## Topic outline

• ### Simplifying Fractions / Reducing Fractions to Simplest Form

• Simplifying Fractions

Fraction is said to be in the simplest (or lowest) form if its numerator and denominator have no common factor except 1.

To simplify a fraction, we can divide the top and bottom of the given number by the highest common factor (HCF) of the numerator and denominator.

Let’s consider fraction 15/75.

Find HCF of 15 and 75.

 5 15,  75 3 3,   15 1,    5

HCF of 15 and 75 = 5 x 3 = 15

Now, divide the top and bottom of the given number by 15.

Therefore, 1/5 fraction is in lowest term.

Example 1: Write the simplest form of 16/72.

Solution: HCF of 16 and 72.

 2 16,  72 2 8,   36 2 4,   18 2,    9

HCF of 16 and 72 = 2 x 2 x 2 = 8

Now, divide the top and bottom of the given number by 8.

Therefore, 2/9 fraction is in lowest term.

Example 2: Write the simplest form of 17/51.

Solution: HCF of 17 and 51.

 17 17,  51 1,   3

HCF of 17 and 51 = 17

Now, divide the top and bottom of the given number by 17.

Therefore, 1/3 fraction is in lowest term.

Example 3: Write the simplest form of 42/28.

Solution: HCF of 42 and 28.

 2 42,  28 7 21,  14 3,    2

HCF of 42 and 28 = 2 x 7 = 14

Now, divide the top and bottom of the given number by 14.

Therefore, 3/2 fraction is in lowest term.

Example 4: Reduce the fraction 48/60 to simplest form.

Solution: HCF of 48 and 60.

 2 48,  60 2 24,  30 3 12,  15 4,   5

HCF of 48 and 60 = 2 x 2 x 3 = 12

Now, divide the top and bottom of the given number by 12.

Therefore, 4/5 fraction is in lowest term.

Example 5: Is 49/64 in its simplest form?

Solution: HCF of 49 and 64.

 1 49,  64 49,  64

HCF of 49 and 64 = 1

Fraction is in the simplest (or lowest) form because numerator and denominator of the given number have no common factor except 1.

• 