Adding and subtracting fractions with unlike denominators means combining or taking away fractions that have different bottom numbers (denominators). To do this correctly, both fractions must first have the same denominator so they represent parts of the same whole.
Always find a common denominator before adding or subtracting fractions. Without it, the fractions do not represent the same size pieces.
The common denominator is a shared multiple of both denominators. The simplest way is to find the least common denominator (LCD), which is the smallest number both denominators divide into evenly.
Example: To add 14 and 16:
When you change the denominator, you must also change the numerator so the fraction keeps the same value. Multiply both numerator and denominator by the same number.
To add fractions with unlike denominators, first find the common denominator, then add the numerators and keep the denominator the same.
When adding fractions, only the numerators change. The denominator stays the same after you make them common.
When subtracting fractions with unlike denominators, follow the same steps as addition: find a common denominator, rewrite the fractions, and then subtract the numerators.
If the numerator in the top fraction is smaller, you may need to borrow or rename mixed numbers to subtract correctly.
Word problems using fractions describe real-world situations. To solve them, identify what operation to use (addition or subtraction), find a common denominator, and simplify your answer if possible.
Problem: Olivia baked a pie. She ate 13 of it, and her friend ate 14. How much of the pie did they eat altogether?
When reading a word problem, look for clue words like “in all” (add) or “how much more” (subtract) to decide which operation to use.
After solving, always check if your fraction can be simplified. Simplify by dividing both numerator and denominator by their greatest common factor (GCF).
A simplified fraction is easier to understand and is the correct final form of your answer.