# Video: Division Patterns with Decimals

Rupert works out that 64 ÷ 16 = 4. Use this fact to calculate 640 ÷ 16. Use a similar approach to find 64 ÷ 1.6. Again, use Rupert’s working out to help you find 6.4 ÷ 0.16.

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### Video Transcript

Rupert works out that 64 divided by 16 is equal to four. Use this fact to calculate 640 divided by 16. Use a similar approach to find 64 divided by 1.6. Again, use Rupert’s working to help you find 6.4 divided by 0.16.

We are told in the question that 64 divided by 16 is equal to four. We need to work out the answers to three similar calculations, 640 divided by 16, 64 divided by 1.6, and 6.4 divided by 0.16. One way of answering this question is to look at place value and what happens to a number when we multiply or divide by 10, 100, and 1000.

As 64 divided by 16 was equal to four, this can be written as 64 over 16 is equal to four over one. The first calculation we need to work out is 640 divided by 16, or 640 over 16. We have multiplied the numerator on the left-hand side by 10, as 64 multiplied by 10 is equal to 640. This means that we need to multiply the numerator of the right-hand side by 10. Whatever you did to the left-hand side you must do to the right-hand side. This gives us 40 over one. As 640 over 16 is equal to 40 over one, we know that 640 divided by 16 is it equal to 40.

We can use a similar approach for the second part, 64 divided by 1.6. In this case, the denominator has been divided by 10, as 16 divided by 10 is equal to 1.6. Dividing the denominator of the right-hand side by 10 gives us 0.1, as one divided by 10 is equal to 0.1. We can then multiply the numerator and denominator of this fraction to eliminate the decimal points.

Four multiplied by 10 is equal to 40. And 0.1 multiplied by 10 is equal to one. As 64 over 1.6 is equal to 40 over one, then 64 divided by 1.6 is equal to 40.

The final part of our question asked us to calculate 6.4 divided by 0.16. From the second part of the question, we know that 64 divided by 1.6 is equal to 40 over one. If we divide the numerator and denominator of the left-hand side by 10, we get 64 over 0.16. 64 divided by 10 is equal to 6.4. And 1.6 divided by 10 is equal to 0.16. This means that 64 over 1.6 is equivalent, or equal to, 6.4 divided by 0.16. This must also be equal to the fraction 40 over one.

Our third calculation, 6.4 divided by 0.16 is equal to 40. In fact, we have proved that 640 divided by 16, 64 divided by 1.6, and 6.4 divided by 0.16 all give us answers of 40. This is because all three of the fractions are equivalent. 640 over 16 is equal to 64 over 1.6 and is equal to 6.4 over 0.16.