Fractions and Decimals

The fraction bar means divide. $\frac{3}{8}$ is $3\div8=0.375$. A decimal is a fraction whose denominator is a power of ten: $0.75=\frac{75}{100}=\frac{3}{4}$. Either form can be used; choose the one that makes the next step easier.

Fractions can only be added when the pieces are the same size. Rewrite with a common denominator first, then add the numerators only.

• $\frac{1}{2}+\frac{1}{4}=\frac{2}{4}+\frac{1}{4}=\frac{3}{4}$
• $\frac{5}{6}-\frac{3}{4}=\frac{10}{12}-\frac{9}{12}=\frac{1}{12}$
• Decimals: line up the decimal points. $7.25+0.80=8.05$, not $7.33$.

• Multiply straight across: $\frac{2}{3}\times\frac{3}{5}=\frac{6}{15}=\frac{2}{5}$.
• Mixed numbers first become improper fractions: $2\tfrac{1}{2}\times4=\frac{5}{2}\times4=10$.
• To divide, multiply by the reciprocal of the divisor: $\frac{3}{4}\div\frac{1}{2}=\frac{3}{4}\times\frac{2}{1}=\frac{3}{2}$.
• Decimals: multiply as whole numbers, then count the decimal places. $0.2\times0.4=0.08$ (two places).

A 1.5 kg pack of sugar is repacked into $\frac{3}{8}$ kg bags. How many bags? We need how many $\frac{3}{8}$ fit into $1.5$, so divide: $1.5\div\frac{3}{8}=\frac{3}{2}\times\frac{8}{3}=4$ bags. Check: $4\times0.375=1.5$. ✓

Convert everything to decimals (or to a common denominator) before comparing. More digits does not mean a bigger number: $0.65<\frac{2}{3}\approx0.667$.

• Adding numerators and denominators: $\frac{1}{2}+\frac{1}{4}\ne\frac{2}{6}$.
• Turning $0.75$ into $\frac{75}{10}$: two decimal places means hundredths.
• Dividing the denominator by the numerator when converting ($8\div3$ instead of $3\div8$).
• Multiplying only the whole part of a mixed number.