Fractions, Decimals and Percentages
Primary 5 · Mathematics
Fractions, Decimals and Percentages
Lesson 2 of 3
14 min
Let's begin
Keza's family fills one jerrycan with water at the tap. Before school they use 14 of it. In the evening they use another 12 of it.
Keza wants to know how much water the family used altogether. She writes 14 + 12 in her book and then stops, because the two fractions do not match at all. One is built from quarters and the other from halves.
By the end of this lesson you will finish Keza's sum without even reaching for a pencil.
Picture a chapati cut into 7 equal pieces. You take 2 pieces. Then you take 3 more pieces. How many pieces do you have?
27 + 37 = 57
The pieces never changed size, so the bottom number stays 7. Only the number of pieces changed, so you add the top numbers only.
Watch out. Never add the bottoms. 27 + 37 is not 514. Sevenths are bigger than fourteenths, so 514 would actually be less than the 37 you started with, and taking more food cannot leave you with less!
59 − 29 = 39. You had 5 of the ninths, you gave away 2 of them, and 3 ninths remain.
Always look at your answer and ask whether it can be simplified. Both 3 and 9 divide by 3, so 39 = 13. That is the tidiest way to write it.
Now back to Keza: 14 + 12.
Step 1 find the LCM of 4 and 2. The multiples of 4 are 4, 8, 12. The multiples of 2 are 2, 4, 6. The smallest number in both lists is 4.
Step 2 dress both fractions in quarters. 14 is already in quarters. For 12, multiply the top and the bottom by 2: 12 = 24.
Step 3 now the pieces match, so add the tops. 14 + 24 = 34.
Answer: Keza's family used 34 of the jerrycan.
Worked example
Work out 23 + 14.
Step 1 find the LCM of 3 and 4. Multiples of 3: 3, 6, 9, 12. Multiples of 4: 4, 8, 12. The LCM is 12.
Step 2 change both fractions into twelfths. 12 ÷ 3 = 4, so multiply the top and bottom of 23 by 4: 23 = 812. And 12 ÷ 4 = 3, so multiply the top and bottom of 14 by 3: 14 = 312.
Step 3 add the tops. 812 + 312 = 1112.
Step 4 can 1112 be simplified? The only number dividing both 11 and 12 is 1, so it is already in its simplest form.
Answer: 1112.
Worked example
(subtracting). Work out 34 - 25.
Step 1 the LCM of 4 and 5 is 20.
Step 2: 34 = 1520 (top and bottom times 5) and 25 = 820 (top and bottom times 4).
Step 3: 1520 − 820 = 720.
Answer: 720.
Gatete had one full bag of beans and sold 38 of it. How much is left?
A whole one can wear any fraction clothes you like, as long as the top and the bottom are the same number. Here you need eighths, so write 1 as 88.
88 − 38 = 58
So 58 of the bag is left.
Work out 56 + 34.
The LCM of 6 and 4 is 12. So 56 = 1012 and 34 = 912.
1012 + 912 = 1912
But 12 twelfths make one whole, and you have 19 of them, so the answer is more than 1. How many whole ones? 12 goes into 19 once, and 7 twelfths are left over.
Answer: 1912 = 1 712.
What does 35 × 4 mean? It means four lots of 35. Written as an addition it is:
35 + 35 + 35 + 35
Every piece is a fifth, so you just add the tops: 3 + 3 + 3 + 3 = 12. The bottom stays 5. That gives 125.
So here is the shortcut: multiply the top number by the whole number and keep the bottom number the same.
And 125 is more than one whole. 5 goes into 12 twice, with 2 fifths left over, so 125 = 2 25.
Worked example
One tin of beans has a mass of 23 kg. What is the mass of 6 tins?
Step 1 six tins means 23 × 6.
Step 2: multiply the top by 6 and keep the bottom: 2 × 6 = 12, so you have 123.
Step 3: 123 means 12 ÷ 3, which is 4.
Answer: the 6 tins have a mass of 4 kg.
The little word of is an instruction to multiply. To find 25 of 30 mangoes:
Step 1 divide by the bottom number to find one fifth. 30 ÷ 5 = 6.
Step 2: multiply by the top number, because you want two of those fifths. 6 × 2 = 12.
Answer: 25 of 30 mangoes is 12 mangoes.
Tip
You can only add or subtract pieces that are the SAME SIZE. Nobody would say that 2 avocados plus 3 bananas makes 5 avocados. In exactly the same way, thirds and quarters cannot be added until you have turned them both into twelfths.
So the very first thing you write down, every single time, is the LCM of the two denominators. Once the bottoms match, the sum is easy: add the tops and leave the bottom alone.
Do each one on paper first, then tap Show answer to check.
310 + 410
Answer: the bottoms already match, so add the tops only: 3 + 4 = 7. The answer is 710.
12 + 13
Answer: the LCM of 2 and 3 is 6. 12 = 36 and 13 = 26. Then 36 + 26 = 56.
78 - 12
Answer: the LCM of 8 and 2 is 8. 12 = 48. Then 78 − 48 = 38.
27 × 3
Answer: multiply the top by 3 and keep the bottom: 2 × 3 = 6, so the answer is 67.
A packet of sugar has a mass of 34 kg. What is the mass of 6 packets?
Answer: 34 × 6 = 184. Now 4 goes into 18 four times with 2 left over, so 184 = 4 24, and 24 simplifies to 12. The mass is 4 12 kg.
There are 20 pupils in Mutesi's group and 34 of them walk to school. How many pupils walk?
Answer: 20 ÷ 4 = 5 (that is one quarter), then 5 × 3 = 15. So 15 pupils walk to school.
What you learned today
Quick check
Work out 2/9 + 5/9.
