Question

How do you simplify 28/56

Answer 1

28/56

a) You notice you have even numbers, so you will simlify both by 2:

28:2 = 14

56:2 = 28

b) They are again even numbers. Divide by 2:

14:2 = 7

28:2 = 14

c) 7 is a prime number, you can only simplify it by 1 and by 7:

7:7 = 1

14:7 = 2

In conclusion, you can simplify 28/56 by 1 x 2 x 2 x 7 and you will obtain the following simplified fraction: 1/2

Answer 2

In any fraction, you can simplify a multiplicative factor that appears in both numerator and denominator.

Be sure that it is a multiplicative factor!! For example, you can't simplify 2 in the following fraction

`\cfrac{x+2}{y+2} \\eq \cfrac{x}{y}`

because in this case, 2 is an additive term. But in this other example, you can simplify all multiplicative factor appearing in both numerator and denominator:

`\cfrac{a\cdot b\cdot c\cdot d\cdot e}{c\cdot d\cdot e\cdot f\cdot g} = \cfrac{a\cdot b}{f\cdot g}`

Because c, d and e appeared in both numerator and denominator.

So, the idea is to find common factors of 28 and 56, so that we can cancel them out. The easiest way to find factors of a number is its prime factorization:

`28 = 2^2 \cdot 7,\quad 56 = 2^3 \cdot 7`

So, the fraction can be written as

`\cfrac{28}{56} = \cfrac{2^2 \cdot 7}{2^3 \cdot 7} = \cfrac{2\cdot 2 \cdot 7}{2\cdot 2 \cdot 2 \cdot 7} = \cfrac{1}{2}`

Since 1 and 2 have no common factors, the fraction is fully simplified.