What is ratio?

Ratio is used to compare the size of different parts of a whole. For model, the full number of students in a course is 30. There are 10 girls and 20 boys. The proportion of girls : boys is 10:20 or 1:2. For every one girl there are two boys .

Uses of ratio

You might see ratios written on maps to show the scale of the map or use ratios to determine the currency exchange pace if you are going on vacation to another state .
Ratio will be seen as a topic in its own right vitamin a well as appearing within early topics. An exemplar of this might be the area of two shapes being in a given ratio or the angles of a shape being in a given ratio.

When Third Space tutors work through ratio in the one to one online lessons,
visual representations are a really useful way in.

Ratio in Middle School and High School

In middle school, proportion questions will involve write and simplifying ratios, using equivalent ratios, dividing quantities into a given proportion and will begin to look at solving problems involving proportion. At high school, these skills are recapped and the focus will be more on proportion password problems which will require you to conduct trouble solving using your cognition of proportion .

Proportion and ratio

Ratio frequently appears aboard proportion and the two topics are related. Whereas proportion compares the size of different parts of a whole, proportion compares the size of one share with the whole. Given a proportion, we can find a proportion and frailty versa .
Take the case of a box containing 7 counters ; 3 red counters and 4 blue counters :

The ratio of loss counters : amobarbital sodium counters is 3:4 .
For every 3 bolshevik counters there are four bluing counters .
The proportion of bolshevik counters is \frac { 3 } { 7 } and the proportion of blue counters is \frac { 4 } { 7 }
3 out of every 7 counters are red and 4 out of every 7 counters are gloomy .

Direct proportion and inverse proportion

From 7th grade onwards, students learn about direct proportion and inverse proportion. When two things are directly proportional to each other, one can be written as a multiple of the other and therefore they increase at a specify proportion .

How to solve a ratio problem

When looking at a proportion problem, the key pieces of information that you need are what the ratio is, whether you have been given the whole sum or a part of the whole and what you are trying to work out .
If you have been given the solid amount you can follow these steps to answer the motion :

1. Add together the parts of the ratio to find the total number of shares
2. Divide the total amount by the total number of shares
3. Multiply by the number of shares required

If you have been been given a separate of the unharmed you can follow these steps :

1. Identify which part you have been given and how many shares it is worth
2. Use equivalent ratios to find the other parts
3. Use the values you have to answer your problem

How to solve a proportion problem

As we have seen, ratio and proportion are strongly linked. If we are asked to find what proportion something is of a sum, we need to identify the amount in interview and the full measure. We can then write this as a fraction :
\ [ \frac { \text { amount in question } } { \text { total amount } } \ ]
symmetry problems can frequently be solved using scaling. To do this you can follow these steps :

1. Identify the values that you have been given which are proportional to each other
2. Use division to find an equivalent relationship
3. Use multiplication to find the required relationship

Real life ratio problems and proportion problems

Ratio is all around us. Let ’ s look at some examples of where we may see ratio and proportion :

Cooking ratio question

When making yogurt, the proportion of crank yogurt to milk should be 1:9. I want to make 1000ml of yogurt. How much milk should I use ?
here we know the full measure – 1000ml .
The proportion is 1:9 and we want to find the total of milk .

1. Total number of shares = 1 + 9 = 10
2. Value of each share: 1000 ÷ 10 = 100
3. The milk is 9 shares so 9 × 100 = 900

I need to use 900ml of milk .

Maps ratio question

The scale on a map is 1:10000. What distance would 3.5cm on the map represent in substantial life ?
here we know one contribution is 3.5. We can use equivalent ratios to find the other part .

The outdistance in real life would be 35000cm or 350m .

Speed proportion question

I travelled 60 miles in 2 hours. Assuming my accelerate doesn ’ t change, how far will I travel in 3 hours ?
This is a proportion wonder .

