Mastering Fractions: Learn Key Operations

Understanding Fractions

Every fraction has two parts: the numerator (top number) and the denominator (bottom number). Think of fractions like pieces of a cake - the denominator tells you how many pieces the cake is cut into, whilst the numerator shows how many pieces you actually have.

There are three main types you'll encounter: proper fractions $like 3/4$, improper fractions $like 4/3$, and mixed numbers $like 2 3/4$. Converting between them is dead simple - just divide the top by the bottom for the whole number, and the remainder becomes your new fraction.

When adding or subtracting fractions, you need a common denominator first. Multiply both fractions to get the same bottom number, then add or subtract the tops. For example, 3/5 + 7/11 becomes 33/55 + 35/55 = 68/55.

Top Tip: Always simplify your final answer unless you're told not to!

Dividing fractions is actually easier than it looks - just flip the second fraction and multiply instead. So 15/20 ÷ 5/10 becomes 15/20 × 10/5. Then multiply straight across: tops with tops, bottoms with bottoms.

Fractions of Amounts

Finding fractions of amounts is something you'll use constantly in real life - from calculating tips to working out sale prices. The trick is surprisingly straightforward once you get the hang of it.

Start by dividing the amount by the denominator. For example, to find 1/2 of 6, you divide 6 by 2 to get 3. Job done! But when the numerator isn't 1, you need an extra step.

For trickier examples like 2/3 of 6, first divide 6 by 3 (which gives you 2), then multiply that answer by 2 to get 4. The key is remembering that two-step process: divide by the bottom number, then multiply by the top number.

Remember: Always check if the numerator is something other than 1 - that's when you need to multiply by it at the end!