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Ratio, Fraction and Percentage Bars

How fractions, ratios and percentages are the same idea in different clothes, all solvable with units.

⏱ 5 min · 🎯 4 things to master

Here is a secret that makes the second half of the PSLE paper much easier: fractions, ratios and percentages are the same idea wearing different clothes. "Three-fifths are girls", "girls to boys is 3 to 2", and "60% are girls" all describe the same class. Once you turn any of them into bar-model units, you solve them the exact same way — find one unit.

Parents: let your child convert between the three forms before revealing. The "Method tip" boxes name the move a marker rewards — converting to units, then solving once.

By the end you'll be able to switch between fraction, ratio and percentage and solve with units. Let's connect them.

Three names, one bar

Take a class where three-fifths are girls. The bar is 5 equal units; 3 are girls and 2 are boys. As a that is girls : boys = 3 : 2. As a , each unit is one-fifth = 20%, so girls are 3 × 20% = 60%. Same bar, three names.

🤔 Predict first: Three-fifths of a class are girls. What is the ratio of girls to boys?

Turn it into units and solve

Because all three forms become units, every problem is a find-one-unit problem. Suppose 60% of a class are girls and there are 8 more girls than boys. As units, girls : boys = 3 : 2, so the difference is 1 unit = 8 children. Step one unit until the gap between the bars is 8.

60% girls — find the class size

Predict first: 60% girls and 40% boys is the same as which ratio?

With 1 unit = 8, the difference of 1 unit is 8 (correct), girls are 3 × 8 = 24, boys are 2 × 8 = 16, and the whole class is 5 × 8 = 40.

The whole is 100%

For percentage problems, remember the whole is always 100%. A 20% discount leaves 80%; a 15% increase makes 115%. If 115% is $920, then 1% = $8 and the original (100%) is $800. The bar for the whole is 100 units — set the right number of them equal to the amount you know.

🤔 Predict first: A price went up by 15% to $920. The $920 represents what percentage of the original price?

Watch out — these are easily mixed up

Quick recap

🎯 Mastery check

Answer all 6 — your progress is saved on this device.

  1. Two-fifths of a bag of sweets are red. What percentage are red?

  2. 75% of a group are adults. What is the ratio of adults to children?

  3. Girls to boys is 3 : 2 and there are 8 more girls than boys. How many children in total?

  4. A $200 item has a 20% discount. What percentage of the price do you pay, and how much?

  5. After a 15% increase, a price is $920. What was the original price?

  6. Why is it useful to turn a percentage problem into ratio units?