Ratio Word Problems 7th Grade
Welcome to our Ratio Word Problems 7th grade page.
Here you will find our range of 7th Grade Ratio Problem worksheets
which will help your child apply and practice their Math skills to solve a range of different ratio problems.
There is also a quick quiz at the bottom of the page where you can test your skill online and get immediate feedback!
Ratio Word Problems 7th Grade
If you are looking for a comprehensive set of ratio problems designed specially for 7th grade students then look no further!
We have a range of different ratio problems covered in our worksheets including:
- part-part and part-whole ratio problems
- problems involving scaling up and scaling down ratios
- simplifying ratio problems
- completing missing numbers in ratio tables
- identifying correct and incorrect ratios in tables
- solving ratio problems involving fractional and decimal values
The sheets involve using and applying knowledge to ratios to solve problems.
The sheets in each section have been put in order of difficulty, with the easiest first. They are aimed at students in 7th grade.
Each problem sheet comes complete with an answer sheet.
Using these sheets will help your child to:
- apply their ratio skills;
- apply their knowledge of fractions and proportional relationships;
- solve a range of word problems.
- solving word problems involving ratio and probability
Ratio Problems for 7th Graders Worked Examples
Here are some worked examples for each type of ratio problems.
Part-to-Part Ratio Problems
- Part-to-part ratio problems involve solving typical ratio problems where you are looking at the ratio of one thing to another thing.
- These problems often involve scaling up or scaling down ratios
Example 1) The ratio of goats to sheep to horses in a field is 3:5:1. If there are 144 animals in the field, how many of each?
The first step is to write the ratio down:
The ratio is 3 goats : 5 sheep : 1 horse
This makes a total of 9 animals in a group.
The next step is to divide the total number of animals by 9 to find out how many groups we need.
144 ÷ 9 = 16
Next we multipy the ratio by 16 to find out how many of each animal.
3 goats : 5 sheep : 1 horse = 48 goats : 80 sheep : 16 horses
Check 48 goats + 80 sheep + 16 horses = 144 animals
This means that there will be 48 goats, 80 sheep and 16 horses.
Example 2) Frazer cycles 12 miles in 45 minutes at a steady speed. How far would he be able to travel in an hour at this speed?
The first step is to write the ratio down:
The ratio is 12 miles : 45 minutes
The next step is to simplify this ratio.
3 is a common factor of both numbers, so we can divide both numbers by 3.
12 miles : 45 minutes = 4 miles : 15 minutes
Next we need to scale up the ratio to find out how far he travels in an hour.
1 hour = 60 minutes, so we need to multiply both sides by 4
4 miles : 15 minutes = 16 miles : 60 minutes
So he travels 16 miles in an hour.
Part-to-Whole Ratio Problems
- Part-to-whole ratios involve looking at the ratio of one thing compared to the whole set of things.
- Part-to-whole ratios are very similar to proportion - the only difference is that proportion is normally written as a fraction.
Example 3) The ratio of swimmers to non-swimmers in a group of students is 5:3.
Write this as a ratio of swimmers to the whole group.
The first step is to write the ratio down:
5 swimmers : 3 non-swimmers
Total of students = 8
So the ratio of swimmers to the whole group is 5:8
What proportion of students in the group can swim?
There are 5 out of 8 swimmers.
The proportion of the group which are swimmers is 5/8
Scaling up and Scaling down Ratios
- we can find an equivalent ratio by scaling ratios up and scaling ratios down
- we scale ratios up by multiplying all the ratio parts by the same number.
- we scale ratios down by dividing all the ratio parts by the same number.
- we often use ratio tables for scaling up ratios lots of time
Examples of scaling ratios up
4:5 can scale up to an equivalent ratio 8:10 by multiplying both ratio parts by 2
3:5:2 can scale up to an equivalent ratio 30:50:20 by multiplying all the ratio parts by 10
Simplifying Ratio Problems
- simplifying ratios involves scaling ratios down until there are no more common factors
- we scale the ratios down by dividing all the ratio parts by the same number
Example 4) There are 24 ducks and 18 geese in a pond. Write this as a ratio in simplest form.
The first step is to write the ratio down:
24 ducks : 18 geese
A common factor of 24 and 18 is 2, so we need to divide both ratio parts by 2
24 ducks : 18 geese = 12 ducks : 9 geese
A common factor of 12 and 9 is 3, so we need to divide both ratio parts by 3.
12 ducks : 9 geese = 4 ducks : 3 geese
There are no more common factors so we have finished.
So the ratio of ducks to geese is 4:3 in simplest form
Ratio and Probability Problems
- ratio and probability are two concepts which are often used together
- the probability of an event occurring is usually recorded as a fraction and has a value between 0 (impossible) and 1 (certain).
Example 5) There are 6 white balls and 15 blue balls in a bag. Simplify this ratio and work out the probability of choosing a white ball at random from the bag.
The first step is to write the ratio down:
6 white balls : 15 blue balls
A common factor of 6 and 15 is 3, so we need to divide both ratio parts by 3.
6 white balls : 15 blue balls = 2 white balls : 5 blue balls
There are no more common factors, so the ratio has been simplified.
The simplified ratio is 2 white balls : 5 blue balls
Next we need to find the probability of picking out a white ball at random from the bag.
There are 6 white balls in the bag. There are 6 +15 = 21 balls in total in the bag.
The probability of picking a white ball at random is 6 out of 21 = 6/21
We can simplify this fraction by dividing the numerator and denominator by 3.
6/21 = 2/7
So the probability of picking a white ball at random is 2/7
Ratio Word Problems 7th Grade Worksheets
Equivalent Ratios in Tables
Sheet 7:1 involves finding the incorrect ratio in each table.
Sheet 7:2 involves selecting all of the ratios which are equivalent to a given ratio.
Sheet 7:3 involves filling in the missing numbers to make an equivalent ratio.
Ratios and Probability Problems 7th Grade
Sheet 7:1 involves the probability of taking out a particular ball from a bag containing balls of different colors
Sheet 7:2 involves tree planting with 3 different types of tree and the probability of choosing a particular tree.
Each of these sheets involves solving some ratio and some probability problems.
Ratio Word Problems 7th Grade Mixed Problems
All the worksheets involve solving a range of different ratio problems.
The sheets are all graded with the easier sheets coming first. Each answer sheet comes with working out to show how the answer is obtained.
More Recommended Math Worksheets
Take a look at some more of our worksheets similar to these.
Looking for some easier Ratio Problems?
We have created a set of 6th grade ratio problems which are at a more basic level than the problems on this page.
How to do Ratio Problems
Need some help understanding what a ratio is and how to solve ratio problems?
Our How to do Ratio Problems page has all the information you need to master this skill!
More Ratio & Unit Rate Worksheets
These sheets are a great way to introduce ratio of one object to another using visual aids.
The sheets in this section are at a more basic level than those on this page.
We also have some ratio and proportion worksheets to help learn these interrelated concepts.
Ratio Word Problems Online Quiz
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Ratio Word Problems Online Quiz
This quick quiz tests your knowledge and skill at solving word problems involving ratios.
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