Unit 2 · Topic 04 · Operations
456 sweets, 15 children, share them equally.
Kabir's calculator said 30.4.
He announced that each child gets thirty sweets and four tenths of a sweet, and the class started arguing about who would cut them.
Ms. Rao had brought in a jar with 456 sweets and asked how to share them equally among the 15 children in the group.
Kabir typed it in. "Thirty point four each."
"Show me four tenths of a sweet," said Ms. Rao.
There was a pause. Anaya said, "You'd have to cut it."
"And these are boiled sweets. So what does the point four actually mean here?"
Kabir looked at his screen. He did not know.
Ms. Rao set the long division out on the board instead, and named each step as she did it. "Divide. Multiply. Subtract. Bring down. Then start again."
15 into 45 goes 3 times. 3 × 15 = 45. 45 − 45 = 0. Bring down the 6.
15 into 6 goes 0 times. Write 0 in the quotient. 0 × 15 = 0. 6 − 0 = 6. Nothing left to bring down.
"Quotient 30, remainder 6," she said. "Now — thirty sweets each, and six sweets left in the jar. Nobody cuts anything."
Kabir compared the two answers. 30.4 and 30 remainder 6. "Are they both right?"
"They are the same division. The calculator turned the leftover six into a fraction of fifteen, which is 0.4. That is correct and useless. You cannot hand a child 0.4 of a boiled sweet. When the things are whole, the remainder is the honest answer."
She wrote the check underneath: 15 × 30 + 6 = 450 + 6 = 456.
"That is how you know you have not slipped. Divisor times quotient, plus remainder, must give you back exactly what you started with."
Then she gave them one more. "A rope 1000 cm long, cut into 35 cm pieces. How many pieces?"
28 pieces, remainder 20. Anaya said, "So 28 pieces and a 20 cm offcut."
"And if I had asked how many 35 cm pieces you can get, the answer is 28. Not 28.57. The leftover is not a piece."
Long division repeats one four-step cycle until there is nothing left to bring down: DIVIDE, MULTIPLY, SUBTRACT, BRING DOWN.
Divide asks how many times the divisor fits into the current working number. Multiply that answer by the divisor. Subtract to find what is left over. Bring down the next digit, and start the cycle again.
The remainder must always be SMALLER than the divisor. If it is not, the divisor could have gone in at least one more time, so the quotient digit was too small.
Every division can be checked exactly: divisor × quotient + remainder must return the original number. And in a real sharing problem the remainder is usually the honest answer — you cannot give a child 0.4 of a sweet, so 30 each with 6 left over says more than 30.4 does.
Count the pages in a book and divide by 7 to see how many full weeks of reading it is, and how many pages are left over.
Check your answer with divisor × quotient + remainder. If it does not return the page count, find the step where a digit went missing.
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