To add dissimilar fractions (fractions with different denominators), follow these steps:
- Find the Least Common Denominator (LCD) : Determine the least common multiple (LCM) of the denominators. This LCD will be the common denominator for both fractions.
- Convert to Equivalent Fractions : Rewrite each fraction as an equivalent fraction with the LCD as the new denominator. To do this, divide the LCD by the original denominator and multiply the result by the numerator. This gives the new numerator.
- Add the Numerators : Once the fractions have the same denominator, add their numerators together and keep the LCD as the denominator.
- Simplify the Result : If possible, reduce the resulting fraction to its simplest form by dividing the numerator and denominator by their greatest common factor (GCF). If the fraction is improper (numerator larger than denominator), convert it to a mixed number.
Example:
- Add 23+35\frac{2}{3}+\frac{3}{5}32+53
- LCD of 3 and 5 is 15.
- Convert: 23=1015\frac{2}{3}=\frac{10}{15}32=1510, 35=915\frac{3}{5}=\frac{9}{15}53=159
- Add: 1015+915=1915\frac{10}{15}+\frac{9}{15}=\frac{19}{15}1510+159=1519
- Simplify: 1915=1415\frac{19}{15}=1\frac{4}{15}1519=1154 (mixed number form)
This process ensures you can add any two fractions with unlike denominators
