Level 3 · Ages 11–13
Read it again any time, including while you work through the exercises.
Between 3 and 4 lies a whole world of numbers: 3.1, 3.5, 3.72... These are decimal numbers. The decimal point separates the whole part (on the left) from the decimal part (on the right). Right after the point come the tenths (a unit cut into 10), then the hundredths (cut into 100). So 3.72 is 3 units, 7 tenths and 2 hundredths.
First trap to avoid: more digits does not mean bigger! 0.8 is bigger than 0.35, because 0.8 = 0.80, and 80 hundredths beat 35 hundredths. To compare, pad with zeros so both numbers have the same number of digits after the point.
To add or subtract decimals, one single rule: line up the decimal points. Units fall under units, tenths under tenths, and the sum works exactly like with whole numbers. Tip: 10 can be written 10.00 if you need digits after the point.
To multiply, pretend the decimal point does not exist, then put it back: the result must have as many digits after the point as both numbers combined. For example 3.2 × 2.4: compute 32 × 24 = 768, and since there are two digits after the points in total, the result is 7.68.
Finally, keep your common sense switched on: 2.5 × 1.2 should be close to 2.5. If you get 30, the decimal point got lost along the way!
Compute 12.7 + 3.45.
12,7 = 12,70
I line up the decimal points and pad with a zero so both numbers have two digits after the point.
70 + 45 = 115 (centièmes)
I add column by column: 0 + 5 = 5 in the hundredths, 7 + 4 = 11 in the tenths, I write 1 and carry 1.
12 + 3 + 1 = 16
I add the whole parts with the carry, and place the decimal point under the other points.
Result: 12.7 + 3.45 = 16.15
Compute 3.2 × 2.4.
32 × 24 = 768
I ignore the decimal points and multiply the whole numbers: 32 × 24 = 768.
1 + 1 = 2 chiffres après la virgule
3.2 has one digit after the point, 2.4 too: the result must have two.
768 → 7,68
I put the decimal point back: 7.68. Check: 3 × 2 = 6, so a result near 7 makes sense.
Result: 3.2 × 2.4 = 7.68