Question

13Let's find27First write the subtraction with a common denominator.Then subtract.13=----1=27.Х5?

Answer 1

`(1)/(2)-(3)/(7)=`

Fractions that don't have the same denominator are called dissimilar fractions.

In order to subtract dissimilar fractions, we first have to convert them into similar fractions in which they will have the same denominator.

For our fractions to have the same denominators, we need to find their LCM or Least Common Multiple. Let's list down the multiples of 2 and 7.

`\begin{gathered} \text{Multiples of 2: }2,4,6,8,10,12,14,16,\ldots \\ \text{Multiples of 7}\colon7,14,21,28,\ldots \end{gathered}`

Looking at the multiples of 2 and 7, we can see that the least common multiple to both of them is 14.

To make the fractions above have the denominator 14, we shall multiply 7/7 to 1/2 and 2/2 to 3/7.

`\begin{gathered} ((7)/(7)*(1)/(2))-((2)/(2)*(3)/(7)) \\ =(7)/(14)-(6)/(14) \end{gathered}`

Since both fractions now have the same denominator, we can now easily subtract the fractions by just subtracting their numerator only. Copy the denominator.

`=(7)/(14)-(6)/(14)=(1)/(14)`

To complete the boxes in the question, we have:

`(1)/(2)-(3)/(7)=(7)/(14)-(6)/(14)=(1)/(14)`