Adding and Subtracting Fractions

Study Notes

Adding and Subtracting Fractions

Like Denominators

When adding or subtracting fractions with the same denominator, simply add or subtract the numerators and keep the same denominator.
Example: 1/4 + 2/4 = 3/4, 3/6 - 2/6 = 1/6

Unlike Denominators

When adding or subtracting fractions with different denominators, find the least common multiple (LCM) of the two denominators and convert both fractions to have the LCM as the denominator.
Example: 1/4 + 1/6 =?, find the LCM of 4 and 6, which is 12. Convert both fractions: 1/4 = 3/12, 1/6 = 2/12, then add: 3/12 + 2/12 = 5/12

Mixed Numbers

A mixed number is a combination of a whole number and a fraction.
To add or subtract mixed numbers, follow these steps:
1. Convert the mixed numbers to improper fractions.
2. Add or subtract the improper fractions.
3. Convert the result back to a mixed number if necessary.
Example: 2 1/4 + 1 3/4 =?, convert to improper fractions: 9/4 + 7/4 = 16/4, convert back to a mixed number: 4 0/4 = 4

Improper Fractions

An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
To convert an improper fraction to a mixed number, divide the numerator by the denominator and find the remainder.
Example: 7/4 =?, divide 7 by 4, quotient is 1, remainder is 3, so the mixed number is 1 3/4
To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator.
Example: 2 1/4 =?, multiply 2 by 4 and add 1, result is 9/4

Description

Learn how to add and subtract fractions with like and unlike denominators, and how to work with mixed numbers and improper fractions. Understand the steps to follow when converting between different forms of fractions.