Set Up Proportions 2

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. For example, if a/b = c/d, then a, b, c, and d are in proportion.

Front

How do you set up a proportion?

Back

To set up a proportion, identify two ratios that you want to compare and set them equal to each other. For example, if you know that 5 notebooks cost $1.25, you can set up the proportion \( \frac{5 \text{ notebooks}}{1.25 \text{ dollars}} = \frac{d}{250 \text{ notebooks}} \) to find the cost of 250 notebooks.

Front

What is the cross-multiplication method?

Back

Cross-multiplication is a method used to solve proportions. If \( \frac{a}{b} = \frac{c}{d} \), then cross-multiplying gives you \( a \cdot d = b \cdot c \).

Front

What does it mean for two ratios to be equivalent?

Back

Two ratios are equivalent if they represent the same relationship between quantities. For example, \( \frac{1}{2} \) and \( \frac{2}{4} \) are equivalent ratios.

Front

How can you find an unknown in a proportion?

Back

To find an unknown in a proportion, set up the proportion with the known values and use cross-multiplication to solve for the unknown.

Front

What is the formula for setting up a proportion based on a unit rate?

Back

The formula for setting up a proportion based on a unit rate is \( \frac{part}{whole} = \frac{part}{whole} \). For example, if 5 people pay $15, the unit rate is \( \frac{15}{5} \) dollars per person.

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities when they are combined together. It is often expressed as a quantity per one unit of another quantity.

Front

How do you determine if two ratios form a proportion?

Back

To determine if two ratios form a proportion, check if the cross-products are equal. If \( a/b = c/d \), then check if \( a \cdot d = b \cdot c \).

Front

What is the relationship between ratios and fractions?

Back

Ratios can be expressed as fractions. For example, the ratio of 3 to 4 can be written as the fraction \( \frac{3}{4} \).

Front

How do you solve a proportion with a variable?

Back

To solve a proportion with a variable, set up the proportion, cross-multiply, and then isolate the variable to find its value.