solve a proportion?

Back

Cross-multiply the terms: if \( \frac{a}{b} = \frac{c}{d} \), then \( a \cdot d = b \cdot c \).

Front

What is the first step in solving the proportion \( \frac{n}{13} = \frac{11}{26} \)?

Back

Cross-multiply: \( n \cdot 26 = 11 \cdot 13 \).

Front

What is the solution to the proportion \( \frac{n}{13} = \frac{11}{26} \)?

Back

n = 5.5.

Front

If hamburger sells for 3 pounds for $6, how much does it cost per pound?

Back

Cost per pound = $6 / 3 pounds = $2 per pound.

Front

If Shane can bake 120 dozen cookies in 5 days, how many cookies can he bake in 1 day?

Back

Cookies per day = 120 dozen / 5 days = 24 dozen per day.

Front

How do you set up a proportion for Shane's cookie baking scenario?

Back

Set up as \( \frac{120 \text{ dozen}}{5 \text{ days}} = \frac{800 \text{ dozen}}{x \text{ days}} \).