Study guides › Level 6 · Master

Adding and multiplying fractions

Level 6 · Master · for questions like “2/3 + 1/4 = ?” or “3/5 × 5/6 = ?”

💡 The idea

• Multiplying is the easy one: top × top, bottom × bottom.
• Adding needs the same bottom number (denominator) first, because you can only add pieces of the same size.

🪜 The steps

To multiply: multiply the tops, multiply the bottoms, then simplify.

To add:

1. Find a common bottom. The two bottoms multiplied together always works.
2. Rewrite each fraction with that bottom.
3. Add the tops, keep the bottom, then simplify.

✏️ Worked examples

1. 3/5 × 5/6: (3 × 5)/(5 × 6) = 15/30 = 1/2.

2. 2/3 + 1/4: the common bottom is 12. 2/3 = 8/12 and 1/4 = 3/12. 8/12 + 3/12 = 11/12.

⚠️ Watch out

• Never add the bottoms. 1/2 + 1/3 is not 2/5. It's 3/6 + 2/6 = 5/6.
• Always simplify: divide the top and bottom by the same number.

🎯 Try these

1. 1/2 + 1/3
2. 2/3 × 3/4
3. 3/4 + 1/6

Answers: 1) 5/6 2) 1/2 3) 11/12

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.