2/3 of ? = 14
- 2 parts = 14, so 1 part = 14 ÷ 2 = 7
- 3 parts = 7 × 3 = 21
- The original amount is 21
Year 9 maths lesson · Fractions
Finding the Original Amount
Work backwards from a fractional amount to find the original whole. Given that a fraction of an unknown equals a value, use division and multiplication to recover the total.
- About 3–6 minutes
- 5 quick questions as you go
- Then about 5 minutes of practice
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Worked examples
2/5 of ? = $22
- 2 parts = $22, so 1 part = $22 ÷ 2 = $11
- 5 parts = $11 × 5 = $55
- The original amount is $55
Jake ate 2/5 of a bag and has 18 sweets left. How many sweets were in the bag?
- Ate 2/5, so 3/5 remain → 3 parts = 18
- 1 part = 18 ÷ 3 = 6
- 5 parts = 6 × 5 = 30
- The bag originally had 30 sweets
Before this lesson
It helps to be comfortable with:
- Fraction of an amount
- Multiplication and division
Lesson transcript
Everything the lesson says, word for word
Two thirds of some unknown number of candies is 14. How many candies are there altogether? We know these 14 candies make up two thirds. Let’s move them into the bar evenly. Now, to find one third, we divide by 2. 14 divided by 2 is 7. One third is 7 candies. To find the whole, we multiply by 3. 7 times 3 is 21. The original amount is 21 candies.
Two fifths of an amount is $22. What’s the original amount? We can see two fifths here, and that equals $22. To find one fifth, we divide by 2. $22 divided by 2 is $11. One fifth is $11. Now multiply by 5 to get the whole. $11 times 5 is $55. The original amount is $55.
After eating two fifths of a bag of sweets, Jake has 18 left. How many were in the bag originally? Jake ate two fifths, so the 18 sweets left must be three fifths. Now we find one fifth. 18 divided by 3 is 6. One fifth is 6 sweets. Finally, multiply by 5 to get the whole. 6 times 5 is 30. The bag originally had 30 sweets.
More Fractions lessons
- Simplifying and Equivalent FractionsSimplify fractions and find equivalent fractions using common factors.
- Mixed Numbers and Improper FractionsConvert between mixed numbers and improper fractions.
- Adding and Subtracting FractionsFind common denominators and add or subtract fractions with confidence.
- Multiplying FractionsMultiply fractions together and multiply fractions by whole numbers.
- Dividing FractionsDivide fractions and divide whole numbers by fractions — multiply by the reciprocal.
- Fractions of an AmountCalculate a fraction of a quantity — a key everyday maths skill.
- Expressing a Quantity as a FractionWrite one quantity as a fraction of another and simplify.
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