# Ratio

How to write the ratio in simplist form (colon form, fraction form): examples and their solutions.

## Example 1: Colon Form

The colon form of 6 to 8 is [6 : 8].

6 : 8 can be simplified
by dividing both numbers by 2:
6/2 : 8/2 = 3 : 4.

There's no other way to make [3 : 4] simpler.
(Both of the numbers should be integers.)

So [3 : 4] is the answer.

Just like this solution,
change the ratio in simplist form.

## Example 2: Fraction Form

The fraction form of 15 to 50 is 15/50.

Change 15/50 in simplist form.

Divide both of the numerator and the denominator
by 5:
(15 ÷ 5)/(50 ÷ 5) = 3/10.

There's no other way to make 3/10 simpler.

## Example 3

When there's no other direction,
write the ratio in fraction form.

18 to 3 is 18/3.

Change 18/3 in simplist form
by dividing both of the numerator and the denominator
by 3:
(18 ÷ 3)/(3 ÷ 3) = 6/1 = 6.

It's obvious that 6 is the simplist form.

## Example 4

If there's no other direction,
the ratio's numbers should have the same unit.

So first write the given numbers:
12 min, 32 min.

Then use the numbers to write the ratio:
12/32.

Change 12/32 in simplist form
by dividing both of the numerator and the denominator
by 4:
(12 ÷ 4)/(32 ÷ 4) = 3/8.

There's no other way to make 3/8 simpler.

## Example 5

2 weeks and 6 days have different units.

But the ratio's numbers should have the same unit.

So change 2 weeks unit, [week], to [days]:
(2 weeks) × (7 days)/(1 week) = 14 days.

By doing this, the [week] units are cancelled.

So the given numbers are 14 days and 6 days.

Use 14 days and 6 days to write the ratio:
14/6.

Change 14/6 in simplist form
by dividing both of the numerator and the denominator
by 2:
(14 ÷ 2)/(6 ÷ 2) = 7/3.

There's no other way to make 7/3 simpler.