☰ Year plan · Mathematics

Reciprocals, fraction division and decimals

Week 17 · Fraction division by the reciprocal; multiplying and dividing decimals · 3 lessons
3

Multiplying and dividing decimals by shifting the point

Discover Mathematics P6: Term 2, Unit 8, Lessons 3–4
GoalMultiply and divide decimals using powers of 10, and divide by a decimal by moving the point in both numbers.
New words
decimal point · the dot that separates the whole part from the parts smaller than 1power of 10 · 10, 100, 1,000 and so ondecimal places · the digits after the decimal point
Explanation

Multiplying by 10, 100 or 1,000 moves every digit left by 1, 2 or 3 places, so the decimal point seems to move right. Dividing by 10, 100 or 1,000 moves it left. To multiply two decimals, ignore the points and multiply as whole numbers, then give the answer as many decimal places as the two numbers have together. To divide by a decimal, multiply both numbers by the same power of 10 so that the divisor becomes a whole number: the answer does not change, because the same thing was done to both. Always estimate to see if the answer is sensible.

★Remember
× or ÷ by 10, 100, 1,000: shift the point. Divide by a decimal: multiply both numbers by the same power of 10.
Worked examples
CalculationAnswer
4.35 × 1043.5
4.35 × 100435
4.35 × 1,0004,350
4.35 ÷ 100.435
The pattern for 4.35. Each time we multiply by 10 the point moves one place to the right; each time we divide by 10 it moves one place to the left.
Multiplying decimals. 2.5 × 1.2: 25 × 12 = 300, and the numbers have 2 decimal places together, so the answer is 3.00 = 3. A kilogram of tomatoes costs 12.5 LE, so 2.4 kg cost 12.5 × 2.4: 125 × 24 = 3,000, with 2 decimal places that is 30.00, so 30 LE. Estimate: 12 × 2.5 = 30.
Dividing by a decimal. 3.75 kg of nuts are packed in bags of 0.125 kg. 3.75 ÷ 0.125: multiply both numbers by 1,000, which gives 3,750 ÷ 125 = 30 bags. Check: 0.125 × 30 = 3.75. Another: 4.8 ÷ 0.6 = 48 ÷ 6 = 8.
Class activity

Shopping shift. At a market, choose a fruit that costs a price with a decimal, for example 8.5 LE per kg. Work out the cost of 10 kg, 100 kg and 0.1 kg by shifting the point, and then of 2.4 kg by multiplying decimals.

Practice
1
Find 7.2 × 100 and 7.2 ÷ 10.
2
Find 0.8 × 0.5.
3
Find 3.6 × 2.5.
4
A rope of 9 m is cut into pieces of 0.75 m. How many pieces?
5
Salma says 0.5 ÷ 0.1 = 0.05. Is she right? Find the correct answer.