Here you will learn about ratio problem solving, including how to set up and solve problems. You will also look at real life ratio word problems.
Students will first learn about ratio problem solving as part of ratio and proportion in 6 th grade and 7 th grade.
Ratio problem solving is a collection of ratio and proportion word problems that link together aspects of ratio and proportion into more real life questions. This requires you to be able to take key information from a question and use your knowledge of ratios (and other areas of the curriculum) to solve the problem.
A ratio is a relationship between two or more quantities. They are usually written in the form a : b where a and b are two quantities. When problem solving with a ratio, the key facts that you need to know are:
As with all problem solving, there is not one unique method to solve a problem. However, this does not mean that there aren’t similarities between different problems that you can use to help you find an answer.
The key to any problem solving is being able to draw from prior knowledge and use the correct piece of information to allow you to get to the next step and then the solution.
Let’s look at a couple of methods you can use when given certain pieces of information.
When solving ratio word problems, it is very important that you are able to use ratios. This includes being able to use ratio notation.
For example, Charlie and David share some sweets in the ratio of 3 : 5. This means that for every 3 sweets Charlie gets, David receives 5 sweets.
Charlie and David share 40 sweets, how many sweets do they each get?
You use the ratio to divide 40 sweets into 8 equal parts.
Then you multiply each part of the ratio by 5.
3\times 5:5\times 5=15 : 25
This means that Charlie will get 15 sweets and David will get 25 sweets.
There can be ratio word problems involving different operations and types of numbers.
Here are some examples of different types of ratio word problems:
A bag of sweets is shared between boys and girls in
the ratio of 5:6. Each person receives the same
number of sweets. If there are 15 boys, how many
girls are there?
(18)
If \frac students are right handed, write the ratio of
right handed students to left handed students.
(9:1)
Simplify the ratio 10:15.
(2:3)
Write the ratio 4:15 in the form 1:n.
(1:3.75)
If £1:\$1.37, how much is £10 in US dollars?
(\$13.70)
In a class of 30 students, the ratio of boys to girls is
3:2. If 40\% of the boys and 60\% of the girls passed
a math test, how many students passed the test?
(14)