Solving Proportions

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 solve a proportion?

Back

To solve a proportion, you can use cross-multiplication. If a/b = c/d, then a*d = b*c.

Front

What is cross-multiplication?

Back

Cross-multiplication is a method used to solve proportions by multiplying the numerator of one ratio by the denominator of the other ratio.

Front

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

Back

x = 9. (Cross-multiply: 3*12 = 4*x, so 36 = 4x, thus x = 9.)

Front

What is the first step in solving the proportion 5/x = 15/20?

Back

The first step is to cross-multiply: 5*20 = 15*x.

Front

What does it mean if two ratios are equivalent?

Back

Two ratios are equivalent if they represent the same relationship or proportion, meaning they simplify to the same fraction.

Front

How can you check if two ratios are in proportion?

Back

You can check if two ratios are in proportion by cross-multiplying and seeing if the products are equal.

Front

If a/b = c/d, what is the relationship between a, b, c, and d?

Back

The relationship is that the product of the means (b and c) equals the product of the extremes (a and d).

Front

What is an example of a real-life situation that can be modeled with proportions?

Back

A real-life example is cooking: if a recipe requires 2 cups of flour for 4 servings, you can find out how much flour is needed for 10 servings using proportions.

Front

What is the formula for finding a missing value in a proportion?

Back

The formula is: missing value = (known value * other known value) / other known value.