Đại số sơ cấp Ví dụ

$1275.5 \div 7.5$

Bước 1

Lập bài toán chia ở dạng phép chia số lớn.

$7$

$5$

$1$

$2$

$7$

$5$

Bước 2

Di chuyển số thập phân ở cả hai số cùng một số lượng vị trí cho đến khi số chia là một số nguyên không âm.

$7$

$5$

$1$

$2$

$7$

$5$

Bước 3

Chia $127$ cho $75$ . Đặt chữ số này vào thương số trên biểu tượng chia.

				$1$
$7$	$5$	$1$	$2$	$7$	$5$	$5$

Bước 4

Nhân chữ số mới nhất của thương số $(1)$ với số chia $75$ .

				$1$
$7$	$5$	$1$	$2$	$7$	$5$	$5$
		$-$	$7$	$5$

Bước 5

Trừ $75$ khỏi $127$ .

				$1$
$7$	$5$	$1$	$2$	$7$	$5$	$5$
		$-$	$7$	$5$
			$5$	$2$

Bước 6

Hạ số tiếp theo của số bị chia xuống.

				$1$
$7$	$5$	$1$	$2$	$7$	$5$	$5$
		$-$	$7$	$5$
			$5$	$2$	$5$

Bước 7

Chia $525$ cho $75$ . Đặt chữ số này vào thương số trên biểu tượng chia.

				$1$	$7$
$7$	$5$	$1$	$2$	$7$	$5$	$5$
		$-$	$7$	$5$
			$5$	$2$	$5$

Bước 8

Nhân chữ số mới nhất của thương số $(7)$ với số chia $75$ .

				$1$	$7$
$7$	$5$	$1$	$2$	$7$	$5$	$5$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$

Bước 9

Trừ $525$ khỏi $525$ .

				$1$	$7$
$7$	$5$	$1$	$2$	$7$	$5$	$5$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$

Bước 10

Hạ số tiếp theo của số bị chia xuống.

				$1$	$7$
$7$	$5$	$1$	$2$	$7$	$5$	$5$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$

Bước 11

Chia $5$ cho $75$ . Đặt chữ số này vào thương số trên biểu tượng chia.

				$1$	$7$	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$

Bước 12

Nhân chữ số mới nhất của thương số $(0)$ với số chia $75$ .

				$1$	$7$	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$

Bước 13

Trừ $0$ khỏi $5$ .

				$1$	$7$	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$

Bước 14

Thêm một $0$ vào cuối số bị chia.

				$1$	$7$	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$

Bước 15

Hạ số tiếp theo của số bị chia xuống.

				$1$	$7$	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$

Bước 16

Chia $50$ cho $75$ . Đặt chữ số này vào thương số trên biểu tượng chia.

				$1$	$7$	$0$	.	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$

Bước 17

Nhân chữ số mới nhất của thương số $(0)$ với số chia $75$ .

				$1$	$7$	$0$	.	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$
						$-$		$0$

Bước 18

Trừ $0$ khỏi $50$ .

				$1$	$7$	$0$	.	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$
						$-$		$0$
							$5$	$0$

Bước 19

Thêm một $0$ vào cuối số bị chia.

				$1$	$7$	$0$	.	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$
						$-$		$0$
							$5$	$0$

Bước 20

Hạ số tiếp theo của số bị chia xuống.

				$1$	$7$	$0$	.	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$
						$-$		$0$
							$5$	$0$	$0$

Bước 21

Chia $500$ cho $75$ . Đặt chữ số này vào thương số trên biểu tượng chia.

				$1$	$7$	$0$	.	$0$	$6$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$
						$-$		$0$
							$5$	$0$	$0$

Bước 22

Nhân chữ số mới nhất của thương số $(6)$ với số chia $75$ .

				$1$	$7$	$0$	.	$0$	$6$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$
						$-$		$0$
							$5$	$0$	$0$
						$-$	$4$	$5$	$0$

Bước 23

Trừ $450$ khỏi $500$ .

