Question Video: Determining the Divisibility of Numbers by Finding Their Quotient and Remainder Mathematics

Fill in the blanks in the table.


Video Transcript

Fill in the blanks in the following table.

There are four headings in the table. Division, quotient, remainder, and divisibility. In the top row of the table, the division calculation is 220 divided by 64. We’re told that the answer to this calculation is three remainder 28. There are three 64s in 220. And we have a remainder of 28. As there’s a remainder, 220 is not divisible by 64. We can check this answer by firstly multiplying 64 by three, using standard column multiplication. Three multiplied by four is equal to 12. We put a two in the units column and carry the one. Three multiplied by six is equal to 18. Adding the one that we carried gives us 19. Therefore, 64 multiplied by three is 192.

To calculate the remainder, we need to subtract 192 from 220. Zero minus two would give us a negative number. Therefore, we need to go next door and borrow one from the tens column. 10 minus two is equal to eight. Once again, we need to borrow, this time from the hundreds column. This leaves us with 11 minus nine in the tens column. This is equal to two. And one minus one equals zero. Therefore, our remainder is 28. 220 divided by 64 is equal to three remainder 28.

We can fill in the blanks by working out the division calculation 195 divided by 28. We could do this using the bus stop method. However, as 28 doesn’t go into 19, we would still have to divide 195 by 28. It is therefore easier to start by writing the numbers in the 28 times table. One multiplied by 28 is equal to 28. Two multiplied by 28 is equal to 56. A quick way of doing this is adding 28 to our previous answer. 28 plus 20 is equal to 48. And adding eight to this gives us 56. We can work out three multiplied by 28 by adding 28 to 56. This gives us 84 as 56 plus 20 is 76. And adding eight to this gives us 84.

We can repeat this method to work out four, five, six, and seven multiplied by 28. We can stop at this stage as 196, the answer to seven multiplied by 28, is greater than 195. This means that our quotient will be six. There are six 28s in 195. To work out the remainder, we need to subtract 168 from 195. Once again, our first step is to borrow one from the tens column. 15 minus eight is equal to seven. Eight minus six is equal to two. Finally, one minus one is equal to zero. This means that the remainder is 27. As there is a remainder, we can say that 195 is not exactly divisible by 28. The calculation 195 divided by 28 is equal to six remainder 27.

It’s important to note at this point that the remainder can never be higher than the number we’re dividing by. In this case, the remainder has to be less than 28. The highest possible remainder in this case is 27 as 196 divided by 28 would be equal to seven. If we’re dividing any of the numbers in the 28 times table by 28, there will be no remainder. And the number will be divisible.

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