Fractions, Decimals and Percentages
Primary 5 · Mathematics
Fractions, Decimals and Percentages
Lesson 3 of 3
15 min
Let's begin
At the market, Umutoni's mother asks for 1.5 kg of rice. The trader tips rice onto the scale until the needle stops at 1.5. Then she asks for half a kilogram of sugar, and this time the scale shows 0.5.
Umutoni thinks about that on the way home. Half is 12, but the scale wrote it as 0.5. And that same afternoon her test paper came back saying she had scored 50%.
One amount, three sets of clothes: 12, 0.5 and 50%. Today you will learn to change between them as easily as changing a shirt.
The decimal point separates the whole ones from the parts of one. Every step you take to the right makes the piece ten times smaller.
| Ones | Tenths | Hundredths | Thousandths |
|---|---|---|---|
| 3 | 4 | 2 | 7 |
The number in that table is 3.427. You read it out as three point four two seven. You say the digits after the point one at a time, never as four hundred and twenty seven.
3.427 means 3 + 410 + 2100 + 71000.
So inside 3.427, the 4 is worth 0.4 (4 tenths), the 2 is worth 0.02 (2 hundredths) and the 7 is worth 0.007 (7 thousandths).
Which is bigger, 0.7 or 0.65?
Many pupils answer 0.65 because it has more digits. That is the trap. Longer does not mean bigger. Compare the tenths first: 0.7 has 7 tenths and 0.65 has only 6 tenths. So 0.7 is bigger.
A safe trick is to give both numbers the same number of decimal places by writing a zero on the end, which never changes the value: 0.7 = 0.70. Now you are comparing 70 hundredths with 65 hundredths, and it is obvious.
The golden rule: put the decimal points one underneath the other. Then add or subtract exactly as you do with whole numbers, and bring the point straight down into the answer.
Worked example
Add 4.6 + 2.35.
4.6 has one decimal place and 2.35 has two, so first write 4.6 as 4.60. Adding that zero changes nothing at all, but it keeps the columns tidy.
| 4 | . | 6 | 0 | |
| + | 2 | . | 3 | 5 |
| 6 | . | 9 | 5 |
Hundredths: 0 + 5 = 5. Tenths: 6 + 3 = 9. Ones: 4 + 2 = 6. The point comes straight down.
Answer: 6.95.
Worked example
Subtract 9.05 - 4.6.
Write 4.6 as 4.60 so that both numbers have two decimal places.
| 9 | . | 0 | 5 | |
| - | 4 | . | 6 | 0 |
| 4 | . | 4 | 5 |
Hundredths: 5 − 0 = 5. Tenths: you cannot take 6 from 0, so borrow one whole from the 9. The 9 becomes 8, and the 0 tenths becomes 10 tenths. Now 10 − 6 = 4. Ones: 8 − 4 = 4.
Answer: 4.45.
If the denominator is 10, 100 or 1000 it is very easy, because the decimal places are tenths, hundredths and thousandths.
710 = 0.7
23100 = 0.23
9100 = 0.09 (the zero is needed to hold the tenths place empty)
1251000 = 0.125
If the denominator is something else, first build an equivalent fraction with 10 or 100 on the bottom.
Worked example
Change 35 into a decimal.
Step 1 5 × 2 = 10, so multiply the top and the bottom by 2. 35 = 610.
Step 2: 610 = 0.6.
Worked example
Change 14 into a decimal.
Step 1 4 × 25 = 100, so multiply the top and the bottom by 25. 14 = 25100.
Step 2: 25100 = 0.25.
Say the decimal out loud and then write down what you hear.
0.6 is six tenths, so 0.6 = 610. Simplify by dividing both by 2: 0.6 = 35.
0.45 is forty-five hundredths, so 0.45 = 45100. Both 45 and 100 divide by 5: 45 ÷ 5 = 9 and 100 ÷ 5 = 20. So 0.45 = 920.
The words per cent mean out of 100. Think of a metre, which is made of 100 centimetres. So 45% is just another way of writing 45100.
Percentage into fraction: write it over 100 and simplify. 25% = 25100 = 14. And 60% = 60100 = 35.
Percentage into decimal: 45% = 45100 = 0.45. Because you are dividing by 100, the point hops two places to the left. So 8% = 0.08.
Decimal into percentage: hop the point two places to the right. 0.7 = 70% and 0.05 = 5%.
Fraction into percentage: make the denominator 100. 34 = 75100 = 75%. And 15 = 20100 = 20%.
These are worth learning by heart, because they come up again and again:
| Fraction | Decimal | Percentage |
|---|---|---|
| 12 | 0.5 | 50% |
| 14 | 0.25 | 25% |
| 34 | 0.75 | 75% |
| 15 | 0.2 | 20% |
| 25 | 0.4 | 40% |
| 110 | 0.1 | 10% |
| 310 | 0.3 | 30% |
| one whole | 1.0 | 100% |
Worked example
A shop in Kigali takes 10% off the price of a pair of shoes. The shoes cost 6000 Frw. What is the new price?
Step 1 10% means 10100, which simplifies to 110.
Step 2: 110 of 6000 is 6000 ÷ 10 = 600 Frw. That is the money taken off.
Step 3: the new price is 6000 − 600 = 5400 Frw.
Worked example
Ishimwe scored 18 out of 25 in the Maths test. What is his score as a percentage?
Step 1 as a fraction, his score is 1825.
Step 2: a percentage needs 100 on the bottom. 25 × 4 = 100, so multiply the top by 4 as well: 18 × 4 = 72.
Step 3: 1825 = 72100.
Answer: Ishimwe scored 72%.
Tip
Remember the hop. Going from a decimal to a percentage, the point hops two places to the RIGHT and the number looks bigger: 0.35 becomes 35%. Going from a percentage back to a decimal, the point hops two places to the LEFT and the number looks smaller: 35% becomes 0.35.
And if you forget everything else, hold on to this one sentence: per cent means out of 100. Write the percentage over 100 and you can always work out the rest from there.
Work each one out first, then tap Show answer to check.
What is the value of the digit 6 in 4.365?
Answer: the digits after the point are tenths, then hundredths, then thousandths. The 3 is in the tenths place and the 6 is in the hundredths place. So the 6 is worth 6 hundredths, which is 0.06.
Add 5.7 + 2.45.
Answer: write 5.7 as 5.70 and line up the points. Hundredths: 0 + 5 = 5. Tenths: 7 + 4 = 11, so write 1 and carry 1 into the ones. Ones: 5 + 2 + 1 = 8. The answer is 8.15.
Write 45 as a decimal and as a percentage.
Answer: for the decimal, 5 × 2 = 10, so 45 = 810 = 0.8. For the percentage, 5 × 20 = 100, so 45 = 80100 = 80%.
Write 0.35 as a fraction in its simplest form.
Answer: 0.35 is thirty-five hundredths, so 0.35 = 35100. Both 35 and 100 divide by 5: 35 ÷ 5 = 7 and 100 ÷ 5 = 20. The answer is 720.
There are 40 pupils in Uwase's class and 30% of them are in the football team. How many pupils is that?
Answer: 30% = 30100 = 310. Now find 310 of 40: first 40 ÷ 10 = 4, then 4 × 3 = 12. So 12 pupils are in the team.
Which is bigger, 0.4 or 35%?
Answer: put them in the same clothes. Hop the point two places right: 0.4 = 40%. And 40% is bigger than 35%, so 0.4 is bigger.
What you learned today
Quick check
What is the value of the digit 7 in 2.574?
