Back to: Mathematics Primary 4
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Multiplication is the process of calculating the total of one number multiplied by another. Multiplying means repeated addition of a number. (The number must all be the same before we can use it to multiply.)
When you think of it this way, learning the Times Tables makes sense.
Let’s take the 3 times tables, for example. Students usually learn the 3 times tables this way:
1 x 3 = 3
2 x 3 = 6
3 x 3 = 9
and so on.
Using the idea of groups, we have:
1 x 3 = 3 (1 group of 3)
2 x 3 = 3 + 3 = 6 (2 groups of 3)
3 x 3 = 3 + 3 + 3 = 9 (3 groups of 3) and so on.
So if your child knows the answer to 3 x 4 is 12, but cannot remember the answer to
4 x 4, they will just need to add 4 to 12 to get the answer.
4 x 4 = 12 + 4
Now let’s look at something interesting:
3 groups of 5 = 5 + 5 + 5 = 15
5 groups of 3 = 3 + 3 + 3 + 3 + 3 = 15
3 groups of 5 has the same answer as 5 groups of 3!
So, 3 x 5 = 5 x 3
This means that when you multiply 2 numbers, the order of the numbers (which number is first and which is second) does not matter, the answer will still be the same.
Multiplication of 3 digit by 1 digit
. 7 1 2 2 1 9 4 1 5
× 3 × 6 × 5
2 1 3 6 1 3 0 4 2 0 7 5
Multiplication of 2digit by digits 2
3 1 3 8 8 8
4 6 5 7 3 4
1 8 6 2 3 8 3 5 2
1 2 4 1 9 0 2 6 4
1 4 4 6 2 1 3 8 2 9 9 2
Multiplication of 3 digit by 2 digits
3 1 2 3 7 8 1 4 3
× 1 4 × 6 6 × 2 2
1 2 4 8 2 2 6 8 2 8 6
3 1 2 2 2 6 8 2 8 6
4 3 6 8 2 4 9 4 8 3 1 4 6
Multiplication of Decimals
To multiply decimal numbers:
- Multiply the numbers just as if they were whole numbers.
- Line up the numbers on the right – do not align the decimal points.
- Starting on the right, multiply each digit in the top number by each digit in the bottom number, just as with whole numbers.
- Add the products.
- Place the decimal point in the answer by starting at the right and moving a number of places equal to the sum of the decimal places in both numbers multiplied.
Multiplication of Decimal by Decimal
Multiplying decimals is the same as multiplying whole numbers except for the placement of the decimal point in the answer. When you multiply decimals, the decimal point is placed in the product so that the number of decimal places in the product is the sum of the decimal places in the factors
Here are the rules for multiplying decimal numbers:
- Multiply the numbers just as if they were whole numbers:
- Line up the numbers on the right–do not align the decimal points.
- Starting on the right, multiply each digit in the top number by each digit in the bottom number, just as with whole numbers.
- Add the products.
- Place the decimal point in the answer by starting at the right and moving the point the number of places equal to the sum of the decimal places in both numbers multiplied.
Example
37.7 x 2.8 = ? —>
37.7 ( 1 decimal place )
x 2.8 ( 1 decimal place )
3016
+754
105.56 ( 2 decimal places, move point 2 places left )
Note: Use estimating to help you check the placement of the decimal point. You could round 37.7 to 40 and 2.8 to 3. It’s easy to multiply 3 x 40 so you know your answer should be close to 120.
Here’s a “mental math” shortcut: When multiplying a number by a multiple of ten, just move the decimal point one space to the right for every zero.
10 x 0.6284 = 6.284 (1 zero, 1 space right)
100 x 0.6284 = 62.84 (2 zeroes, 2 spaces right)
1000 x 0.6284 = 628.4 (3 zeroes, 3 spaces right)
10,000 x 0.6284 = 6284 (4 zeroes, 4 spaces right)
100,000 x 0.6284 = 62,840 (5 zeroes, 5 spaces right)
Example
- Find the product of 9.683 x 6.1 = ?
Line up the numbers on the right, multiply each digit in the top number by the each digit in the bottom number (like whole numbers), add the products, and mark off decimal places equal to the sum of the decimal places in the numbers being multiplied.
9.683 ( 3 decimal places)
x 6.1 ( 1 decimal place)
9683 (1 x 9683)
+ 58098 (6 x 96830)
59.0663 (3 + 1 = 4 decimal places)
- Jackie just bought a new convertible. How far will she get on the highway before she runs out of gas and has to call a tow truck?
First, estimate your answer to the tens place. Then make an exact calculation, using the calculator.
Estimate:
24.5 -> 20 15.2 -> 20 20 x 20 = 400 miles
Exact calculation:
24.5 x 15.2 = 372.40
You can drop the trailing zero in a decimal number. For example, 372.40 is the same as 372.4. This is because the “.40” part of the number is the same as “.4”. This is the same as saying that 40/100 is the same as 4/10
Quiz
- Find the product of 654 and 54.
- Multiply 2.75 by 0.5
- Multiply 6.24 by 1000
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