Fractions and Decimals - Converting between Fractions, Decimals, and Percentages

Understanding the Relationship: Fractions, decimals, and percentages are different ways of showing the same value. Imagine a 'Hundred Square' grid; if 25 squares are shaded, it represents the fraction $\frac{25}{100}$, the decimal $0.25$, and the percentage $25\%$.

Percentages as 'Per Hundred': The word percent means 'for every 100'. Visually, any percentage can be seen as a portion of a whole divided into 100 equal pieces. For example, $7\%$ is simply 7 out of 100 equal parts, written as $\frac{7}{100}$.

Converting Fractions to Decimals: To turn a fraction into a decimal, divide the numerator by the denominator. On a number line, $\frac{1}{2}$ is located exactly at $0.5$ because $1 \div 2 = 0.5$.

Converting Decimals to Percentages: To change a decimal to a percentage, multiply the decimal by $100$ and add the $\%$ symbol. This is visually represented by moving the decimal point two places to the right. For example, $0.85$ becomes $85\%$.

Converting Percentages to Decimals: To change a percentage to a decimal, divide the number by $100$ and remove the $\%$ symbol. This shifts the decimal point two places to the left. For instance, $40\%$ becomes $0.40$ or $0.4$.

Converting Fractions to Percentages: One common method is to find an equivalent fraction with a denominator of $100$. If you have $\frac{4}{5}$, you can multiply both the numerator and denominator by $20$ to get $\frac{80}{100}$, which equals $80\%$.

Simplifying Fractions: When converting decimals or percentages back to fractions, always simplify. If $60\%$ is $\frac{60}{100}$, we can divide both numbers by $20$ to reach the simplest form, $\frac{3}{5}$. Visually, a bar model split into 5 parts with 3 shaded is the same as a bar with 100 parts and 60 shaded.