Proportions

Front

What is a proportion?

Back

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

Front

How do you solve a proportion?

Back

To solve a proportion, cross-multiply the two ratios and set the products equal to each other.

Front

If 3/4 = x/12, what is x?

Back

x = 9 (Cross-multiply: 3 * 12 = 4 * x) => 36 = 4x => x = 9.

Front

What does it mean for two quantities to vary directly?

Back

Two quantities vary directly if they increase or decrease together at a constant rate.

Front

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

Back

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

Front

If 3 people can complete a project in 7 days, how long will it take 5 people?

Back

It will take 4.2 days (More people means less time, calculated using the inverse relationship).

Front

What is the formula for direct variation?

Back

The formula for direct variation is y = kx, where k is the constant of variation.

Front

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

Back

It costs $2 per pound (Divide $6 by 3 pounds).

Front

How do you find the constant of variation in a direct variation problem?

Back

The constant of variation (k) can be found by dividing y by x in the equation y = kx.

Front

What is the relationship between ratios and proportions?

Back

Ratios are comparisons of two quantities, while proportions state that two ratios are equal.