# Ratio

How to write a ratio (colon form, fraction form, with unit): 5 examples and their solutions.

## Example 1

### Solution

4 to 6 in colon form is 4 : 6.

4 and 6 have the common factor 2,
which is greater than 1.

Then divide both 4 and 6 by 2.
4/2 = 2
6/2 = 3

So 4 : 6 = 2 : 3.

2 and 3 only have the common factor 1.
So 2 : 3 is the simplest form.

## Example 2

### Solution

4 to 6 in colon form is 4/6.

4 and 6 have the common factor 2,
which is greater than 1.

Then divide both 4 and 6 by 2.
4/2 = 2
6/2 = 3

So 4/6 = 2/3.

2 and 3 only have the common factor 1.
So 2/3 is the simplest form.

## Example 3

### Solution

It says to write the ratio in simplist form.
Then write the ratio in fraction form:
the fraction form is the default.

So the ratio is 35/50.

35 and 50 have the common factor 5,
which is greater than 1.

Then divide both 35 and 50 by 5.
35/5 = 7
50/5 = 10

So 35/50 = 7/10.

7 and 10 only have the common factor 1.
So 7/10 is the simplest form.

## Example 4

### Solution

The ratio is (9 min)/(15 min).

Cancel the minute units.

9 and 15 have the common factor 3,
which is greater than 1.

Then divide both 9 and 15 by 3.
9/3 = 3
15/3 = 5

So 9/15 = 3/5.

3 and 5 only have the common factor 1.
So 3/5 is the simplest form.

## Example 5

### Solution

2 weeks and 6 days have different units.
To make the units the same,
change 2 weeks to days.

Change Unit (Measure)

First write (2 weeks).

To remove the unit [weeks],
you need [week] in the denominator.
And you need the unit [days] in the numerator.

1 week = 7 days

So multiply [7 days]/[1 week].

Cancel the [week(s)] units.

Then (2)⋅(7 days)/1 = 14 days.

So 2 weeks is 14 days.

It says write the ratio 2 weeks to 6 days.
2 weeks is 14 days.
So write the ratio 14 days to 6 days:
(14 days)/(6 days).

Cancel the [days] units.

14 and 6 have the common factor 2,
which is greater than 1.

Then divide both 14 and 6 by 2.
14/2 = 7
6/2 = 3

So 14/6 = 7/3.

7 and 3 only have the common factor 1.
So 7/3 is the simplest form.