Equivalent representations
Keep the exact value while changing the form
- Equivalent fractions Multiply or divide both parts by the same non-zero number
- Decimal place value The final decimal place gives the power-of-ten denominator before simplifying
- Mixed numbers Multiply the whole part by the denominator and add the numerator to get an improper fraction
- Percentage Percent means per hundred \(\displaystyle p\%=\frac{p}{100}\)
Common mistakes
Scaling only one part
✕\(\displaystyle \frac{3}{4}=\frac{6}{4}\)✓\(\displaystyle \frac{3}{4}=\frac{6}{8}\)
Scaling only the numerator doubles the value rather than preserving itWrong place-value denominator
✕\(\displaystyle 0.09=\frac{9}{10}\)✓\(\displaystyle 0.09=\frac{9}{100}\)
The nine is in the hundredths placeLosing the percent unit
✕\(\displaystyle 0.35=35\)✓\(\displaystyle 0.35=35\%\)
Thirty-five hundredths is not thirty-five wholesDifficulty levels
introConvert familiar positive fractions, decimals and percentages
standardInclude exact terminating decimals with more places and values above one
challengeTrack larger counts while preserving the exact value and requested form
examSelect exact equivalent forms from the retained conversion bank
Questions about this topic
Does every fraction have a terminating decimal?+
No. This section practises exact terminating conversions. Some fractions have recurring decimals, which need repeating notation rather than a rounded replacement
Can a value greater than one be a fraction?+
Yes. An improper fraction can count more parts than one whole contains
\[\frac{13}{5}=2\frac{3}{5}\]
Can I use a calculator?+
No. This topic is practised without a calculator
Which year level and chapter is this?+
Year 7 Mathematics, chapter 2: Rational numbers and calculations
In this chapter
Equivalent fractions, decimals and percentagesCompare and order integersLocate signed fractions and decimalsAdd and subtract integersRound decimals and check estimatesMultiply and divide positive fractions and decimalsCalculate with positive fractions and decimalsPercentages of quantities and percentage comparisonsRatios, equivalent groups and sharingModel practical problems with rational numbers