Ratio

Ratio

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

Example 1: Colon Form

Write the given ratio in colon form. 6 to 8

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,
when writing a ratio answer,
change the ratio in simplist form.

Example 2: Fraction Form

Write the given ratio in fraction form. 15 to 50

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.

So 3/10 is the answer.

Example 3

Write the given ratio in simplist form. 18 to 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.

So 6 is the answer.

Example 4

Write the given ratio in simplist form. 12 min to 32 min

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.

So 3/8 is the answer.

Example 5

Write the given ratio in simplist form. 2 weeks to 6 days

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.

So 7/3 is the answer.