Fractions

Add Fractions — Unlike Denominators

Add 1/4 + 1/6. Find the LCD of 4 and 6, which is 12. Convert each fraction: 1/4 = 3/12 and 1/6 = 2/12. Then add: 3/12 + 2/12 = 5/12.

lcd-for-addition You cannot add fractions with different denominators until they measure the same size pieces. Use the LCD to find equivalent fractions with a common denominator, then add the numerators as usual.

Example

Add 1/4 and 1/6 by rewriting with LCD 12.

highlighted = computed this step

Step 1 — Set up

Set up the fraction expression.

14+16\frac{1}{4} + \frac{1}{6}
Start with the two fractions1/41/6

Step 2 — Find LCD

Find a common denominator: LCD(4, 6) = 12.

LCD(4,6)=12\mathrm{LCD}( 4 , 6 )= \hl{12}
Use common denominator 121/41/6

Step 3 — Convert left fraction

Convert the left fraction by multiplying by 3 over 3.

14×33=312\frac{1}{4} \times \frac{3}{3} = \hlmath{\frac{3}{12}}
Convert 1/4 to 3/123/121/6

Step 4 — Convert right fraction

Convert the right fraction by multiplying by 2 over 2.

16×22=212\frac{1}{6} \times \frac{2}{2} = \hlmath{\frac{2}{12}}
Convert 1/6 to 2/123/122/12

Step 5 — Add numerators

Add the converted numerators: 3 + 2 = 5.

312+212=512\frac{3}{12} + \frac{2}{12} = \hlmath{\frac{5}{12}}
Add shaded parts: 3 + 2 = 53/122/125/123/12 + 2/12 = 5/12

Step 6 — Result

Read the final result.

14+16=512\frac{1}{4} + \frac{1}{6} = \frac{5}{12}
1/4 + 1/6 = 5/123/122/125/123/12 + 2/12 = 5/12