				$1$	$7$	$0$	.	$0$	$6$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$
						$-$		$0$
							$5$	$0$	$0$
						$-$	$4$	$5$	$0$
								$5$	$0$

Bước 24

Thêm một $0$ vào cuối số bị chia.

				$1$	$7$	$0$	.	$0$	$6$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$	$0$	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$
						$-$		$0$
							$5$	$0$	$0$
						$-$	$4$	$5$	$0$
								$5$	$0$

Bước 25

Hạ số tiếp theo của số bị chia xuống.

				$1$	$7$	$0$	.	$0$	$6$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$	$0$	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$
						$-$		$0$
							$5$	$0$	$0$
						$-$	$4$	$5$	$0$
								$5$	$0$	$0$

Bước 26

Chia $500$ cho $75$ . Đặt chữ số này vào thương số trên biểu tượng chia.

				$1$	$7$	$0$	.	$0$	$6$	$6$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$	$0$	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$
						$-$		$0$
							$5$	$0$	$0$
						$-$	$4$	$5$	$0$
								$5$	$0$	$0$

Bước 27

Nhân chữ số mới nhất của thương số $(6)$ với số chia $75$ .

				$1$	$7$	$0$	.	$0$	$6$	$6$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$	$0$	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$
						$-$		$0$
							$5$	$0$	$0$
						$-$	$4$	$5$	$0$
								$5$	$0$	$0$
							$-$	$4$	$5$	$0$

Bước 28

Trừ $450$ khỏi $500$ .

				$1$	$7$	$0$	.	$0$	$6$	$6$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$	$0$	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$
						$-$		$0$
							$5$	$0$	$0$
						$-$	$4$	$5$	$0$
								$5$	$0$	$0$
							$-$	$4$	$5$	$0$
									$5$	$0$

Bước 29

Kết quả của phép chia của $1275.5 \div 7.5$ là $170.066 \dots$ .

$170.066 \dots$

				$1$	$7$
$7$	$5$	$1$	$2$	$7$	$5$	$5$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$

				$1$	$7$
$7$	$5$	$1$	$2$	$7$	$5$	$5$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$

				$1$	$7$	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$

				$1$	$7$	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$

				$1$	$7$	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$

				$1$	$7$	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$

				$1$	$7$	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$

				$1$	$7$	$0$	.	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$

				$1$	$7$	$0$	.	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$
						$-$		$0$

				$1$	$7$	$0$	.	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$
						$-$		$0$
							$5$	$0$

				$1$	$7$
$7$	$5$	$1$	$2$	$7$	$5$	$5$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$

				$1$	$7$
$7$	$5$	$1$	$2$	$7$	$5$	$5$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$

				$1$	$7$	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$

				$1$	$7$	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$

				$1$	$7$	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$

				$1$	$7$	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$

				$1$	$7$	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$

				$1$	$7$	$0$	.	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$

				$1$	$7$	$0$	.	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$
						$-$		$0$

				$1$	$7$	$0$	.	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$
						$-$		$0$
							$5$	$0$

				$1$	$7$
$7$	$5$	$1$	$2$	$7$	$5$	$5$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$

				$1$	$7$
$7$	$5$	$1$	$2$	$7$	$5$	$5$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$

				$1$	$7$	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$

				$1$	$7$	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$

				$1$	$7$	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$

				$1$	$7$	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$

				$1$	$7$	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$

				$1$	$7$	$0$	.	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$

				$1$	$7$	$0$	.	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$
						$-$		$0$

				$1$	$7$	$0$	.	$0$
$7$	$5$	$1$	$2$	$7$	$5$	$5$	.	$0$
		$-$	$7$	$5$
			$5$	$2$	$5$
		$-$	$5$	$2$	$5$
					$0$	$5$
				$-$		$0$
						$5$	$0$
						$-$		$0$
							$5$	$0$