Common core division

Common core division is a way of dividing by using multiplication and subtraction instead. It subtracts in small chunks, in easy multiples like 2 or 10 or 100. You keep note of how many lots have been taken away to give the final answer.

Common core division is multiplication and subtraction

Common core division – Take chunks away from the core.

Common core divison = Repeated subtraction

NOTE:

Using this method means there are many different ways to subtract chunks from the division and so no two solutions to the problem will be the same.

Example 1

$420div3$

	$3$	$4$	$2$	$0$
		$3$	$0$	$0$		$100$
		$1$	$2$	$0$
			$3$	$0$		$10$
			$9$	$0$
			$3$	$0$		$10$
			$6$	$0$
			$3$	$0$		$10$
			$3$	$0$
			$3$	$0$		$10$
				$0$		$140$

To see every step broken down

Common core division step by step

Example 1

$420div3$


		$3$	$4$	$2$	$0$			At first put the $3$ in front of a division sign and the $420$ inside just as the traditional method.


		$3$	$4$	$2$	$0$				But unlike the traditional method we subtract easy amounts in small chunks. Such as $3xx100$ and keep a running total.
	$3xx100rArr$		$3$	$0$	$0$		$100$


		$3$	$4$	$2$	$0$
	Take away to give:		$3$	$0$	$0$		$100$
	Take away to give:		$1$	$2$	$0$				Take away the $300$ from the $420$


		$3$	$4$	$2$	$0$
			$3$	$0$	$0$		$100$
			$1$	$2$	$0$				Subtract $3xx10$ and add $10$ to the running total.
	$3xx10rArr$			$3$	$0$		$10$		Subtract $3xx10$ and add $10$ to the running total.


		$3$	$4$	$2$	$0$
			$3$	$0$	$0$		$100$
			$1$	$2$	$0$
	Take away to give:			$3$	$0$		$10$
	Take away to give:			$9$	$0$				Take $30$ away from the $120$


		$3$	$4$	$2$	$0$
			$3$	$0$	$0$		$100$
			$1$	$2$	$0$
				$3$	$0$		$10$
				$9$	$0$				Subtract $3xx10$ again and add to the running total.
	$3xx10rArr$			$3$	$0$		$10$		Subtract $3xx10$ again and add to the running total.


		$3$	$4$	$2$	$0$
			$3$	$0$	$0$		$100$
			$1$	$2$	$0$
				$3$	$0$		$10$
				$9$	$0$
	Take away to give:			$3$	$0$		$10$
	Take away to give:			$6$	$0$				Take $30$ away from $90$


		$3$	$4$	$2$	$0$
			$3$	$0$	$0$		$100$
			$1$	$2$	$0$
				$3$	$0$		$10$
				$9$	$0$
				$3$	$0$		$10$
				$6$	$0$				Subtract $3xx10$ again and add to the running total.
	$3xx10rArr$			$3$	$0$		$10$		Subtract $3xx10$ again and add to the running total.


		$3$	$4$	$2$	$0$
			$3$	$0$	$0$		$100$
			$1$	$2$	$0$
				$3$	$0$		$10$
				$9$	$0$
				$3$	$0$		$10$
				$6$	$0$
	Take away to give:			$3$	$0$		$10$		Take $30$ away from $60$
	Take away to give:			$3$	$0$


		$3$	$4$	$2$	$0$
			$3$	$0$	$0$		$100$
			$1$	$2$	$0$
				$3$	$0$		$10$
				$9$	$0$
				$3$	$0$		$10$
				$6$	$0$
				$3$	$0$		$10$
				$3$	$0$				Subtract $3xx10$ again and add to the running total.
	$3xx10rArr$			$3$	$0$		$10$		Subtract $3xx10$ again and add to the running total.


