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`