Functional Skills: Multiplication

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Functional Skills: Multiplication Revision

Multiplication

Multiplication means “how many lots of”. The 2 methods used to multiply large numbers without a calculator are the column method and the grid method. If you have a calculator, then multiplication problems are usually straightforward, you just need to know when to multiply.

Make sure you are happy with the following topics before continuing.

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When to Multiply

You can recognise questions that require multiplication in two ways:

  1. Questions that use the word “multiply” or “times“, or similar words like “multiplication“.
  2. Questions that use the times sign, \times.
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Method 1: Column Method

Example: Calculate 281 \times 23

Step 1: Write the two numbers in the multiplication above each other, with the bigger one on top. Write the values so that the units, the 10s, the 100s etc. all line up in the correct column.

Step 2: Multiply the final digit from the bottom number with every digit from the top number, in turn, and write the results underneath from right to left, making sure to carry forward when the values go above 10.

3\times1 = 3,   3\times8=24,   3\times2 = 6

Step 3: The second digit from the right is the tens digit. For this, write a 0 underneath the previous step’s working so that everything is shifted to the left by one space.

Then, multiply this digit by every digit from the top number, and write the results underneath the last step from right to left.

Step 4: Add up the final numbers using column method for addition, and write the results under another line.

Therefore,

281 \times 23 = \textcolor{black}{6463}

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Method 2: Grid Method

Example: Calculate 213 \times 74

Step 1: Split each number into units, 10s, 100s etc. and write each part of one number along the left side of the grid, and each part of the other number across the top.

\textcolor{red}{2} = \textcolor{red}{200}

\textcolor{blue}{1} = \textcolor{blue}{10}

\textcolor{limegreen}{3} = \textcolor{limegreen}{3}

\textcolor{maroon}{7} = \textcolor{maroon}{70}

\textcolor{purple}{4} = \textcolor{purple}{4}

Step 2: Fill in each square of the grid by individually multiplying each part of one number by each part of the other number.

Step 3: Finally, add up all answers from the grid to get the final answer:

14000+700+210+800+40+12= \textcolor{black}{15762}

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Multiplying on a Calculator

The above methods are for multiplying without a calculator. Multiplying with a calculator is much simpler. You press each digit individually for the first number, then the times symbol which looks like this: \times, then each digit individually for the second number, then equals.

Example: Multiply 23 and 571 using a calculator.

Press 2 then 3 then \times then 5 then 7 then 1 then =

You should see a result of 13133.

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

  • To multiply by \textcolor{red}{\boldsymbol{10}}, you move the decimal point one place to the right.
  • To multiply by \textcolor{red}{\boldsymbol{100}}, you move the decimal point two places to the right.
  • To multiply by \textcolor{red}{\boldsymbol{1000}}, you move the decimal point three places to the right.

This rule can be used for multiplying by 10000, 100000..., just move the decimal point to the right the same amount as the amount of zeros after the 1.

Remember: For whole numbers the decimal point doesn’t look like it’s there, but it is. For example 25 can be written as 25.0

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Square Numbers

Multiplying a number by itself is called squaring a number, for instance 6 squared =6\times6=36

Often squared numbers are written using a small 2 – e.g. 6^2

For more difficult squares, like 19^2, if you don’t have a calculator you may have to use the multiplication methods described above, or break the multiplication down into smaller chunks.

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Example 1: Multiplication Problems

Aimee buys \textcolor{blue}{60} boxes of pencils for her school. Each box contains \textcolor{red}{40} pencils, with each pencil costing 15p.

How much does she spend on pencils altogether?

[2 marks]

We need to calculate the cost for one box of pencils:

Cost of 1 box = \textcolor{red}{40} \times 15 = 600p

Then multiply by the number of boxes, 60, to find the total cost:

Total cost = 600 \times \textcolor{blue}{60} = 36000p =\textcolor{blue}{£360}

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Example 2: Multiplying by \boldsymbol{10}, \boldsymbol{100} and \boldsymbol{1000}

Calculate:

a) 5.7\times100

b) 42\times10

c) 13.1\times1000

 

[3 marks]

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Example 3: Square Numbers

Calculate:

a) 13^2

b) 22^2

[2 marks]

a) 13^2=13\times13=10\times13+3\times13=130+39=169

b) 22^2=22\times20+22\times2=440+44=484

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Functional Skills: Multiplication Example Questions

Here, we will use the long multiplication method, multiplying 619 by 5 and then by 40, and then adding the results:

 

\begin{array}{r}619\\\times45\\\hline3095\\+24760 \\\hline27855 \end{array}

Here, we will use the long multiplication method, multiplying 52 by 1 and then by 30, and then adding the results:

 

\begin{array}{r}\begin{array}{r}52\\\times31\\\hline52\\+1560\\\hline 1612\end{array}\end{array}

We need to calculate the cost for one pack of paving slabs:

Cost of 1 pack = 8 \times £9 = £72

 

Then multiply by the number of packs, 15, to find the total cost:

Total cost = 15 \times £72 = £1080

a) Multiplying by 100 means we move the decimal point two places to the right.

So

5.61\times100=561

 

b) Multiplying by 10000 means we move the decimal point four places to the right.

So

13\times10000=130000

 

c) Multiplying by 10 means we move the decimal point one place to the right.

So

0.73\times10=7.3

a) 8^2=8\times8=64

 

b) 11^2=11\times11=121

 

c) 26^2=26\times26=26\times20+26\times6=520+156=676

Additional Resources

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Exam Tips Cheat Sheet

FS Level 2
PFS

Formula Booklet

FS Level 2

Functional Skills: Multiplication Worksheet and Example Questions

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Multiplication E3

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Multiplication L1

FS Level 1NewOfficial PFS
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Multiplication L2

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