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 2 apples and 3 oranges, the ratio of apples to oranges is 2 : 3.

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

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.

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.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 is proportional to c : d.

Tags

CCSS.7.RP.A.2A

Front

How do you solve a word problem involving ratios?

Back

1. Identify the quantities involved. 2. Write the ratio based on the information given. 3. Set up a proportion if necessary. 4. Solve for the unknown quantity.

Front

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

Back

The ratio of B to A is the inverse of A to B, which is 4 : 3.

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

Front

What does it mean if a ratio is expressed in simplest form?

Back

A ratio is in simplest form when the two numbers have no common factors other than 1. For example, the ratio 10 : 15 can be simplified to 2 : 3.

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

Front

How do you find the total number of items from a ratio?

Back

To find the total number of items from a ratio, add the parts of the ratio together. For example, in the ratio 2 : 3, the total is 2 + 3 = 5 parts.

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.

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

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.

Tags

CCSS.6.RP.A.3A

Front

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

Back

There are 3 times as many carrots as cookies.

Tags

CCSS.6.RP.A.3B