What are some tips and tricks to divide large numbers mentally?

1 Use compatible numbers

One of the simplest ways to divide large numbers mentally is to use compatible numbers, which are numbers that are easy to work with and have round or simple factors. For example, if you want to divide 436 by 14, you can use compatible numbers such as 420 and 15, which are close to the original numbers and have factors of 10 and 5, respectively. Then, you can divide 420 by 15, which is 28, and adjust for the difference. Since 420 is 16 less than 436, and 15 is one more than 14, you can subtract one from 28 and get 27 as the answer.

2 Use halving and doubling

Another useful technique to divide large numbers mentally is to use halving and doubling, which is based on the fact that dividing by 2 is the same as multiplying by 0.5, and vice versa. For example, if you want to divide 720 by 24, you can halve both numbers until you get an easier division. Halving 720 gives you 360, and halving 24 gives you 12. Halving 360 gives you 180, and halving 12 gives you 6. Now, you can divide 180 by 6, which is 30, and that is the same as dividing 720 by 24.

4 Use chunking

A fourth method to divide large numbers mentally is to use chunking, which is a way of breaking down the large number into smaller parts or chunks that are easy to divide by the divisor. For example, if you want to divide 1548 by 12, you can use chunking to split 1548 into two chunks: 1200 and 348. Then, you can divide each chunk by 12 separately and add the results. Dividing 1200 by 12 gives you 100, and dividing 348 by 12 gives you 29. Adding 100 and 29 gives you 129, which is the answer.

5 Use factors and multiples

A fifth option to divide large numbers mentally is to use factors and multiples, which are numbers that divide or multiply into another number evenly. For example, if you want to divide 640 by 16, you can use factors and multiples to simplify the division. You can notice that both 640 and 16 have common factors of 2 and 4, which you can divide out. Dividing both numbers by 2 gives you 320 and 8, and dividing both numbers by 4 gives you 80 and 2. Now, you can divide 80 by 2, which is 40, and that is the same as dividing 640 by 16.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?