Extending Mixing Colours

I am learning to solve difficult ratio problems.

Do not start this lesson unless you have an excellent understanding of Mixing colours.

The tables below show different mixtures for making green paint. green is made from mixing blue and yellow. The greater the proportion of blue, the darker the green.

Mixture A Mixture B Mixture CBlue Yellow Blue Yellow Blue Yellow

2 3 3 6 10 15

2:3 3:6 10:15

To work out which mixture is lightest we can convert the ratios into percentages.

In Mixture ‘A’ 2 parts are blue out of the 5 parts (2 + 3 = 5)

As a fraction that is 52 We know from earlier lessons that is the

same as or 40%. 52

10040

We can also work out the percentage by… 52

= 2 ÷ 5 = 0.4 = 40%

Now let’s work out the percentage for Mixture ‘B’.

Mixture A Mixture B Mixture CBlue Yellow Blue Yellow Blue Yellow

2 3 3 6 10 15

2:3 3:6 10:15

40%

In Mixture ‘B’ 3 parts are blue out of the 9 parts (3 + 6 = 9)

As a fraction that is 93 This is the same as or 33.3%.

31

We can also work out the percentage by… 93

= 3 ÷ 9 = 0.333 = 33.3%

Now let’s work out the percentage for Mixture ‘C’.

Mixture A Mixture B Mixture CBlue Yellow Blue Yellow Blue Yellow

2 3 3 6 10 25

2:3 3:6 10:15

40% 33.3%

In Mixture ‘C’ 10 parts are blue out of the 25 parts (10 + 15 = 25)

As a fraction that is 2510 This is the same as or 40%.

10040

We can also work out the percentage by… 2510

= 10 ÷ 25 = 0.4 = 40%

It’s easy to see now that Mixture ‘B’ would make the lightest green as it has the smallest percentage of blue.

Mixture A Mixture B Mixture CBlue Yellow Blue Yellow Blue Yellow

2 3 3 6 10 25

2:3 3:6 10:15

40% 33.3% 40%

Now let’s complete the percentages row for the table below. Again, we want to find out which mix will make the lightest green.

Mixture A Mixture B Mixture CBlue Yellow Blue Yellow Blue Yellow

7 13 4 6 8 17

7:13 4:6 8:17

% % %

7 + 13 = 20 4 + 6 = 10 8 + 17 = 25

7 ÷ 20 = 0.35 4 ÷ 10 = 0.4 8 ÷ 25 = 0.32

35 40 32

1) Find the total number of parts. 2) Express the amount of blue as a fraction.

3) Convert this fraction to a decimal and then a percentage.

207

104

258

Now try these questions on your own.

Click again when you have worked out all the percentages.

Need some more practise? Try Teacher Tools Fractions, Decimals and Percentages Book Numeracy resources

Complete the percentages row of the table below so that you can find the mix that will make the darkest green. You may use a calculator to help you with the division.

Mixture A Mixture B Mixture CBlue Yellow Blue Yellow Blue Yellow

4 16 6 9 8 17

4:16 6:9 5:15

% % %20 40 25

Which mixture will make the darkest green? Mixture B