Multiplication and Division

Multiplication and Division

Multiplication and division are fundamental skills that underpin a lot of questions that your child may get asked on their exam. It is important that they have a good grasp on the techniques used in this section. We will also look at tricks for multiplying and dividing by 10, 10010,,100 and 10001000.

Multiplying by 10, 100boldsymbol{10,,100} and 1000boldsymbol{1000}

These are some helpful rules for your child to learn to make multiplying easier!

  • Multiplying by 10textcolor{green}{10}: move the decimal point 1textcolor{green}{1} place to the right.
  • Multiplying by 100textcolor{green}{100}: move the decimal point 2textcolor{green}{2} places to the right.
  • Multiplying by 1000textcolor{green}{1000}: move the decimal point 3textcolor{green}{3} places to the right.

These rules can be generalised for other values such as 10 000, 100 000…10,000,, 100,000 … just move the decimal point to the right the same number of places as the number has zeros after the 1.1.

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Dividing by 10, 100boldsymbol{10,,100} and 1000boldsymbol{1000}

Multiplying and dividing are opposite operations, therefore the rules your child needs to remember for division are the opposite of the rules for multiplication.

  • Dividing by 10textcolor{blue}{10}: move the decimal point 1textcolor{blue}{1} place to the left.
  • Dividing by 100textcolor{blue}{100}: move the decimal point 2textcolor{blue}{2} places to the left.
  • Dividing by 1000textcolor{blue}{1000}: move the decimal point 3textcolor{blue}{3} places to the left.

Like with the rules for multiplication these rules can be generalised for other values… just move the decimal point to the left the same number of places as the number of zeros after the 11.

Example 1: Multiplication Using a Written Method

Your child can use a method called the written method to multiply large numbers or decimals.

Calculate 43×6643 times 66

Step 1boldsymbol{1}: First, write the numbers one above the other making sure the units, tens and hundreds columns line up. In this case, both numbers are two digits so can be lined up quite easily.

Step 2boldsymbol{2}: Next, multiply the digit in the units column of the bottom number by every digit in the top number.

6×3=18textcolor{blue}{6} times 3 = textcolor{red}{1}8

The 1textcolor{red}{1} is carried over as 1818 is greater than 1010.

6×4=24textcolor{blue}{6} times 4 = 24

Don’t forget to add on the 1textcolor{red}{1} that has been carried over!

24+1=2524 + textcolor{red}{1} = 25

Therefore, 6×43=258textcolor{blue}{6} times 43 = 258

Step 3boldsymbol{3}: The next row is a little different, we are now multiplying all the digits in the top number by 60textcolor{blue}{60} so we must add a 0textcolor{purple}{0} to the units column before we begin to multiply.

Now, we can treat it as before and multiply each digit by 6textcolor{blue}{6}.

6×3=18textcolor{blue}{6} times 3 = 18

Remember to carry the 1textcolor{red}{1}!

6×4=24textcolor{blue}{6} times 4 = 24

24+1=2524+textcolor{red}{1} = 25

Therefore, 60×43=258060 times 43 = 2580

Step 4boldsymbol{4}: Add these values using the column method for addition discussed in an earlier topic.

2580+258=28382580 + 258 = 2838

So,

43×66=283843 times 66 = 2838

This method can also be used to multiply numbers with decimal points. A good thing for your child to remember is to always make sure the decimal points of the numbers they are multiplying together are lined up correctly.

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Example 2: Bus Stop Method for Division

The bus stop method is a memorable way for your child to divide numbers and gets its name as it looks a bit like the number is waiting inside a bus stop.

Calculate 1071÷71071 div 7

Step 1boldsymbol{1}: Set up the bus stop. The number we are dividing by, in this case 77, goes outside the bus stop and the number we are dividing into, in this case 10711071 goes inside the bus stop.

Step 2boldsymbol{2}: Next, see how many times 77 divides into 1textcolor{green}{1}. 1textcolor{green}{1} is less than 77 so divides 00 times. A 00 goes above the 1textcolor{green}{1} on the bus stop and the 1textcolor{red}{1} gets carried to the next digit.

This means our next number to divide into is not 0textcolor{blue}{0} but is 10textcolor{red}{1}textcolor{blue}{0}.

Step 2boldsymbol{2}: Next, how many times does 77 divide into 10textcolor{red}{1}textcolor{blue}{0}? Well 1×7=71 times 7 = 7 so the answer is once with 3textcolor{red}{3} leftover.

Step 3boldsymbol{3}: Then, how many times does 77 divide into 37textcolor{red}{3}textcolor{purple}{7}? Well 5×7=355times 7 = 35 so the answer is 55 times with 2textcolor{red}{2} leftover.

Step 4boldsymbol{4}: Finally, how many times does 77 divide into 21textcolor{red}{2}textcolor{orange}{1}? Well 3×7=213 times 7 = 21 so 33 times exactly.

Therefore,

1071÷7=1531071 div 7 = 153

 

Multiplication and Division Example Questions

Question 1: Calculate the following:

a) 2.4×1002.4 times 100

b) 908÷100 000908 div 100,000

c) 0.004×100.004 times 10

[3 marks]

a) Multiplying by 100100 means we move the decimal point 22 places to the right.

So,

2.4×100=2402.4 times 100 = 240

b) Dividing by 100 000100,000 means we move the decimal point 55 places to the left as there are 55 zeros after the 11.

So,

908÷100 000=0.00908908 div 100,000 = 0.00908

c) Multiplying by 1010 means we move the decimal point 11 place to the right.

So,

0.004×10=0.040.004 times 10 = 0.04

Question 2: Michael buys 88 packs of chocolate bars.

Each pack contains 44 individual bars and each individual bar costs £1.20£1.20

How much money does Michael spend on chocolate bars altogether?

[2 marks]

Total number of individual chocolate bars bought:

8×4=328 times 4 = 32 bars

Then find the total cost of 3232 individual chocolate bars.

Total cost:

32×£1.20=£38.4032 times pounds 1.20 = pounds 38.40

Question 3: Catherine has 131131 cupcakes that she needs to to in boxes to be sent to a bakery.

Each box can fit 88 cupcakes.

How many boxes will she need to transport all of the cupcakes to the bakery?

The calculation needed is:

131÷8131 div 8

Therefore 88 divides 1616 times into 131131 with a remainder of 33. This means that the numbers don’t divide exactly.

1616 boxes will hold 16×8=12816 times 8 = 128 cupcakes but there will be still be 33 cupcakes without a box.

Therefore, 1717 boxes are needed to transport all of the cupcakes to the bakery.