Ratios and Proportions in Word Problems

Front

What is a ratio?

Back

A ratio is a comparison of two quantities that shows the relative size of one quantity to another, often expressed as 'a : b'. For example, if there are 5 apples and 3 oranges, the ratio of apples to oranges is 5 : 3.

Front

How do you simplify a ratio?

Back

To simplify a ratio, divide both terms by their greatest common divisor (GCD). For example, to simplify the ratio 8 : 12, divide both by 4 to get 2 : 3.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. For example, if 1/2 = 2/4, then 1 : 2 is proportional to 2 : 4.

Front

How do you solve a proportion?

Back

To solve a proportion, cross-multiply the terms and set the products equal to each other. For example, in the proportion a/b = c/d, cross-multiply to get ad = bc.

Front

What does it mean to find the missing term in a ratio?

Back

Finding the missing term in a ratio involves using the known values to calculate the unknown value that maintains the equality of the ratio.

Front

If the ratio of A to B is 3 : 4 and A = 12, what is B?

Back

If A = 12, then B can be found by setting up the proportion 3/4 = 12/B. Cross-multiplying gives 3B = 48, so B = 16.

Front

What is the relationship between ratios and fractions?

Back

Ratios can be expressed as fractions. For example, the ratio 3 : 4 can be written as the fraction 3/4.

Front

How do you compare two ratios?

Back

To compare two ratios, convert them to fractions and find a common denominator or cross-multiply to see which is larger.

Front

What is a part-to-whole ratio?

Back

A part-to-whole ratio compares a part of a quantity to the entire quantity. For example, if there are 2 red balls and 8 total balls, the part-to-whole ratio of red balls is 2 : 8 or 1 : 4.

Front

If the ratio of cookies to carrots is 3 : 9, how many times as many cookies are there as carrots?

Back

There are 1/3 as many cookies as carrots.