		$3$	$4$	$2$	$0$
			$3$	$0$	$0$		$100$
			$1$	$2$	$0$
				$3$	$0$		$10$
				$9$	$0$
				$3$	$0$		$10$
				$6$	$0$
				$3$	$0$		$10$
				$3$	$0$				Now take away the final $30$ leaving nothing.
	Take away to give:			$3$	$0$		$10$		Then add up the running totals on the right.
	Take away to give:				$0$		$140$

Answer: $420div3=140$

Answer: $420div3=140$

Example 2

$300div3$

	$3$	$3$	$0$	$0$
		$3$	$0$	$0$		$100$
				$0$		$100$

To see every step broken down

Answer: $300div3=100$

Example 3

$3684div24$

	$24$	$3$	$6$	$8$	$4$
		$2$	$4$	$0$	$0$		$100$
		$1$	$2$	$8$	$4$
		$1$	$2$	$0$	$0$		$50$
				$8$	$4$
				$4$	$8$		$2$
				$3$	$6$
				$2$	$4$		$1$
				$1$	$2$		$153$

To see every step broken down

Common core division step by step

Example 3

$3684div24$


		$24$	$3$	$6$	$8$	$4$				At first put the $24$ in front of a division sign and the $3684$ inside just as the traditional method


		$24$	$3$	$6$	$8$	$4$				But unlike the traditional method we subtract easy amounts in small chunks. Start with $24xx100=2400$ and keep a running total on the right
	$100xx24rArr$		$2$	$4$	$0$	$0$		$100$


		$24$	$3$	$6$	$8$	$4$
	Take away to give:		$2$	$4$	$0$	$0$		$100$		Take $2400$ from $3684$ .
	Take away to give:		$1$	$2$	$8$	$4$


		$24$	$3$	$6$	$8$	$4$
			$2$	$4$	$0$	$0$		$100$
			$1$	$2$	$8$	$4$				Subtract $50xx24$ and add $50$ to the running total.
	$50xx24rArr$		$1$	$2$	$0$	$0$		$50$		Subtract $50xx24$ and add $50$ to the running total.


		$24$	$3$	$6$	$8$	$4$
			$2$	$4$	$0$	$0$		$100$
			$1$	$2$	$8$	$4$
	Take away to give:		$1$	$2$	$0$	$0$		$50$		Take $1200$ from $1284$ .
	Take away to give:				$8$	$4$


		$24$	$3$	$6$	$8$	$4$
			$2$	$4$	$0$	$0$		$100$
			$1$	$2$	$8$	$4$
			$1$	$2$	$0$	$0$		$50$
					$8$	$4$				Subtract $2xx24$ and add $2$ to the running total.
	$2xx24rArr$				$4$	$8$		$2$		Subtract $2xx24$ and add $2$ to the running total.


		$24$	$3$	$6$	$8$	$4$
			$2$	$4$	$0$	$0$		$100$
			$1$	$2$	$8$	$4$
			$1$	$2$	$0$	$0$		$50$
					$8$	$4$
	Take away to give:				$4$	$8$		$2$
	Take away to give:				$3$	$6$				Take $48$ from $84$ to leave $36$ .


		$24$	$3$	$6$	$8$	$4$
			$2$	$4$	$0$	$0$		$100$
			$1$	$2$	$8$	$4$
			$1$	$2$	$0$	$0$		$50$
					$8$	$4$
					$4$	$8$		$2$
					$3$	$6$				Subtract $1xx24$ and add $1$ to the running total.
	$1xx24rArr$				$2$	$4$		$1$		Subtract $1xx24$ and add $1$ to the running total.


		$24$	$3$	$6$	$8$	$4$
			$2$	$4$	$0$	$0$		$100$
			$1$	$2$	$8$	$4$
			$1$	$2$	$0$	$0$		$50$
					$8$	$4$
					$4$	$8$		$2$
					$3$	$6$				Take $24$ from $36$ to leave $12$ .
	Take away to give:				$2$	$4$		$1$		Add the running totals on the right.
	Take away to give:				$1$	$2$		$153$

Answer: $3684div24=153$ remainder $12$

Answer: $3684div24=153$ remainder $12$

Example 4

$4673div15$

	$15$	$4$	$6$	$7$	$3$
		$1$	$5$	$0$	$0$		$100$
		$3$	$1$	$7$	$3$
		$1$	$5$	$0$	$0$		$100$
		$1$	$6$	$7$	$3$
		$1$	$5$	$0$	$0$		$100$
			$1$	$7$	$3$
			$1$	$5$	$0$		$10$
				$2$	$3$
				$1$	$5$		$1$
					$8$		$311$

To see every step broken down

Common core division step by step

Example 4

$4673div15$


		$15$	$4$	$6$	$7$	$3$				At first put $15$ in front of a division sign and the $4673$ inside just as the traditional method.


