Fractions, Decimals & Percentages
Look for and use mathematical structure: exploit the relationship between fractions, decimals, and percentages; use factor pairs to simplify multiplication; apply angle facts to find unknowns; use properties of regular polygons systematically
What a learner can do afterwards
- Use the structure 25 × 16 = 25 × 4 × 4 = 100 × 4 = 400 by exploiting factor pairs
- Recognise that 0.75 = 3/4 = 75% and use whichever form is most efficient for the problem
- Use the fact that angles on a straight line sum to 180° as a structural tool to find missing angles
The lesson
A fraction, a decimal, and a percentage can all show the exact same amount. 3/4 of a pizza, 0.75 of a pizza, and 75% of a pizza are the same slice, just written in different clothes. Once you can switch between the three, you pick whichever one makes a problem easiest.
A jacket costs 40 pounds and is 25% off. Instead of working with the percentage, Zara thinks: 25% is the same as 1/4. So the discount is 40 divided by 4, which is 10 pounds.
Multiplying gets easier if you break a number into a factor pair first. 16 is the same as 4 times 4, so 25 times 16 becomes 25 times 4 times 4, which is 100 times 4, which is 400. Look for friendly pairs before you multiply.
Angles on a straight line always add up to 180 degrees. If you know one angle, subtract it from 180 to find the missing one straight away.
Fractions, decimals, and percentages are the same amount in different forms, and factor pairs and angle facts are shortcuts hiding in plain sight.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.