Question

Reduce the following ratios in the simplest form:
A) 324:144
B) 186:403

Answer 1

Hint:
Simplest form means the ratio that is not divisible further. So, it means that we need to divide the given numbers till division can't be applied further.

Complete step by step solution:
A) 324:144
First we need to find the HCF of the two numbers so that we can reduce the number to its lowest and simplest form.

Number	Factors
324	1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324.
144	1, 2, 4, 6, 8, 9, 12, 18, 24, 36, 72, 144

Now the highest common factor is 36 .
Divide the ratio with 36. We will get,
\[\dfrac{{324 \div 36}}{{144 \div 36}} = \dfrac{9}{4}\]

Given ratio: 324:144
Simplest form: 9:4

B) 186:403
First we need to find the HCF of the two numbers so that we can reduce the number to its lowest and simplest form.

Number	Factors
186	1,2,3,6,31,62,93,186
403	1,13,31,403

Now the highest common factor is 31.
Divide the ratio with 31. We will get,

\[\dfrac{{186 \div 31}}{{403 \div 31}} = \dfrac{6}{{13}}\]

Given ratio 186:403

Simplest form 6:13

Note:
1) Simplest form of ratio is nothing but dividing both the numbers with their highest common factor.
2) Ratios are observed in numbers representing the same quantity like liquid, solid ,gas or anything but of the same nature.
3) Ratios are helpful in many mathematical operations like percentages, fractions etc.