Discover Mathematics P4: Term 2, Unit 10, Lessons 5–8
GoalShow a decimal and a fraction as the same part of one whole, and use the whole to find what is left.
New words
one whole · all of the object before it is cut; 1 = 1.0 = 10/10 = 100/100part of a whole · some of the equal parts of one wholeshaded · coloured in on a picture to show a part
Explanation
A decimal and a fraction can name the very same part of one whole. Cut a square into 100 equal small squares. If 25 are shaded, the shaded part is 25/100 and also 0.25. Each full column holds 10 squares, which is one tenth, so 2 full columns and 5 more squares are 2 tenths and 5 hundredths: 0.25. The whole is all 100 squares: 100/100 = 1.00 = 1. To find what is left, take the shaded part away from the whole. Here 1 − 0.25 = 0.75, and we can check on the grid: 100 − 25 = 75 squares are not shaded. Shaded part and unshaded part always add up to the whole: 0.25 + 0.75 = 1.
Worked examples
A tray of kunafa is cut into 10 equal pieces. Mina eats 3 pieces. She ate 3/10 of the tray, which is 0.3. What is left is 10 − 3 = 7 pieces, so 7/10 = 0.7 of the tray. Check: 0.3 + 0.7 = 1, the whole tray.
A school garden is a square of 100 equal plots. Onions grow in 64 plots. The onion part is 64/100 = 0.64 of the garden. The other plots are 100 − 64 = 36, so 36/100 = 0.36 of the garden has other plants. Check: 0.64 + 0.36 = 1.
Where is 0.8 on a number line from 0 to 1 with 10 equal steps? It is at the same place as 8/10: make 8 steps of one tenth from 0. The point marked is both 8/10 and 0.8.
Class activity
Colour the page. On squared paper draw a square of 10 by 10 small squares. Colour 37 squares blue and 20 squares yellow. Write each colour as a fraction and as a decimal. Then work out the decimal for the squares left white. The three decimals must add up to 1.
Practice
1
On a hundred grid 30 squares are shaded. Write the shaded part as a fraction and as a decimal.
30/100 = 0.30 = 0.3.
2
0.45 of a hundred grid is shaded. How many squares are not shaded? Write that part as a decimal.
45 squares are shaded, so 100 − 45 = 55 are not: 55/100 = 0.55.
3
Hana cuts a ribbon into 10 equal parts and uses 9 parts. Write the used part and the part left as decimals.
Used: 9/10 = 0.9. Left: 1 part, 1/10 = 0.1.
4
Write 1 as a fraction with denominator 100 and as a decimal with two places.
100/100 = 1.00.
5
Seif says 0.5 of a hundred grid is 5 squares. Is he right?
No. 0.5 = 5/10 = 50/100, which is 50 squares (5 full columns).
