Short division
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Otis
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Hello Andy. I'm assuming that your brother's son already understands longhand division, so that he could do the division shown above were he to know all the digits.
When I look at the 'quotient' above (that's the 3-digit number 2_7), I note two things:
1) There's no remainder shown to the right of the quotient, so we know the number _8 divides the number _175 evenly. Or, said another way, we know that _8 times 2_7 equals _175 exactly.
2) The first digit of the quotient (which is 2) has been written directly above the 1 in the 'dividend' (the dividend is the 4-digit number being divided). Therefore, we know that the number _8 goes into some 2-digit number _1 two times. Or, said another way, we want _8 times 2 to be less than or equal to the 2-digit number _1, just as if we were starting the division with known numbers.
Now we can experiment with different possibilities for the divisor _8.
2×18 = 36, so if the divisor _8 is actually 18, then _175 would have to be 4175. Can you see why? Think about dividing 4175 by 18 longhand. We would write 2 in the quotient because 18 goes into 41 two times.
2×28 = 56, so if the divisor is 28, then _175 would have to be 6175 because 28 goes into 61 two times.
I hope this is enough information for your brother's son to reason out the solution, by making educated guesses and checking the possibilities.
?
When I look at the 'quotient' above (that's the 3-digit number 2_7), I note two things:
1) There's no remainder shown to the right of the quotient, so we know the number _8 divides the number _175 evenly. Or, said another way, we know that _8 times 2_7 equals _175 exactly.
2) The first digit of the quotient (which is 2) has been written directly above the 1 in the 'dividend' (the dividend is the 4-digit number being divided). Therefore, we know that the number _8 goes into some 2-digit number _1 two times. Or, said another way, we want _8 times 2 to be less than or equal to the 2-digit number _1, just as if we were starting the division with known numbers.
Now we can experiment with different possibilities for the divisor _8.
2×18 = 36, so if the divisor _8 is actually 18, then _175 would have to be 4175. Can you see why? Think about dividing 4175 by 18 longhand. We would write 2 in the quotient because 18 goes into 41 two times.
2×28 = 56, so if the divisor is 28, then _175 would have to be 6175 because 28 goes into 61 two times.
I hope this is enough information for your brother's son to reason out the solution, by making educated guesses and checking the possibilities.
?
Steven G
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To OP:
Otis gave you a great starting.
Unless I am missing something Otis made a slight mistake by saying
2×18 = 36, so if the divisor _8 is actually 18, then _175 would have to be 4175. Can you see why? Think about dividing 4175 by 18 longhand. We would write 2 in the quotient because 18 goes into 41 two times.
Since 3*18 = 54, I feel that the divisor _8 is actually 18, then _175 could be 4175 OR 5175.
Unfortunately this gives more cases to consider.
Otis gave you a great starting.
Unless I am missing something Otis made a slight mistake by saying
2×18 = 36, so if the divisor _8 is actually 18, then _175 would have to be 4175. Can you see why? Think about dividing 4175 by 18 longhand. We would write 2 in the quotient because 18 goes into 41 two times.
Since 3*18 = 54, I feel that the divisor _8 is actually 18, then _175 could be 4175 OR 5175.
Unfortunately this gives more cases to consider.
Steven G
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Wait a minute. There is something wrong with this problem!
When you multiply ?8 by 2?7 the answer should be ?175 but this can NOT happen!
1st note that 8*7 = 56 ends in a 6.
So ?8 times 2?7 MUST end in a 6. Therefore the product can not be ?175 as that number ends in a 5.
So no solution!!
When you multiply ?8 by 2?7 the answer should be ?175 but this can NOT happen!
1st note that 8*7 = 56 ends in a 6.
So ?8 times 2?7 MUST end in a 6. Therefore the product can not be ?175 as that number ends in a 5.
So no solution!!
Otis
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You're correct, Jomo; I goofed. And it's even worse than you think. I didn't catch the 8×7=56 issue when mentally checking my strategy, as I clearly remember thinking 8×7=35. ?
I'll be in the corner, if anybody needs me …
\(\;\)
Steven G
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Don't worry about being in the corner alone as I will probably be there soon.