Ratios

A ratio compares values.

A ratio says how much of 1 thing there is compared to another thing.

ratio 3:1
There are three bluish squares to 1 yellow square

Ratios can be shown in different ways:

Use the ":" to separate the values: 3 : ane
Or we can utilise the word "to": iii to 1
Or write information technology like a fraction: three 1

A ratio tin be scaled upwards:

ratio 3:1 is also 6:2
Here the ratio is too three blue squares to 1 xanthous square,
fifty-fifty though there are more squares.

Effort it Yourself

images/ratio-slider.js

Using Ratios

The pull a fast one on with ratios is to always multiply or split up the numbers by the aforementioned value.

Example:

4 : v is the aforementioned as four×ii : 5×two = 8 : ten

ratio 4:5 times 2 is 8:10

Recipes

Example: A Recipe for pancakes uses iii 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 eight cups of milk.

The ratio is still the same, and then the pancakes should be merely as yummy.

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

The examples so far accept been "part-to-part" (comparing ane office to another part).

Simply a ratio tin besides show a part compared to the whole lot.

Example: There are v pups, 2 are boys, and iii are girls

five pups

Part-to-Office:

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

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

Role-to-Whole:

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

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

Try It Yourself

images/ratio.js

Scaling

We can apply ratios to calibration drawings up or down (by multiplying or dividing).

The superlative to width ratio of the Indian Flag is 2:iii

So for every 2 (inches, meters, whatever) of height
at that place should be 3 of width.

 indian flag

If nosotros made the flag xx inches loftier, it should be thirty inches wide.

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

Example: To depict a horse at one/10th normal size, multiply all sizes by i/10th

scale horse

This equus caballus in existent life is 1500 mm loftier and 2000 mm long, so the ratio of its acme to length is

1500 : 2000

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

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

Nosotros can brand whatsoever reduction/enlargement we want that manner.

Big Foot?

Foot Allie measured her human foot and it was 21cm long, then she measured her Mother'due south foot, and information technology was 24cm long.

"I must accept big anxiety, my foot is nearly equally long as my Mom's!"

Only and then she idea to measure out heights, and institute she is 133cm tall, and her Mom is 152cm tall.

In a table this is:

Allie Mom
Length of Human foot: 21cm 24cm
Height: 133cm 152cm

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

Allie: 21 133 Mom: 24 152

We tin can simplify those fractions like this:

Allie: 21/7 133/vii Mom: 24/8 152/8

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

Allie: 3 19 Mom: three 19

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

"Then my foot is but as big every bit it should be for my superlative, and is not really as well big."

Do

You can practice your ratio skills by Making Some Chocolate Crispies

1709, 1710, 1711, 1712, 1713, 1714, 1715, 1716, 3603, 3604