Setting up proportions

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. It can be written in the form \( \frac{a}{b} = \frac{c}{d} \).

Front

How do you set up a proportion to find an unknown value?

Back

To set up a proportion, identify two ratios that are equivalent and set them equal to each other. For example, if you know \( \frac{a}{b} = \frac{c}{x} \), you can cross-multiply to solve for \( x \).

Front

If 6 pairs of shoes cost $140, how do you find the cost of 5 pairs?

Back

Set up the proportion \( \frac{6}{140} = \frac{5}{x} \) and solve for \( x \).

Front

What is the first step in solving a proportion?

Back

The first step is to cross-multiply the two ratios. For example, in \( \frac{a}{b} = \frac{c}{d} \), you would calculate \( a \cdot d = b \cdot c \).

Front

How do you find a percentage of a total using proportions?

Back

Set up a proportion where the part is over the whole, and the percentage is over 100. For example, to find 27% of 155, use \( \frac{27}{100} = \frac{x}{155} \).

Front

What does it mean if two ratios are equivalent?

Back

If two ratios are equivalent, it means they represent the same relationship between quantities. For example, \( \frac{1}{2} \) is equivalent to \( \frac{2}{4} \).

Front

How can you use proportions to solve real-world problems?

Back

Proportions can be used to compare quantities and find unknown values in various situations, such as shopping, cooking, or budgeting.

Front

What is the relationship between fractions and proportions?

Back

Proportions are a specific type of equation that involves fractions. They show that two fractions are equal.

Front

If you have 48 cookies and 1/4 are chocolate chip, how do you find the number of chocolate chip cookies?

Back

Set up the proportion \( \frac{1}{4} = \frac{x}{48} \) and solve for \( x \).

Front

What is the formula for finding the cost per item using proportions?

Back

To find the cost per item, set up the proportion \( \frac{total\,cost}{number\,of\,items} = \frac{cost\,per\,item}{1} \).