Level 3 · Ages 11–13
Read it again any time, including while you work through the exercises.
A bottle of juice costs 2.30 coins and you buy 3: how much will you pay? That is a decimal times a whole number, the kind of computation we meet every day. In this lesson, the decimal point will hold no more secrets for you.
The big principle for multiplying two decimals: pretend the decimal point does not exist, then put it back at the end. For 2.3 × 1.4: I compute 23 × 14 = 322. Then I count the digits after the decimal point in both factors: one digit in 2.3, one digit in 1.4, so two in total. I place the point so there are two digits after it: 3.22.
Always keep a critical eye thanks to estimation: 2.3 × 1.4 is about 2 × 1.5 = 3. If you get 32.2 or 0.322, the decimal point is in the wrong place! And beware of a very common false idea: multiplying does not always make things bigger. For instance 2.5 × 0.4 = 1: multiplying by a number smaller than 1 means taking only a part, so the result shrinks.
For division, two situations. Dividing a decimal by a whole number is a fair share: 8.4 ÷ 4, I share 8 ones then 4 tenths, keeping the decimal point in the right place: 2.1. Dividing by a decimal asks "how many times?": 3 ÷ 0.5 asks how many halves fit in 3. Answer: 6, because each unit contains 2 halves. So dividing by a number smaller than 1 makes the result bigger!
Ready to juggle the decimal point? Let's go.
Compute 2.3 × 1.4.
23 × 14 = 322
I forget the decimal points and multiply the whole numbers: 23 × 14 = 23 × 10 + 23 × 4 = 230 + 92 = 322.
1 + 1 = 2 chiffres après la virgule
I count the digits after the decimal point: one in 2.3 and one in 1.4, so two in total in the result.
322 -> 3,22
I place the point so two digits sit after it: 3.22.
2 × 1,5 = 3
I check the estimate: 2.3 × 1.4 should be about 3. With 3.22, everything is consistent!
Result: 2.3 × 1.4 = 3.22
Compute 3 ÷ 0.5.
3 ÷ 0,5 = « combien de 0,5 dans 3 ? »
Dividing by 0.5 asks how many halves fit into 3.
1 = 2 × 0,5
Each unit contains 2 halves. With 3 units, I have 3 × 2 halves.
3 ÷ 0,5 = 6
The result is 6, bigger than 3: dividing by a number smaller than 1 makes things grow! Check: 6 × 0.5 = 3.
Result: 3 ÷ 0.5 = 6