In the last post, we looked at **multiplying and dividing by 10, 100 and 1000. **We are now going to look at how children can apply this skill to help them with other mental maths questions which will arise in the arithmetic test and during **grid method** for multiplication.

**Multiplying a two digit number by a one digit number**

Example 1: 34 x 5

Children can partition the number into tens and ones: 34 = 30 and 4

Then multiply each of these numbers by 5: 30 x 5 = 150 and 4 x 5 = 20

Then add the answers together: 150 + 20 = 170

If children struggle with the 30 x 5 part, they can divide 30 ÷ 10 (moving numbers one place to the right) to allow them to answer 3 x 5 = 15, which they know from their tables. Then, they need to multiply the answer by 10 (moving numbers one place to the left): 15 x 10 = 150.

Example 2: 63 x 4

Children can partition the number into tens and ones: 63 = 60 and 3

Then multiply each of these numbers by 4: 60 x 4 = 240 and 3 x 4 = 12

Then add the answers together: 240 + 12 = 252

If children struggle with the 60 x 4 part, they can divide 60 ÷ 10 (moving numbers one place to the right) to allow them to answer 6 x 4 = 24, which they know from their tables. Then, they need to multiply the answer by 10 (moving numbers one place to the left): 24 x 10 = 240.

**Using known facts to multiply and divide**

This is a Year 5 and 6 skill which depends on children being confident with their times tables. For more help with tables, see How to help your child learn their times tables and How to make times table learning fun!

Once children are confident with their times tables, they can use their times table facts to work with multiples of 10, 100 and 1000.

The general idea to make it easier to answer the question is to get back to the original times table by dividing each number (if needed, it may only be one of the numbers) by 10, 100 or 1000 (depending on the number of zeros in the number). Then, multiply the answer by the same amount.

e.g. Using their knowledge of 6 x 7 = 42 and their skills of multiplying and dividing by 10, 100 and 1000, they can try:

60 x 7 = 420 | Divide the 60 by 10 so that you can answer 6 x 7 then multiply the answer by 10. |

60 x 70 = 4200 | Divide the 60 by 10 and the 70 by 10 so that you can answer 6 x 7 then multiply the answer by 100*.
*The reason you multiply by 100 is because you divided both numbers by 10 and 10 x 10 = 100. |

600 x 7 = 4200 | Divide the 600 by 100 so that you can answer 6 x 7 then multiply the answer by 100. |

600 x 700 = 420 000 | Divide the 600 by 100 and divide the 700 by 100 so that you can answer 6 x 7 then multiply the answer by 10 000*.
*The reason you multiply by 10 000 is because you divided both numbers by 100 and 100 x 100 = 10 000. |

420 ÷ 6 = 70 | Divide 420 by 10 then answer 42 ÷ 6 and multiply by the answer by 10. |

4200 ÷ 7 = 600 | Divide 4200 by 100 then answer 42 ÷ 7 and multiply by the answer by 100. |

4200 ÷ 700 = 6 | Note: When you are dividing and you have to do the same to both numbers to get back to the original number e.g. in this case divide both numbers by 100 to answer 42 ÷ 7, you do not need to do anything to the answer as 4200 ÷ 700 = 6, which is the same answer as 42 ÷ 7 = 6. |

Now try these with your child: 7 x 8 , 70 x 8, 7 x 800, 70 x 80, 70 x 800, 560 ÷ 8, 5600 ÷ 70, 560 ÷ 70.

**Grid method**

When you are confident with multiplying and dividing by 10, 100 and 1000, it will be really useful for grid method. For further information, take a look at my post on multiplication written methods, including grid method.

Below is an example of grid method. The final answer is found by adding together the red amounts.

x | 3000 | 200 | 70 | 6 |

3 | 9000 | 600 | 210 | 18 |

Again, the general idea to make it easier to answer the question is to get back to the original times table by dividing each number (if needed, it may only be one of the numbers) by 10, 100 or 1000 (depending on the number of zeros in the number). Then, multiply the answer by the same amount.

If your child finds 3000 x 3 tricky, they can do 3000 ÷ 1000 = 3, which allows them to answer 3 x 3 = 9. Then, they need to multiply the answer by 1000 so 9 x 1000 = 9000.

If your child finds 200 x 3 hard to answer, they can do 200 ÷ 100 = 2, which allows them to answer 2 x 3 = 6. Then, they need to multiply the answer by 100 so 6 x 100 = 600.

To help with 70 x 3, they can do 70 ÷ 10 = 7, which allows them to answer 7 x 3 = 21. Then, they need to multiply the answer by 10 so 21 x 10 = 210.

For more information on private tutoring to help your child in Numeracy and/or Literacy, please see the Private Tutoring page.

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