Find the value of 3.6 × 40 without using a calculator.
3.6 × 40 = 3.6 × 4 × 10 = 14.4 × 10 = 144
Ans: 144
How to solve it
Split the multiple into two factors: 200 is 100 times 2, so divide by 100 first, then by 2.
Dividing by 100 moves each digit 2 places to the right, so 84 becomes 0.84. The decimal point stays fixed.
Keep the divide by 2: 0.8 divided by 2 is 0.4, and 0.04 divided by 2 is 0.02, so 0.84 divided by 2 is 0.42.
To multiply by 300, use 3 times 100. Multiply by 3 first: 2.045 times 3 is 6.135.
Then times 100 moves each digit 2 places to the left, so 6.135 becomes 613.5.
Use both factors every time: 40 is 4 times 10, so 3.6 times 4 is 14.4, and 14.4 times 10 is 144.
Each digit has its value from its place. A multiple has two factors, and we use both.
For parents
How do you multiply and divide decimals by 10, 100 and 1000 in P5?
This page teaches multiplying and dividing a decimal with up to 3 decimal places by 10, 100, 1000 and their multiples, without a calculator.
What your child learns here
This page teaches multiplying and dividing a decimal with up to 3 decimal places by 10, 100, 1000 and their multiples, without a calculator. It is the first outcome of the Primary 5 Decimals chapter.
Multiplying by 10, 100 or 1000 moves each digit 1, 2 or 3 places to the left on the place-value chart.
Dividing by 10, 100 or 1000 moves each digit 1, 2 or 3 places to the right, so the answer is smaller.
The decimal point itself stays fixed; it is the digits that change places.
A multiple such as 300 is written as 3 × 100, and both factors are used: 2.045 × 300 = 2.045 × 3 × 100.
For division by a multiple such as 200, divide by 100 first, then by 2, writing each step on one equals chain.
Does the answer make sense?
Multiplying a decimal by a multiple of 10 should give a bigger number, and dividing should give a smaller one. A quick estimate helps too: 84 ÷ 200 is less than half, so an answer of 4.2 is far too large, while 0.42 fits.
How to practise these questions
The Basic questions use a multiple of 1000 on its own, such as a whole number divided by 8000 or a decimal multiplied by 3000, so zeros must be held in place on both sides of the point. Intermediate questions share litres or kilograms equally between many cups or packets, and the answer keeps the unit asked for. Challenge questions chain a multiplication and a division by two different multiples in one line, or give the product and ask for the number that was multiplied by 300. When the point lands in the wrong place, go through the worked solution one line at a time and try that question again later from Revision.
Questions parents ask
Does the decimal point move when we multiply by 10? On this page the point stays still and every digit moves one place to the left. Many books describe the same change as moving the point; both give the same answer.
How do you divide a decimal by a number like 400? Write 400 as 100 × 4. Divide by 100 first by moving the digits two places to the right, then divide the result by 4.
Can my child use a calculator for these? No. The Primary 5 syllabus asks for these calculations without a calculator, so the practice is set that way too.
