Bridging lesson
Fractions and Decimals
Praksyon at Desimal
Add, subtract, multiply and divide fractions and decimals, and switch between the two forms.
About 25 minutes
Why it matters in Grade 11
Wages, discounts, VAT and unit conversions in Term 1 are all fraction and decimal arithmetic in disguise, and the mean, median and percentiles in Data and Descriptive Statistics need fluent division and decimal comparison.
Needed directly for: Earning Money and Percentages (Term 1, Weeks 1–2), Units and Conversion (Term 1, Weeks 6–9), Data and Descriptive Statistics (Term 2, Week 2)
Later topics that build on these: Sequences in Finance, Surface Area and Volume, Trigonometry of Triangles, Practical Measurement and Cost Estimation, Random Variables, The Normal Distribution, Random Sampling, Compound Interest, Annuities and Cash Flows, Business and Consumer Loans, Hypothesis Testing, Correlation and Line of Best Fit.
Lesson
The idea: a fraction is a division
ExplainThe 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.
Adding and subtracting
ExplainFractions 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 $7.33$.
Multiplying and dividing
Explain- 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).
Worked example: a sari-sari store
ElaborateA 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: $4\times0.375=1.5$. ✓
Comparing fractions and decimals
ExplainConvert everything to decimals (or to a common denominator) before comparing. More digits does not mean a bigger number: $0.65<\frac{2}{3}\approx0.667$.
| Number | As a decimal |
|---|---|
| $\frac{2}{3}$ | $0.667$ |
| $0.65$ | $0.650$ |
| $\frac{5}{8}$ | $0.625$ |
| $0.6$ | $0.600$ |
Common errors to watch for
Evaluate- 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.
Check yourself
Three quick items with instant feedback. Answer, then press Check.
Ready? Retake the Fractions and Decimals placement test (12 items) to confirm the skill.
Retake the test