		$15$	$4$	$6$	$7$	$3$				But unlike the traditional method we subtract easy amounts in small chunks. Start with $15xx100=1500$ and keep a running total on the right.
	$15xx100$		$1$	$5$	$0$	$0$		$100$


		$15$	$4$	$6$	$7$	$3$
	Take away to give:		$1$	$5$	$0$	$0$		$100$
	Take away to give:		$3$	$1$	$7$	$3$				Take $1500$ away from $4673$


		$15$	$4$	$6$	$7$	$3$
			$1$	$5$	$0$	$0$		$100$		Subtract $15xx100$ again and add $100$ to the running total on the right.
			$3$	$1$	$7$	$3$
	$15xx100$ again		$1$	$5$	$0$	$0$		$100$


		$15$	$4$	$6$	$7$	$3$
			$1$	$5$	$0$	$0$		$100$
			$3$	$1$	$7$	$3$
	Take away to give:		$1$	$5$	$0$	$0$		$100$		Take $1500$ away from $3173$
	Take away to give:		$1$	$6$	$7$	$3$				Take $1500$ away from $3173$


		$15$	$4$	$6$	$7$	$3$
			$1$	$5$	$0$	$0$		$100$
			$3$	$1$	$7$	$3$
			$1$	$5$	$0$	$0$		$100$		Subtract $15xx100$ again and add $100$ to the running total on the right.
			$1$	$6$	$7$	$3$
	$15xx100$ again		$1$	$5$	$0$	$0$		$100$


		$15$	$4$	$6$	$7$	$3$
			$1$	$5$	$0$	$0$		$100$
			$3$	$1$	$7$	$3$
			$1$	$5$	$0$	$0$		$100$
			$1$	$6$	$7$	$3$
	Take away to give:		$1$	$5$	$0$	$0$		$100$
	Take away to give:			$1$	$7$	$3$				Take $1500$ away from $1673$


		$15$	$4$	$6$	$7$	$3$
			$1$	$5$	$0$	$0$		$100$
			$3$	$1$	$7$	$3$
			$1$	$5$	$0$	$0$		$100$
			$1$	$6$	$7$	$3$
			$1$	$5$	$0$	$0$		$100$
				$1$	$7$	$3$				Subtract $15xx10$ and add $10$ to the running total on the right.
	$15xx10$			$1$	$5$	$0$		$10$


		$15$	$4$	$6$	$7$	$3$
			$1$	$5$	$0$	$0$		$100$
			$3$	$1$	$7$	$3$
			$1$	$5$	$0$	$0$		$100$
			$1$	$6$	$7$	$3$
			$1$	$5$	$0$	$0$		$100$
				$1$	$7$	$3$
	Take away to give:			$1$	$5$	$0$		$10$		Take $150$ away from $173$
	Take away to give:				$2$	$3$				Take $150$ away from $173$


		$15$	$4$	$6$	$7$	$3$
			$1$	$5$	$0$	$0$		$100$
			$3$	$1$	$7$	$3$
			$1$	$5$	$0$	$0$		$100$
			$1$	$6$	$7$	$3$
			$1$	$5$	$0$	$0$		$100$
				$1$	$7$	$3$
				$1$	$5$	$0$		$10$		Subtract $15xx1$ and add $1$ to the running total on the right.
					$2$	$3$
	$15xx1$				$1$	$5$		$1$


		$15$	$4$	$6$	$7$	$3$
			$1$	$5$	$0$	$0$		$100$
			$3$	$1$	$7$	$3$
			$1$	$5$	$0$	$0$		$100$		Take $15$ from $23$ and it leaves $8$ which is less than $15$ , and so is the remainder.
			$1$	$6$	$7$	$3$
			$1$	$5$	$0$	$0$		$100$
				$1$	$7$	$3$
				$1$	$5$	$0$		$10$		Add up the running totals on the right to give the final answer less the remainder.
					$2$	$3$
	Take away to give:				$1$	$5$		$1$
	Take away to give:					$8$		$311$

Answer: $4673div15=311$ remainder $8$

Answer: $4673div15=311$ remainder $8$