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
1 · Read
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.
More to read
Writing fractions as decimals review
Fractions and decimals are two ways to write the same amount. The fraction 3/4 means 3 out of 4 equal parts, and as a decimal that is 0.75. You can see it with money: 3 quarters of a pound are 75 pence. To turn a fraction into a decimal, think of the fraction as division. Work out 3 divided by 4 and you get 0.75. Tenths and hundredths are the easiest: 7/10 is 0.7 and 23/100 is 0.23.
Writing decimals as fractions review
Decimals can be turned back into fractions. The decimal 0.6 means 6 tenths, so it equals 6/10, which simplifies to 3/5. Say the decimal out loud and the fraction appears: 0.25 is 25 hundredths, or 25/100, which is 1/4. Always finish by simplifying when you can. Divide the top and bottom by the same number until nothing divides both. 0.75 is 75/100, and dividing top and bottom by 25 gives 3/4.
Converting between percents, fractions, & decimals
Percent means out of 100, so 75% is 75 out of 100. That is the fraction 75/100, which simplifies to 3/4, and the decimal 0.75. The three forms 75%, 3/4, and 0.75 all name the same amount. Switch between forms to suit the problem. Use 50% when halving a price, 1/2 when sharing a pizza, and 0.5 when typing into a calculator.
Converting decimals and percents review
Decimals and percents swap places easily. To change a decimal to a percent, multiply by 100: 0.4 becomes 40%. To change a percent to a decimal, divide by 100: 60% becomes 0.6. The digits stay the same and only shift place. Common pairs are worth knowing by heart. 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, and 3/4 = 0.75 = 75%. Knowing these by heart speeds up every problem that mixes fractions, decimals, and percents.
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2 · Watch
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Where it sits
Learn first
Optional connections
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
18 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.