Video Transcript
Complete the table. And then, we’re given a table that’s got four different sections to it. The dividend, which doesn’t have a number in it in the moment. This is the number we need to complete. The divisor, which is 69. The quotient, which is 73. And the last section is the remainder, which shows 39.
So, our task is to work out which number belongs in the first box. And to do this, we need to understand what each of the four words mean. First of all, the dividend. In a division calculation, the dividend is the first number, the number that’s being divided by another number. And so, if we were to write out this table as a number sentence, we wouldn’t know what the first number is. This is our missing number.
The divisor in a division calculation is the second number. It’s the number that we’re dividing by. We can see that this number is 69. And so, our number sentence shows something divided by 69. In a division calculation, the quotient is the number of times that the divisor fits into the dividend. In other word, it’s the number of times that 69 fits into our mystery number. And we can see that it fits 73 times. There are 73 lots of 69 in our mystery number.
But the last column in our table shows us that we’ve got something left over. There is a remainder. And so, although we can say that 69 fits into our mystery number 73 times, there’s 39 left over. There’s a remainder of 39. So, how can we use what we know already to help calculate the dividend?
Let’s imagine for a moment that the calculation had no remainder, and that the division was just something divided by 69 equals 73. Well, if this was the case, we could simply work backwards and use the inverse operation to find the dividend. The quotient, which we know is 73, multiplied by the divisor, which we know is 69, we’re multiplying because we’re using the inverse operation, this will give us our dividend.
Remember, this was if we didn’t have a reminder, but we do have a remainder. And so, we need to add on this reminder to our number sentence. Instead of multiplying the quotient by the divisor to get the dividend, we need to multiply the quotient by the divisor and then add the remainder to find the dividend. And so, we need to calculate 73 multiplied by 69 add 39 to find the answer. We don’t actually need the brackets here because the order of operations means we need to multiply first anyway.
To begin with, let’s multiply 73 by 69. There are several ways we could find this answer. 69 is close to 70, so we could multiply 73 by 70, and then take away one lot of 73. Another method we could use is long multiplication. Let’s apply this method to find the answer.
First of all, we need to multiply the digits in 73 by nine. Three times nine equals 27. And seven tens multiplied by nine equals 63 tens, plus the two that we’ve exchanged, takes us to a total of 65 tens, or 650. Now we need to multiply both digits in 73 by the six digit. Remember that this six doesn’t stand for six ones but six tens, or 60. When we multiply by 60, it’s the same as multiplying by 10 and then by six.
If we write zero in the ones column, it shifts our answer one place to the left. This is the same as multiplying it by 10. So, now we can just multiply it by six. Three sixes are 18. And seven sixes are 42, plus the one we’ve exchanged, equals 43.
Now we’ve found out what 73 multiplied by nine and 73 multiplied by 60 are. We can add them together to find out what 73 multiplied by 69 is. Seven ones plus zero one equals seven ones. Five tens plus eight tens equals 13 tens. Six hundred plus three hundred equals nine hundred, plus the one underneath equals 10 hundreds, or 1000. And finally, we have 4000, plus the one we exchanged equals 5000 in the thousands column.
So, we know 73 multiplied by 69 equals 5037. Now all we need to do is to add the remainder. What’s 5037 add 39? We know 37 add 40 equals 77. And so, 37 add one less than 40, or 39, equals one less than 77. And so, our answer, the dividend, is 5076.
We haven’t got enough time in the video left to do this, but we could check our answer by dividing 5076 by 69. And if we worked out the missing number correctly, we’d get an answer of 73 reminder 39. We’ve found the answer by multiplying the divisor and the quotient together and then by adding the amount that was left over, the remainder. The dividend in our table is 5076.
