RATIO AND 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 Ratio Problems

Step 1 | Set up the ratio, writing the terms in the same order that the problem compares the terms.
Step 2 | Simplify the ratio to its lowest terms. (Remember that 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.)

Steps for Solving Multiple Step Ratio Problems

Step 1 | Set up the first ratio, writing the terms in the same order that the problem compares the terms.
Step 2 | Set up an equation to solve for the unknown number needed for the ratio.
Step 3 | Set up a ratio, writing the terms in the same order that the problem compares the terms.
Step 4 | Simplify the ratio to its lowest terms. (Remember that 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.)

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.

Steps for Solving Multistep Proportion Problems

Step 1 | Set up the first ratio using given information.
Step 2 | Set up an equation, if necessary, to solve for any unknown information.
Step 3 | Set up another ratio, if necessary, using the new information.
Step 4 | Form a proportion using two ratios. Use the ratio from either Step 1 or Step 3 for the first ratio in the proportion, and another ratio, set up in the same order, while substituting X for the unknown number.
Step 5 | Apply the Cross-product Rule to solve for X.

Example1: When the mountain lions entered the abominable snowman’s den, 9 out of 19 got excited. If there were 100 mountain lions in all, how many did not get excited? Round answer to the nearest whole number.

Use the Steps for Solving Simple Proportion Problems

Step 1 | Form a proportion using two ratios. Use X for the unknown number.
We know that for every two mountain lions, one mountain lions got excited. That ratio is written .
We know that there were a total of 100 mountain lions. Set up a proportion using the ratio above to determine how many mountain lions got excited.
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 47.
We now know that out of 100 mountain lions , 47 mountain lions got excited. To find the number of mountain lions who did not get excited, which is what this problem asks, simply subtract the number of mountain lions who got excited from the total number.
When the ratio of mountain lions who got excited to the total number of mountain lions is 9 : 19 , then the number of mountain lions who did NOT get excited is 53.

Example 2: The souse chef found that it took 7 huge measures of roux to make 3 poached bacon balls. The souse chef needed to make 339 poached bacon balls. How many huge measures of roux were needed? Round the answer to the nearest whole number.

Use the 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.
To find the missing number in a proportion, cross multiply,
and divide the product by the third number. Round the answer to the nearest whole number. 791 rounded to the nearest whole number is 791.
In the proportion , X is equal to 791.
When it takes 7 huge measures of roux to complete 3 poached bacon balls, it will take 791 huge measures of roux to complete 339 poached bacon balls.

Example 3: The number of students in theater increased 7% this year. If there are 24 more students in theater this year than there were last year, how many students are in theater this year? Increase fractional parts to the next whole number.

Use the Steps for Solving Simple Proportion Problems

There are 24 more students in theater this year than last year, which represents a 7% increase. The total number of students in theater last year will be considered 100% in this problem. The total number of students in theater this year will be 7% more than last year, so that number will be considered 107% in this problem.
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. Increase fractional parts to the next whole number. 366.857 increased to the nearest whole number is 367.
In the proportion, X is equal to 367.
There are 367 students in theater this year.