Understanding how percentages, fractions, and decimals work together is super important for Year 7 math. These three ideas are connected, and being able to switch between them easily is a great skill to have!

The Basics

1. Fractions show parts of a whole. They are written with one number on top (the numerator) and another number on the bottom (the denominator). For example, the fraction $\frac{3}{4}$ means three parts out of four.

2. Decimals are another way to show fractions. For example, the fraction $\frac{1}{2}$ can be written as $0.5$.

3. Percentages tell us how many parts there are out of 100. So, $\frac{25}{100}$ can be written as $25\%$.

Converting Between Them

• From Fraction to Decimal: To change a fraction into a decimal, divide the top number by the bottom number. For example, to change $\frac{3}{4}$ into a decimal, do $3 \div 4 = 0.75$.

• From Decimal to Percentage: To change a decimal into a percentage, multiply it by 100. So, to convert $0.75$ into a percentage: $0.75 \times 100 = 75\%$.

• From Percentage to Fraction: To change a percentage into a fraction, put the number over 100 and simplify it. For example, to change $60\%$ into a fraction: $\frac{60}{100} = \frac{3}{5}$ after simplifying.

Quick Reference Chart

| Type | Example | Conversion | |-------------|-------------------|-----------------------------| | Fraction | $\frac{1}{4}$ | $0.25$, $25\%$ | | Decimal | $0.6$ | $\frac{3}{5}$, $60\%$ | | Percentage | $80\%$ | $0.8$, $\frac{4}{5}$ |

Practice Makes Perfect

To get really good at these conversions, practice is important! Try changing $50\%$, $0.2$, and $\frac{2}{3}$ into the other types. Before long, you’ll be doing it without thinking! Remember, the more you practice, the easier it gets!