1. I travelled 60 miles in 2 hours.
2. Dividing by 2, I travelled 30 miles in one hour
3. Multiplying by 3, I would travel 90 miles in 3 hours

Exam questions feature in all of Third Space Learning’s GCSE online interventions

Middle School ratio questions

Ratio is introduced in center school. Writing and simplifying ratios is explored and the estimate of dividing quantities in a given proportion is introduced using proportion word problems such as the interview below, before being linked with the numerical notation of proportion .
Example Middle School worded question
Richard has a bag of 30 sweets. Richard shares the sweets with a ally. For every 3 sweets Richard eats, he gives his acquaintance 2 sweets. How many sweets do they each corrode ?

Middle School ratio questions

At this degree, proportion questions ask you to write and simplify a proportion, to divide quantities into a given proportion and to solve problems using equivalent ratios. See below the exemplar questions to support test homework .

Ratio questions for 6th grade

1. In Lucy ’ south class there are 12 boys and 18 girls. Write the ratio of girls : boys in its simplest form .

12:30

3:2

18:12

2:3

The motion asks for the ratio girls : boys so girl must be first and male child second. It besides asks for the answer in its simplest phase .

2. Gertie has two grandchild, Jasmine, aged 2, and Holly, aged 4. Gertie divides $ 30 between them in the ratio of their ages. How much do they each contract ?

Jasmine $ 15, Holly $ 15

Jasmine $ 15, Holly $ 7.50

Jasmine $ 10, Holly $ 20

Jasmine $ 2, Holly $ 4
$ 30 is the whole sum .

Gertie divides $ 30 in the proportion 2:4 .

The sum issue of shares is 2 + 4 = 6 .

Each share is worth $ 30 ÷ 6 = $ 5 .

Jasmine gets 2 shares, 2 ten $ 5 = $ 10 .

Holly gets 4 shares, 4 ten $ 5 = $ 20 .

Ratio questions 7th grade

3. The ratio of men : women working in a company is 3:5. What proportion of the employees are women ?

\frac{3}{5}

\frac{3}{8}

\frac{5}{8}

\frac{5}{3}

In this company, the ratio of men : women is 3:5 so for every 3 men there are 5 women .

This means that for every 8 employees, 5 of them are women .

consequently \frac { 5 } { 8 } of the employees are women .

4. The proportion of cups of flour : cups of urine in a pizza dough recipe is 9:4. A pizza restaurant makes a large quantity of dough, using 36 cups of flour. How much urine should they use ?

16 Cups

13 Cups

11 Cups

81 Cups
The proportion of cups of flour : cups of body of water is 9:4. We have been given one part so we can work this out using equivalent ratios .

Ratio questions 8th grade

While the Common Core State Standards does not explicitly include ratio and proportional relationships in the 8th mark, it may pop up on your own curriculums and offers a good opportunity to revisit and extend their cognition of ratio and proportion before they enter high school .

5. The angles in a triangle are in the ratio 3:4:5. Work out the size of each angle .

30^ { \circ }, 40^ { \circ } and 50^ { \circ }

22.5^ { \circ }, 30^ { \circ } and 37.5^ { \circ }

60^ { \circ }, 60^ { \circ } and 60^ { \circ }

45^ { \circ }, 60^ { \circ } and 75^ { \circ }
The angles in a triangle add up to 180 ^ { \circ }. consequently 180 ^ { \circ } is the whole and we need to divide 180 ^ { \circ } in the ratio 3:4:5 .
The full number of shares is 3 + 4 + 5 = 12 .
Each contribution is deserving 180 ÷ 12 = 15 ^ { \circ } .
3 shares is 3 adam 15 = 45 ^ { \circ } .
4 shares is 4 adam 15 = 60 ^ { \circ } .
5 shares is 5 x 15 = 75 ^ { \circ } .

6. paint Pro makes pink paint by mixing red rouge and white paint in the ratio 3:4 .
Colour Co makes pink paint by mixing red paint and white paint in the ratio 5:7 .
Which party uses a higher proportion of red rouge in their mix ?

