Understanding Fractions for 12-Year-Old Year 7 Maths Students

What Are Fractions?

Fractions represent parts of a whole. Imagine you have a pizza cut into equal slices. If you eat some slices, the fraction tells you how much pizza you ate compared to the whole pizza.

Parts of a Fraction

• Numerator: The number on top, showing how many parts you have or are focusing on.
• Denominator: The number on the bottom, showing into how many equal parts the whole is divided.

For example, in the fraction 3/8, you have 3 parts out of 8 equal parts.

Types of Fractions

• Proper fractions: Numerator is smaller than the denominator (e.g., 3/4).
• Improper fractions: Numerator is equal to or larger than the denominator (e.g., 7/4).
• Mixed numbers: A whole number combined with a proper fraction (e.g., 1 3/4).

How to Add and Subtract Fractions

To add or subtract fractions, their denominators need to be the same.

1. Find the lowest common denominator (LCD) – the smallest number both denominators divide into.
2. Convert each fraction so that both denominators are the LCD by multiplying numerator and denominator accordingly.
3. Add or subtract the numerators and keep the denominator the same.
4. Simplify the result if possible.

Example

Add 1/4 and 2/6.

1. The denominators are 4 and 6.
2. LCD of 4 and 6 is 12.
3. Convert fractions:
   1/4 = 3/12 (multiply numerator and denominator by 3)
   2/6 = 4/12 (multiply numerator and denominator by 2)
4. Add numerators: 3 + 4 = 7
5. Result: 7/12

The answer is 7/12.

Summary

Fractions show parts of a whole. Understanding numerators and denominators helps you compare and work with fractions. Learning to find common denominators is key to adding and subtracting fractions easily.