Adding Fractions: Same and Different Denominators

Adding fractions involves combining two or more fractions by finding their sum. There are two main types of fractions to add: those with the same denominator and those with different denominators. When adding fractions with the same denominator, we simply add the numerators and keep the denominator the same. For example, 2/4 + 1/4 = 3/4.

On the other hand, when adding fractions with different denominators, we first need to make their denominators equal by finding the Least Common Multiple (LCM) of the denominators. We then simplify the resulting fraction by dividing its numerator and denominator by the greatest common factor until the numerator is smaller than or equal to the denominator. Finally, we check if the resulting fraction is already in its simplest form or if further simplification is needed.

For instance, to add fractions like 3/5 and 4, we first take their LCM as 5 since it is the highest common factor among both denominators. Then, we multiply both numerator and denominator of one fraction by the LCM to make their denominators equal: 3/5 becomes (3 × 5)/(5 × 5) = 15/25, which equals 6/25 when simplified.

Adding fractions with whole numbers involves converting the whole number into a fraction. For example, if we want to add 3/2 + 2, we convert 3/2 to 3/1 and then perform the addition: (3 + 2)/1 = 5/1 = 5. In this case, we keep the original denominator because there is no need to change it.

There are various resources and worksheets available online to practice adding fractions, such as BYJU'S Fraction Addition Worksheet, Happy Numbers resources on adding fractions, and Cuemath's guide on addition of fractions. These materials can help students master the concept and gain confidence in solving problems related to adding fractions.