They are the same

Paint Pro

Colour Co

It is impossible to tell
The proportion of crimson paint for Paint Pro is \frac { 3 } { 7 }
The proportion of bolshevik paint for Colour Co is \frac { 5 } { 12 }
We can compare fractions by putting them over a common denominator using equivalent fractions
\frac { 3 } { 7 } = \frac { 36 } { 84 } \hspace { 3cm } \frac { 5 } { 12 } =\frac { 35 } { 84 }
\frac { 3 } { 7 } is a bigger fraction so paint Pro uses a higher proportion of red rouge .

High school ratio questions

At high gear school, we apply the cognition that we have of ratios to solve different problems. Ratio can be linked with many different topics, for model similar shapes and probability, american samoa well angstrom appearing as problems in their own right .

Ratio high school questions (low difficulty)

7. The students in Ellie ’ randomness class walk of life, bicycle or driveway to school in the ratio 2:1:4. If 8 students walk, how many students are there in Ellie ’ south class all in all ?

56

16

30

28

We have been given one part so we can work this out using equivalent ratios .

The full number of students is 8 + 4 + 16 = 28

8. A bag contains counters. 40 % of the counters are red and the rest are yellow.

Write down the ratio of red counters : scandalmongering counters. Give your answer in the human body 1 : normality .

1:4

4:6

1:1.5

1:6

If 40 % of the counters are bolshevik, 60 % must be yellow and consequently the ratio of red counters : yellow counters is 40:60. Dividing both sides by 40 to get one on the exit gives us

Since the wonder has asked for the ratio in the form 1 : nitrogen, it is fine to have decimals in the proportion .

9. Rosie and Jim contribution some sweets in the proportion 5:7. If Jim gets 12 sweets more than Rosie, exercise out the number of sweets that Rosie gets .

30

5

2.4

72

Jim receives 2 shares more than Rosie, so 2 shares is equal to 12 .
therefore 1 share is equal to 6. Rosie receives 5 shares : 5 × 6 = 30 .

10. Rahim is saving for a new motorcycle which will cost $ 480. Rahim earns $ 1500 per month. Rahim spends his money on bills, food and supernumerary in the ratio 8:3:4. Of the money he spends on extras, he spends 80 % and puts 20 % into his savings bill .

How long will it take Rahim to save for his raw bicycle ?

1 month

6 months

3 months

5 months
Rahim ’ randomness earnings of $ 1500 are divided in the proportion of 8:3:4 .
The total phone number of shares is 8 + 3 + 4 = 15 .
Each partake is worth $ 1500 ÷ 15 = £100 .
Rahim spends 4 shares on extras therefore 4 × $ 100 = $ 400 .
20 % of $ 400 is $ 80 .
The number of months it will take Rahim is $ 480 ÷ $ 80 = 6

Ratio GCSE exam questions higher

11. The proportion of milk chocolates : white chocolates in a box is 5:2. The proportion of milk chocolates : iniquity chocolates in the lapp box is 4:1 .
If I choose one chocolate at random, what is the probability that that chocolate will be a milk chocolate ?

\frac{53}{35}

\frac{9}{12}

\frac{2}{5}

\frac{20}{33}

To find the probability, we need to find the fraction of chocolates that are milk chocolates. We can look at this using equivalent ratios .
To make the ratios comparable, we need to make the number of shares of milk chocolate the lapp in both ratios. Since 20 is the LCM of 4 and 5 we will make them both into 20 parts .

We can now say that milk : flannel : dark is 20:8:5. The proportion of milk chocolates is \frac { 20 } { 33 } so the probability of choosing a milk chocolate is \frac { 20 } { 33 } .

12. In a school the ratio of girls : boys is 2:3 .
25 % of the girls have school dinners .
30 % of the boys have school dinners .
What is the full share of students at the school who have school dinners ?

55\%

28\%

5\%

140\%

In this question you are not given the number of students so it is best to think about it using percentages, starting with 100 % .
100 % in the ratio 2:3 is 40 % :60 % so 40 % of the students are girls and 60 % are boys .
25 % of 40 % is 10 % .
30 % of 60 % is 18 % .
The total share of students who have school dinners is 10 + 18 = 28 % .

