KS3 · Maths
Multiplying and dividing decimals
Where does 5.2 × 3.7 land: near 2, near 20 or near 200? You can know before working out a single digit, and that habit catches most decimal mistakes.
The whole-number method
Problem
Work out 12.4 × 1.4 using whole numbers.
Count the decimal places… then check
When the count isn't the whole story
Each answer is right. Does it have as many decimal places as the count says, fewer, or none at all?
Still to sort
A whole number (0)
No decimal places left at all.
Where the line is: Every expected decimal place has turned into a zero and dropped off.
Fewer places than expected (0)
Still a decimal, but shorter than the count says.
Where the line is: The last digits multiply to something ending in zero, so at least one place drops off — but not all of them.
As many places as expected (0)
The count was right.
Where the line is: The last digits multiply to something that doesn't end in zero, so nothing drops off.
Add up the decimal places in the two numbers and you get the number of places you'd expect in the answer. Every product below is correct. Sort each one.
Dividing by a decimal
Reason it through
Why can you swap 1.2 ÷ 0.4 for 12 ÷ 4 and still get the right answer?
First link · your turn
How else can you write 1.2 ÷ 0.4?
WHAT YOU'VE LEARNED
A quick recap of today's lesson.
No new method needed: make the numbers whole, do the easy sum, then undo the powers of 10.
What you need to know
- Decimals don't need a brand-new method. Turn them into whole numbers using powers of 10, do the easy calculation, then undo the powers of 10.
- Decide the size of an answer first. Place value tells you roughly where a product lands before you work out any digits.
- Multiplying a positive number by something between 0 and 1 makes it smaller; multiplying by something bigger than 1 makes it bigger.
- To divide by a decimal, change it into an equivalent division with a whole-number divisor — one that gives exactly the same answer.
The big picture
To multiply decimals, write each one as a whole number times a power of 10, multiply the whole numbers, then undo the powers of 10: 12.4 × 1.4 = 124 × 14 × 0.01 = 17.36. To divide by a decimal, write the division as a fraction and multiply the top and bottom by the same power of 10 until the divisor is a whole number: 1.2 ÷ 0.4 = 12/4 = 3. Then check every answer twice: its size from place value, and its last digit from the last digits multiplied.
Key points
Worked example
Problem
You know that 456 × 12 = 5472. Use it to find 4.56 × 1.2, then write another multiplication with the same answer.
⚠ Watch out
Placing the decimal point by habit and never checking the size, like writing 192.4 for 5.2 × 3.7: ones times ones can't make hundreds. When dividing, scaling only the divisor or only the dividend changes the answer tenfold. Scale both.
Memory hook
Make it whole, do the sum, undo the tens — then check the size and the last digit.
Check yourself
Without a calculator, work out (a) 2.1 × 1.28 and (b) 4.8 ÷ 0.02. (Answers: (a) 21 × 128 × 0.001 = 2.688; (b) 480 ÷ 2 = 240.)
Flashcards
(15)What is 0.1 × 0.1?
How do you multiply two decimals using whole numbers?
Why can't 5.2 × 3.7 be 192.4?
Is the product of two decimals always bigger than both numbers?
In an area model, what is 0.5 × 0.3?
How does the last-digit check work?
When does a product have fewer decimal places than you'd expect?
Can two decimals multiply to give a whole number?
Given 456 × 12 = 5472, what is 45.6 × 12?
Give two other calculations with the same product as 32.4 × 1.3.
In 30 ÷ 6 = 5, which number is the dividend, the divisor and the quotient?
Why does 1.2 ÷ 0.4 give the same answer as 12 ÷ 4?
Given 26.4 ÷ 0.8 = 33, what is 26.4 ÷ 0.08?
Why simplify 28.8/12 to 7.2/3 before dividing?
What do you do when short division leaves a remainder?
Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.
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Keep me postedMore KS3 Maths topics
- Adding and subtracting positive and negative integers
- Algebraic notation and conventions
- Angle sum in a triangle
- Angles on parallel lines (corresponding, alternate, co-interior)
- Area of a circle
- Area of a trapezium
- Area of a triangle
- Area of composite rectilinear shapes
- Arithmetic sequences and finding the nth term
- Associative, commutative and distributive laws
- Bisecting an angle
- Calculating theoretical probabilities
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