PROPORTION PROBLEMS

WORD PROBLEMS

Concept: A ratio is a comparison of two numbers. It can be written in several ways. For example, when comparing the numbers 1 and 2, we can express the comparison as 1 to 2, or 1 : 2 or ˝.

Always write the terms of the ratio in the same order as the problem compares them.

Just as we can reduce fractions to lowest terms, we can simplify ratios to their lowest terms, although a ratio with a denominator of 1 must still be expressed as a fraction, and ratios that appear to be improper fractions must be left as improper fractions.

Many ratio problems require more than one step.

You may not be given both of the numbers that you need to write a ratio. In this case, you may need to solve another equation to find the missing number.

Finally, when two ratios are written as equal ratios, the equation is called a proportion. For example, is a proportion. In many proportion problems, one of the four terms is missing.

The proportion can be solved using the Cross-product Rule.

Cross-product Rule
To find the missing number in a proportion, cross multiply, and divide the product by the third number. For example, in the proportion , first multiply . Then divide . In this problem .

Steps for Solving Simple Proportion Problems

Step 1 | Form a proportion using two ratios. Use X for the unknown number.
Step 2 | Apply the Cross-product Rule to solve for X.

Example 1: Each group of 13 finger cakes could serve 23 deep sea divers. If there was 1 finger cake, how many deep sea divers could be served? Round to the nearest whole number.

Step 1 | Form a proportion using two ratios. Use X for the unknown number.
Step 2 | Apply the Cross-product Rule to solve for X.
To find the missing number in a proportion, cross multiply,
and divide the product by the third number.
In the proportion, X is equal to 1.77.
1.77 rounded to the nearest whole number is 2.
Each group of 13 finger cakes could serve 23 deep sea divers. If there was 1 finger cake, how many deep sea divers could be served? 2

Example 2: 10 of the 77 elves who worked in the pet mushroom factory had to work the day shift. What percent of the elves had to work the day shift? Round to the nearest hundredth.

Step 1 | Form a proportion using two ratios. Use X for the unknown number.
Step 2 | Apply the Cross-product Rule to solve for X.
To find the missing number in a proportion, cross multiply,
and divide the product by the third number.
In the proportion, X is equal to 12.9870.
12.9870 rounded to the nearest hundredth is 12.98
The percent of the elves who had to work the day shift is 12.98

Example 3: The lumberjacks use 83 gallons of fuel a day. Their saws use a 35:1 mixture of fuel to oil. How much oil do they use a day? Round answer to the nearest hundredth.

Step 1 | Form a proportion using two ratios. Use X for the unknown number.
Step 2 | Apply the Cross-product Rule to solve for X.
To find the missing number in a proportion, cross multiply,
and divide the product by the third number.
In the proportion, X is equal to 2.3714.
2.3714 rounded to the nearest hundredth is 2.37.
The lumberjacks use 2.37 gallons of oil a day.

Example 4: The mess cook prepared blintzes for 87 guests. The recipe called for 13 nutmeg seeds for every 50 units of blintzes. If he needed 21 units of blintzes, how many nutmeg seeds were needed? Round answer to the nearest whole numbers.

Step 1 | Form a proportion using two ratios. Use X for the unknown number.
Step 2 | Apply the Cross-product Rule to solve for X.
To find the missing number in a proportion, cross multiply,
and divide the product by the third number.
In the proportion, X is equal to 5.46.
5.46 rounded to the nearest whole number is 5. | 5 nutmeg seeds are needed.