13. For the cubelike below, a : barn = 3:1 and a : cytosine = 1:2 .

Find an expression for the book of the cuboid in terms of a .

\frac{2}{3}a^{3}

\frac{1}{3}a^{3}

3a^{3}

6a^{3}

If a : bel = 3:1 then b=\frac { 1 } { 3 } a
If a : hundred = 1:2 then c=2a .

\begin { aligned } \text { bulk of a cubelike } & = \text { distance } \times \text { width } \times \text { stature } \\ & = 2a \times \frac { 1 } { 3 } a \times a\\ & =\frac { 2 } { 3 } a^ { 3 } \end { aligned }

Ratio high school questions (average difficulty)

14. Bill and Ben win some money in their local anesthetic lottery. They share the money in the ratio 3:4. Ben decides to give $ 40 to his sister. The total that Bill and Ben have is now in the proportion 6:7.

Calculate the entire measure of money won by Bill and Ben .

$ 560

$ 70

$ 140

$ 600
initially the ratio was 3:4 sol Bill got $ 3a and Ben got $ 4a. Ben then gave away $ 40 so he had $ ( 4a-40 ) .

The new proportion is 3a:4a-40 and this is equal to the proportion 6:7 .

Since 3a:4a-40 is equivalent to 6:7, 7 lots of 3a must be peer to 6 lots of 4a-40 .
\begin { aligned } \\ 7 \times 3a & = 6 \times ( 4a-40 ) \\\\ 21a & =24a-240\\\\ 3a & =240\\\\ a & =80 \end { aligned }

The initial amounts were 3a:4a. a is 80 so Bill received $ 240 and Ben received $ 320 .

The sum sum won was $ 560 .

15. On a farm the ratio of pigs : goats is 4:1. The ratio of pigs : piglets is 1:6 and the ratio of gots : kids is 1:2 .

What fraction of the animals on the farm are babies ?

\frac{1}{8}

\frac{2}{8}

\frac{86}{105}

\frac{55}{80}

The easiest manner to solve this is to think about fractions .
\\ \frac { 4 } { 5 } of the animals are pigs, \frac { 1 } { 5 } of the animals are goats .
\frac { 1 } { 7 } of the pigs are pornographic pigs, so \frac { 1 } { 7 } of \frac { 4 } { 5 } is \frac { 1 } { 7 } \times \frac { 4 } { 5 } = \frac { 4 } { 35 }
\frac { 6 } { 7 } of the pigs are piglets, sol \frac { 6 } { 7 } of \frac { 4 } { 5 } is \frac { 6 } { 7 } \times \frac { 4 } { 5 } = \frac { 24 } { 35 }
\frac { 1 } { 3 } of the goats are adult goats, so \frac { 1 } { 3 } of \frac { 1 } { 5 } is \frac { 1 } { 3 } \times \frac { 1 } { 5 } = \frac { 1 } { 15 }
\frac { 2 } { 3 } of the goats are kids, so \frac { 2 } { 3 } of \frac { 1 } { 5 } is \frac { 2 } { 3 } \times \frac { 1 } { 5 } = \frac { 2 } { 15 }

The total fraction of baby animals is \frac { 24 } { 35 } + \frac { 2 } { 15 } = \frac { 72 } { 105 } +\frac { 14 } { 105 } = \frac { 86 } { 105 }

Looking for more middle school and high school math questions?

Try these :
Do you have students who need extra support in math?
Give your fourthly and fifth rate students more opportunities to consolidate eruditeness and practice skills through personalized elementary mathematics tutoring with their own dedicated on-line mathematics tutor.

Each student receives differentiated education designed to close their individual eruditeness gaps, and scaffolded learn ensures every student learns at the right field pace. Lessons are aligned with your express ’ s standards and assessments, plus you ’ ll receive regular reports every tone of the direction.

Programs are available for fourthly grade and fifth grade, and you can try 6 lessons absolutely barren .