Grade 10 Fractions: Short Notes

10 ශ්‍රේණිය · 3 පරිච්ඡේදය · භාග

96%

of Grade 10 term tests include it (52 of 54)

587

marks in past papers (73 questions)

10 min

full lesson with quick checks

🎯 What you'll learn

Add and subtract fractions and mixed numbers using a common denominator
Multiply fractions and divide by a fraction using its reciprocal
Simplify fraction expressions in the correct order
Find a fraction of a quantity and of a remainder
Find the whole when the value of a fraction of it is known

Amma's salary

Amma gets her Rs 60 000 salary. She puts 1/4 in the bank, then spends 2/3 of what is left on the month's groceries. Is that 2/3 of Rs 60 000? No! The words 'of what is left' are where many students lose marks in the term test.

Adding and subtracting

Same denominator: add or subtract the numerators only. 2/7 + 3/7 = 5/7.Different denominators: first rewrite both over a common denominator (use the LCM).2/3 + 1/4 = 8/12 + 3/12 = 11/12

⚠️ Never add the bottoms

O/L examiners keep seeing 1/2 + 1/3 = 2/5. Think: half a roti plus a third of a roti is more than half, but 2/5 is less than half! The denominator only names the size of the pieces. Make the pieces the same size first: 3/6 + 2/6 = 5/6.

Mixed numbers

Turn mixed numbers into improper fractions first.2 1/3 = (2 × 3 + 1)/3 = 7/3Then work as usual:2 1/3 − 1 3/4 = 7/3 − 7/4 = 28/12 − 21/12 = 7/12Give the final answer in its simplest form (as a mixed number if it is more than 1).

Multiplying: 'of' means ×

Multiply numerator × numerator and denominator × denominator. Cancel common factors first to keep numbers small.2/3 × 3/4 = (2 × 3)/(3 × 4) = 6/12 = 1/2'2/3 of 3/4' means exactly the same thing: 2/3 × 3/4.Multiplying by a fraction less than 1 makes a number smaller.

Dividing: flip and multiply

To divide by a fraction, multiply by its reciprocal (turn it upside down).2 1/4 ÷ 3/8 = 9/4 × 8/3 = 72/12 = 6Meaning: there are 6 pieces of size 3/8 in 2 1/4.Only the fraction after the ÷ sign is flipped.

Order of operations

Fractions follow the same order as whole numbers: brackets, then of, then × and ÷, then + and −.1/2 + 1/3 × 3/4= 1/2 + 1/4 (multiply first)= 3/4Adding first, (5/6) × 3/4 = 5/8, is wrong.

✏️ Simplify step by step

Simplify (2 1/2 − 1 1/3) ÷ 7/9.

1Brackets first: 5/2 − 4/3 = 15/6 − 8/6 = 7/6
2Divide by 7/9 by multiplying by 9/7: 7/6 × 9/7
3Cancel the 7s: 9/6 = 3/2
4As a mixed number: 1 1/2

✅ 1 1/2

A fraction of the remainder

Bank takes 1/4 (blue). The remainder is 3/4. Groceries take 2/3 of that remainder (amber): 2/3 × 3/4 = 1/2 of the whole salary. 1/4 is left.

Three steps for 'of the remainder'

1. Remainder = 1 − (part used). Here 1 − 1/4 = 3/4.2. Fraction of the remainder = fraction × remainder: 2/3 × 3/4 = 1/2.3. Now everything is a fraction of the whole, so you can add, compare or find what is left: 1 − 1/4 − 1/2 = 1/4.

✏️ Back to Amma's salary

Salary Rs 60 000. 1/4 goes to the bank and 2/3 of the remainder to groceries. How much is spent on groceries, and how much is left?

1Bank: 1/4 × 60 000 = Rs 15 000
2Remainder: 60 000 − 15 000 = Rs 45 000
3Groceries: 2/3 × 45 000 = Rs 30 000
4Left: 45 000 − 30 000 = Rs 15 000, which is 1/4 of the salary ✓

✅ Rs 30 000 on groceries; Rs 15 000 left

Finding the whole

If you know what a fraction of something is worth, work back to the whole.3/8 of a water tank is 120 litres.1/8 of the tank = 120 ÷ 3 = 40 litresWhole tank = 40 × 8 = 320 litresShortcut: whole = 120 ÷ 3/8 = 120 × 8/3 = 320.

⚠️ Remainder ≠ whole

In 2017, 2018 and 2019 O/L papers, many candidates took a fraction 'of the remainder' as a fraction of the whole. For Amma's salary that gives 2/3 × 60 000 = Rs 40 000 for groceries, which is wrong. Underline the word remainder (or 'what is left') and find the remainder first.

📌 Remember

• + and −: use a common denominator; add the numerators only.• ×: top × top, bottom × bottom; 'of' means ×.• ÷: multiply by the reciprocal of the second fraction.• Fraction of the remainder: find the remainder first, then multiply.• Whole = known amount ÷ its fraction. Check that the parts add up.

🧾 Quick revision sheet

How do you add 2/3 + 1/4?	Common denominator 12: 8/12 + 3/12 = 11/12.
What does 'of' mean with fractions?	Multiply. 2/3 of 3/4 = 2/3 × 3/4 = 1/2.
How do you divide by a fraction?	Multiply by its reciprocal: a ÷ 3/8 = a × 8/3.
Write 2 1/3 as an improper fraction.	(2 × 3 + 1)/3 = 7/3
1/4 is used. What is 2/3 of the remainder, as a fraction of the whole?	Remainder 3/4; 2/3 × 3/4 = 1/2.
3/8 of a tank is 120 L. How big is the tank?	120 ÷ 3/8 = 120 × 8/3 = 320 L.
Order of operations with fractions?	Brackets, of, × and ÷, then + and −.