Ratios can be shown in different ways:

Use the ":" to separate the values:3 : 1
Or we can use the word "to":3 to 1
Or write it like a fraction:31

A ratio can be scaled up:

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Try it Yourself


Example:

4 : 5 is the same as 4×2 : 5×2 = 8 : 10

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Example: A Recipe for pancakes uses 3 cups of flour and 2 cups of milk.

So the ratio of flour to milk is 3 : 2

To make pancakes for a LOT of people we might need 4 times the quantity, so we multiply the numbers by 4:

3×4 : 2×4 = 12 : 8

In other words, 12 cups of flour and 8 cups of milk.

The ratio is still the same, so the pancakes should be just as yummy.


"Part-to-Part" and "Part-to-Whole" Ratios

The examples so far have been "part-to-part" (comparing one part to another part).

But a ratio can also show a part compared to the whole lot.


Example: There are 5 pups, 2 are boys, and 3 are girls

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Part-to-Part:

The ratio of boys to girls is 2:3 or 2/3

The ratio of girls to boys is 3:2 or 3/2

Part-to-Whole:

The ratio of boys to all pups is 2:5 or 2/5

The ratio of girls to all pups is 3:5 or 3/5


The height to width ratio of the Indian Flag is 2:3

So for every 2 (inches, meters, whatever) of heightthere should be 3 of width.

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If we made the flag 20 inches high, it should be 30 inches wide.

If we made the flag 40 cm high, it should be 60 cm wide (which is still in the ratio 2:3)


Example: To draw a horse at 1/10th normal size, multiply all sizes by 1/10th

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This horse in real life is 1500 mm high and 2000 mm long, so the ratio of its height to length is

1500 : 2000

What is that ratio when we draw it at 1/10th normal size?

1500 : 2000= 1500×1/10 : 2000×1/10
= 150 : 200

We can make any reduction/enlargement we want that way.

Big Foot?

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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 heights, and found she is 133cm tall, and her Mom is 152cm tall.

In a table this is:


The "foot-to-height" ratio in fraction style is:

Allie:21133Mom:24152

We can simplify those fractions like this:

Allie:21/7133/7Mom:24/8152/8

And we get this (please check that the calcs are correct):

Allie:319Mom:319

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

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