Multiplication & Division (OCR GCSE Maths) : Revision Note

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Multiplication

How do I multiply two numbers without a calculator?

  • There are a variety of written methods that can be used to add large numbers

    • You only need to know one method, but be able to use it confidently

    • Four common methods are described below, but there are many other valid methods

How do I use the column method?

  • This is an efficient method if you are confident with multiplication

  • To use the column method:

    • Write one number above the other lining up the digits using place value columns

    • Multiply the first digit (on the right) from the bottom value by each digit in the top value

      • Write the result under the line with the digits in the correct place value columns

    •  Multiply the next digit in the bottom value by each digit in the top value 

      • Always work from right to left

      • Use 0s as place holders when multiplying digits in columns other than the ones column

    • For example, 87 × 426 = 37 062

      bottom enclose table row blank blank blank 8 7 row blank cross times 4 2 6 end table end enclose
bottom enclose table row space blank 5 2 2 row blank 1 7 4 0 row cell space space 3 end cell 4 8 0 0 end table end enclose
table row cell space space 3 end cell 7 0 6 2 end table

How do I use the lattice method?

  • The lattice method is good for numbers with two or more digits

    • This method allows you to work with individual digits

  • To use the lattice method:

    • Draw a grid

      • The number of rows should be the same as the number of digits in one number

      • The number of columns should be the same as the number of digits in the other number

      • Draw diagonal lines through the boxes

    • Multiply each pair of digits, writing the result in the relevant box

      • Ones should be written in the bottom half of the box and tens in the top half of the box

    • Add the digits along the diagonals and write the result in the diagonal outside the grid

      • Carry the tens of any 2 digit result into the next diagonal

  • For example, 3516 × 23 = 80 868

Lattice Complete, IGCSE & GCSE Maths revision notes

How do I use the grid method?

  • This method keeps the value of the larger number intact

    • It may take longer with two larger numbers

    • Be careful lining up numbers with lots of zeros!

  • To use the grid method

    • Draw a grid

      • The number of rows should be the same as the number of digits in one number

      • The number of columns should be the same as the number of digits in the other number

    • Label the rows and columns with the values of each digit

      • E.g. For 3516 you would use 3000, 500, 10 and 6

    • Multiply together the relevant values and put the results in the boxes

    • Add up all of the cells in the boxes 

  • For example, 3516 × 7 = 24 612

Partition Complete, IGCSE & GCSE Maths revision notes
Partition Lined Up, IGCSE & GCSE Maths revision notes

How do I use the repeated addition method?

  • This is best for smaller, simpler cases

    • You may have seen this called ‘chunking’

  • To use the repeated addition method

    • Build up to the answer using simple multiplication facts that can be worked out easily

    • To find 13 × 23 :
      1 × 23 = 23

      2 × 23 = 46

      4 × 23 = 92

      8 × 23 =184

    • So, 13 × 23 = 1 × 23 + 4 × 23 + 8 × 23 = 23 + 92 + 184 = 299

What words are used for multiplication and division?

  • Multiplication may be phrased using the words lots of, times or product

  • Division may be phrased using the words quotient, share and per

Examiner Tips and Tricks

  • A good way to check your answer without a calculator is to estimate it (e.g. by rounding everything to 1 significant figure)

Worked Example

Multiply 2879 by 36.

As you have a 4-digit number multiplied by a 2-digit number then the lattice method is a good choice

Start with a 4×2 grid.…

Lattice Ex1, IGCSE & GCSE Maths revision notes

Notice the use of listing the 8 times table underneath to help with some of the multiplication within the lattice

Use an estimate to check your answer; 3000×40 is equal to 120 000

2879 × 36 = 103 644

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Division

How do I divide a number by another without a calculator?

  • The most common written method for division is short division (or "the bus stop method")

    • There are other methods such as long division, but short division is generally the most efficient

  • While short division is best when dividing by a single digit, for bigger numbers you may need a different approach

  • You can use other number skills to help

    • eg. cancelling fractions, “shortcuts” for dividing by 2 and 10, and the repeated addition (“chunking”) method covered in Multiplication

Short division (bus stop method)

  • Unless you can use simple shortcuts such as dividing by 2 or by 10, this method is best used when dividing by a single digit

  • To find 174 ÷ 3

    • Starting from the left; 3 fits into 1, 0 times, with a remainder of 1

      • Carry the remainder of 1 over to the next digit, which forms 17

    • 3 fits into 17, 5 times, with a remainder of 2

      • Carry the remainder of 2 over to the next digit, which forms 24

    • 3 fits into 24, 8 times, with no remainder

    • So, 174 ÷ 3 = 58

Factoring & cancelling

  • This involves treating division as you would if you were asked to simplify fractions

    • For example, 1008 ÷ 28 can be written as 1008 over 28

    • This can then be simplified

      • 1008 over 28 equals 504 over 14 equals 252 over 7

      • 252 ÷ 7 can then be calculated using short division; the answer is 36

Dividing by 10, 100, 1000, … (Powers of 10)

  • This is a case of shifting digits along the place value columns

    For example

    • 380 ÷ 10 = 38.0 (shifts by 1 column)

    • 45 ÷ 100 = 0.45 (shifts by 2 columns)

    • 28 ÷ 1000 = 0.028 (shifts by 3 columns)

      • For cases like this, it can help to add leading zeros

      • 0028 ÷ 1000 may be easier to visualise

Worked Example

Divide 568 by 8. 

This is division by a single digit so short division would be an appropriate method
If you spot it though, 8 is also a power of 2 so you could just halve three times

Using short division, the bus stop method:

Ex1 Short Divison, IGCSE & GCSE Maths revision notes

8 fits into 5, 0 times, with a remainder of 5
8 fits into 56, 7 times exactly
8 fits into 8, 1 time exactly

Use an estimate to check your answer; 600 ÷ 10 is equal to 60

568 ÷ 8 = 71

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Jamie Wood

Author: Jamie Wood

Expertise: Maths Content Creator

Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.

Dan Finlay

Reviewer: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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