Long Multiplication What is long multiplication? A number multiplied by a 2 digit (or larger) number e.g. 25 x 13 Is there only one way to do? Are there any tips that can help make it easier? October 2007. Kindly contributed to the Adult Basic Skills Resource Centre http://www.skillsworkshop.org/ by Gaye Noel g.noel@parklanecoll.ac.uk Park Lane College, Leeds. Thank you Gaye. Main curriculum links N1/L1.3 Add, subtract, multiply and divide using efficient written methods. N1/L2.2 Carry out calculations with numbers of any size using efficient methods.

Methods of Long Multiplication There are 3 main methods: Lattice method Splitting (grid) method Traditional method

Lattice method – part 1 25 x 5 = ? 1. Make the lattice (grid) as shown 1 2 5 2. Multiply each number above a column by the numbers in every row 3. Write the answers in the lattice. Making sure you have only 1 digit in each triangle

Lattice method – part 2 25 x 5 = ? 1 2 5 1 2 5 Add along the diagonal 2 + 0 = 2

Lattice method – part 1 36 x 8 = ? 1. Make the lattice (grid) as shown 2 4 4 8 2. Multiply each number above a column by the numbers in every row 3. Write the answers in the lattice. Making sure you have only 1 digit in each triangle

Lattice method – part 2 36 x 8 = ? 4 4 8 2 8 8 Add along the diagonal line 4 + 4 = 8

Lattice method – part 1 36 x 13 = ? 1. Make the lattice (grid) as shown 3 6 3 x 3 = 9 2. Multiply each number above a column by the numbers in every row 1 9 8 3. Write the answers in the lattice. Making sure you have only 1 digit in each triangle 3 x 6 = 18

Lattice method – part 2 36 x 13 = ? 9 8 4 6 8 Add along the diagonal line 6 + 1 + 9 = 16

Try the questions at the bottom of the worksheets

Grid Method – part 1 255 x 5 = ? 255 splits into 200, 50, 5 First split the number into hundreds, tens and units. 255 splits into 200, 50, 5 Then, multiply each of the numbers by 5. 200 x 5 = 1000 50 x 5 = 250 5 x 5 = 25 This can be placed in a grid

Grid Method – part 2 255 x 5 = ? x 200 50 5 200 x 5 50 x 5 5 x 5 1000 250 25 Finally, add the three numbers together to get your answer. 1000 + 250 25 = 1275  So 255 x 5 = 1 275

Grid Method – part 1 255 x 25 = 6375 First, split the numbers up. 255 splits into 200, 50 and 5. These go along the top of the grid. 25 splits into 20 and 5. These go down the sides. Put the numbers on the grid

Then, multiply each number in the column by each number in the row Then, multiply each number in the column by each number in the row. Have a look at the grid below.   Grid Method – part 2 255 x 25 = 6375 x 200 50 5 20 4000 1000 100 1000 250 25   Add up each column, then add the resulting numbers together. 4000 + 1000 100 = 5100 250 25 1275 6375 255 x 25 = 6 375

Try the questions again using the splitting method

2 1 x 3 Traditional method 21 x 13 = ? 6 3 2 1 2 7 3 3 x 1 = 3 write down the 3. 6 3 3 x 2 = 6 write down the 6 10 x 1 = 10 write down the 10 2 1 1 x 2 = 2 write down the 2 2 7 3 Add the numbers

4 5 x 3 Traditional method 45 x 34 = ? 1 8 1 3 5 1 5 3 3 1 2 4 x 5 = 20 write down the 0, carry the 2. 1 8 4 x 4 = 16, add 2 write down the 18 30 x 5 = 150 write down the 50, carry the one 1 3 5 3 x 4 =12, add the 1, write down the 13 1 5 3 3 Add the numbers

Try the questions again using the traditional method