Ratios

A ratio shows the relative sizes of two or more values.

There are 3 blue squares to 1 yellow square

Ratios can be shown in different ways:

Example

Example: if there is 1 boy and 3 girls you could write the ratio as: 1:3 (for every one boy there are 3 girls) 1/4 are boys and 3/4 are girls 0.25 are boys (by dividing 1 by 4) 25% are boys (0.25 as a percentage)

Using Ratios

The trick with ratios is to always multiply the numbers in the ratio by the same value.

Scaling

The ratio of the Indian Flag is 2:3, that means that for every 2 (inches, centimeters, whatever) of height there should be 3 of width. If you made this flag 20 cm high, it should be 30 cm wide. If you made this flag 40 inches high, it should be 60 inches wide (that is still in the ratio 2:3)

If you want to draw a horse at 1/10th the normal size, you need to multiply all sizes by 1/10th.
	Example: this horse in real life is 1500mm high and 2000 mm long, so the ratio of its height to length is 1500 : 2000 What is that ratio when you draw it?
Answer: 1500 : 2000 = 1500×1/10 : 2000×1/10 = 150 : 200

You can pick any reduction/enlargement you want that way.

Big Foot?

Allie measured her foot and it was 21cm long, and then she measured her Mother's foot, and it was 24cm long.

"I must have big feet, my foot is nearly as long as my Mom's!"

But then she thought to measure how tall she and her Mom were, and found she was 134cm tall, and her Mom was 153cm.

In a table this was:

To work out the Ratio she simply divided her Mom's measurements by hers:

"Oh!" she said, "the Ratios are nearly the same"

"So my foot is only as big as it should be for my height, and is not really too big."

A "Concrete" Example

A typical mix of cement, sand and stones is written as a ratio, such as 1:2:6. You can multiply all values by the same amount and you will still have the same ratio. 10:20:60 is the same as 1:2:6 So if you used 10 buckets of cement, you should use 20 of sand and 60 of stones.

Example: if you have just put 12 buckets of stones into a wheelbarrow, how much cement and how much sand should you add to make a 1:2:6 mix?

Ley us lay it out in a table to make it clearer:

You can see that you have 12 buckets of stones but the ratio says 6.

That is OK, you simply have twice as many stones as the number in the ratio ... so you need twice as much of everything to keep the ratio.

Here is the solution:

And the ratio 2:4:12 is the same as 1:2:6 (because they show the same relative sizes)

Why are they the same ratio? In the 1:2:6 ratio there is 3 times more Stones as Sand (6 vs 2), and in the 2:4:12 ratio there is also 3 times more Stones as Sand (12 vs 4) ... similarly there is twice as much Sand as Cement in both ratios.

That is the good thing about ratios. You can make the amounts bigger or smaller and so long as the relative sizes are the same then the ratio is the same.

So the answer is: add 2 buckets of Cement and 4 buckets of Sand. (You will also need water and a lot of stirring....)

Practice

You can practice your ratio skills by Making Some Chocolate Crispies