Ratios and Proportional Relationships
Ratio and proportion
Write and simplify ratios, and use them to share amounts and scale recipes.
A ratio compares two amounts by how many times, not by how much more. Saying the red and blue beads are in the ratio 2:3 does not mean there are 2 red and 3 blue — it means that for every 2 red there are 3 blue, so 4 and 6 fit it, and so do 20 and 30. That is why a ratio can be simplified the way a fraction can: dividing both numbers by the same thing describes the very same mix in smaller words.
Count the shares, not the total
The ratio 3:5 has 3 + 5 = 8 shares in it, so the first amount is 3 parts out of 8 — not 3 out of 5. Finding what one share is worth is the step that turns almost every ratio question into a short multiplication.
Worked example
Share 48 marbles between two friends in the ratio 5:3.
Add the parts of the ratio: 5 + 3 = 8 shares altogether.
The 48 is being split into equal shares, and the ratio says how many of them each friend is owed.
The order of the two numbers is part of the answer
3:5 and 5:3 describe different mixes, so write the numbers in the order the question names the two things. If it asks for the ratio of blue to red, the blue number goes first — even when the red one is larger.
Try it together
Now one together. A paint mix uses 9 tins of white to 6 tins of blue.
Simplify the ratio before doing anything else. Everything after that is easier with small numbers.
1.Write the ratio of white to blue in its simplest form. Write it like 4:5.
Have a go
Have a go on your own: share 63 stickers between two children in the ratio 4:5. How many does the first child get?
Hint: Count how many shares there are altogether first.
Ready to practice?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.