Week 9 · Multiplying decimals, first steps · 3 lessons
2
A decimal times a whole number
Discover Mathematics P5: Term 1, Unit 5, Lessons 1–4
GoalMultiply a decimal by a whole number by multiplying as whole numbers and then placing the decimal point.
New words
decimal places · the digits after the decimal pointproduct · the answer to a multiplication
Explanation
To multiply a decimal by a whole number, ignore the decimal point and multiply as if both were whole numbers. Then give the product the same number of decimal places as the decimal factor. For 3.4 × 6: 34 × 6 = 204. The decimal factor 3.4 has one decimal place, so the product has one: 20.4. For 0.25 × 8: 25 × 8 = 200 and there are two decimal places, so the product is 2.00 = 2. For 12.75 × 14 we multiply 1,275 × 14 = 17,850 and the product has two decimal places: 178.50 = 178.5. Always check with an estimate: 3.4 × 6 is close to 3 × 6 = 18, so 20.4 is sensible and 2.04 or 204 would not be.
Multiplication
Without the point
Decimal places
Product
3.4 × 6
34 × 6 = 204
1
20.4
0.25 × 8
25 × 8 = 200
2
2
12.75 × 14
1,275 × 14 = 17,850
2
178.5
Worked examples
Work out 3.4 × 6. 34 × 6 = 204. There is one decimal place, so 3.4 × 6 = 20.4. Estimate: 3 × 6 = 18, so the answer is a little more than 18. As repeated addition: 3.4 + 3.4 + 3.4 + 3.4 + 3.4 + 3.4 = 20.4.
Work out 0.25 × 8. 25 × 8 = 200, and two decimal places give 2.00, which is 2. This makes sense: 0.25 is a quarter and 8 quarters make 2. Seven ribbons of 2.35 m each: 235 × 7 = 1,645, so 2.35 × 7 = 16.45 m.
A microbus fare is 12.75 LE per passenger and a microbus carries 14 passengers. 1,275 × 14 = 12,750 + 5,100 = 17,850. Two decimal places: 178.50. The fares are 178.5 LE, which is 178.50 LE. Estimate: 13 × 14 = 182, close to 178.5.
Class activity
Grocery decimals. Choose three goods with decimal prices per kilogram, such as 18.5 LE, 7.25 LE and 22.75 LE. Work out the price of 4 kg, 6 kg and 12 kg of each. First multiply without the point, then place the point, and check with an estimate. Make a small price list.
Practice
1
Work out 2.6 × 5.
26 × 5 = 130, one decimal place: 13.0 = 13.
2
Work out 0.45 × 12.
45 × 12 = 540, two decimal places: 5.40 = 5.4.
3
Work out 7.08 × 9.
708 × 9 = 6,372, two decimal places: 63.72.
4
A bottle holds 1.5 L. How many litres are in 24 bottles?
