01. Ratio 2-5

Question 1

LEVEL 3

Simplify 2.3 kg : 700 g : 1.8  kg

Select the correct answer from the list below:

A: 40 g : 70 g : 180 g

B: 12 g : 5 g : 18 g

C: 23 g : 70 g : 18 g

D: 23 g : 7 g : 18 g

CORRECT ANSWER: D: 23 g : 7 g : 18 g

WORKED SOLUTION:

Firstly, we can change the units of the ratio we are given so that they are all in grams,  instead of kilograms,

By multiplication the values in kg by 1000 we get, 2300 g : 700 g : 1800 g

Now we can simplify the ratio by dividing by 100, 23 g : 7 g : 18 g

And that’s the answer, as it cannot be simplified an further.

Question 2

LEVEL 3

Two tennis players have a head to head of five matches won by the first player to twenty-five matches won by the second player.

Write this ratio in its simplest form where the first number in the ratio is the amount of matches the first player has won.

Select the correct answer from the list below:

A: 5:30

B: 1:6

C: 5:25

D: 1:5

CORRECT ANSWER: D: 1:5

WORKED SOLUTION:

Worded questions require you to take out the relevant information and answer the question correctly. The first player has won 5 out of their 30 matches, while the second player has won 25 out of 30 matches. The 30 matches have been calculated by adding the 5 and the 25 matches together.

The question asks that the first number in the ratio is the number of matches player one has won. The ratio is therefore 5:25.

Simplest form means you have to divide it by 5, to get 1:5

Question 3

LEVEL 3

Simplify the following ratio 1000  : 540 : 780

Select the correct answer from the list below:

A: 100 : 27 : 39

B: 50 : 13 : 39

C: 16 : 9 : 13

D: 50 : 27 : 39

CORRECT ANSWER:  D: 50 : 27 : 39

WORKED SOLUTION:

To find the simplest form of the ratio, we will divide by the highest common factor of the three numbers which is 20.

1000\div20=50

540\div20=27

780\div20=39

So the ratio simplifies to 50 : 27 : 39

Question 4

LEVEL 3

The ratio of tomato to cheese that Enzo needs to make pizza is 2:3. He needs 8 parts of tomato to make 1 pizza.

How many parts of cheese does he need to make 1 pizza?

Select the correct answer from the list below:

A: 5

B: 8

C: 12

D: 24

CORRECT ANSWER:       C: 12

WORKED SOLUTION:

We know that 8 = 2 \times 4, so we need to multiply the ratio by 4, to get

8:12.

Hence, Enzo needs 12 parts of cheese to make 1 pizza.

Question 5

LEVEL 3

Shaqil has some green and pink counters in a bag. The ratio of green counters to counters is 3:7.

If Shaqil has 9 green counters, how many pink counters does he have?

Select the correct answer from the list below:

A: 9

B: 12

C: 21

D: 36

CORRECT ANSWER:       B: 12

WORKED SOLUTION:

3 out of 7 counters are green, so 7 - 4 = 3 out of every 7 counters are pink. So for every 3 green counters there are 4 pink counters,

We need to scale up this ratio, so that the left is equal to 9. So we multiply the ratio by 3.

So, Shaqil has 12 pink counters.

Question 6

LEVEL 3

Declan has 3 footballs, 5 rugby balls and 7 tennis balls.

Write the number of footballs as a fraction of the total number of balls Declan has, in its simplest form.

Select the correct answer from the list below:

A: \dfrac{1}{5}

B: \dfrac{1}{3}

C: \dfrac{7}{15}

D: \dfrac{3}{15}

CORRECT ANSWER:       A: \dfrac{1}{5}

WORKED SOLUTION:

There are 3 + 5 + 7 = 15 balls in total.

So there are 3 out of 15 balls that are footballs.

As a fraction, we can write this as

\dfrac{3}{15} which can be simplified to \dfrac{1}{5} by dividing by 3.