How to do long division with remainders?

 
Master Long Division Practice Workbook: Improve Your Math Fluency Series (Volume 8)

Basic Math and Pre-Algebra Workbook For Dummies 

Division, Ages 7-12 (Workbook w/Music CD) 

 

Solution for 768978 ÷ 358 - with remainder

Step 1 Long division works from left to right. Since 358 will not go into 7, a grey 0 has been placed over the 7 and we combine the first two digits to make 76. In this case, 76 is still too small. A further 0 is added above 6 and a third digit is added to make 768. Note the other digits in the original number have been turned grey to emphasise this. The closest we can get to 768 without exceeding it is 716 which is 2 × 358. These values have been added to the division, highlighted in red.

0 0 2  rem 352 358 7 6 8 9 7 8 7 1 6

358 × table 1 × 358 = 358 2 × 358 = 716 3 × 358 = 1074 4 × 358 = 1432 5 × 358 = 1790 6 × 358 = 2148 7 × 358 = 2506 8 × 358 = 2864 9 × 358 = 3222

Step 2 Next, work out the remainder by subtracting 716 from 768. This gives us 52. Bring down the 9 to make a new target of 529.	2  rem 352 358 7 6 8 9 7 8 7 1 6 5 2 9
358 × table 1 × 358 = 358 2 × 358 = 716 3 × 358 = 1074 4 × 358 = 1432 5 × 358 = 1790 6 × 358 = 2148 7 × 358 = 2506 8 × 358 = 2864 9 × 358 = 3222

Step 3 With a target of 529, the closest we can get is 358 by multiplying 358 by 1. Write the 358 below the 529 as shown.	2 1  rem 352 358 7 6 8 9 7 8 7 1 6 5 2 9 3 5 8
358 × table 1 × 358 = 358 2 × 358 = 716 3 × 358 = 1074 4 × 358 = 1432 5 × 358 = 1790 6 × 358 = 2148 7 × 358 = 2506 8 × 358 = 2864 9 × 358 = 3222

Step 4 Next, work out the remainder by subtracting 358 from 529. This gives us 171. Bring down the 7 to make a new target of 1717.	2 1  rem 352 358 7 6 8 9 7 8 7 1 6 5 2 9 3 5 8 1 7 1 7
358 × table 1 × 358 = 358 2 × 358 = 716 3 × 358 = 1074 4 × 358 = 1432 5 × 358 = 1790 6 × 358 = 2148 7 × 358 = 2506 8 × 358 = 2864 9 × 358 = 3222

Step 5 With a target of 1717, the closest we can get is 1432 by multiplying 358 by 4. Write the 1432 below the 1717 as shown.	2 1 4  rem 352 358 7 6 8 9 7 8 7 1 6 5 2 9 3 5 8 1 7 1 7 1 4 3 2
358 × table 1 × 358 = 358 2 × 358 = 716 3 × 358 = 1074 4 × 358 = 1432 5 × 358 = 1790 6 × 358 = 2148 7 × 358 = 2506 8 × 358 = 2864 9 × 358 = 3222

Step 6 Next, work out the remainder by subtracting 1432 from 1717. This gives us 285. Bring down the 8 to make a new target of 2858.	2 1 4  rem 352 358 7 6 8 9 7 8 7 1 6 5 2 9 3 5 8 1 7 1 7 1 4 3 2 2 8 5 8
358 × table 1 × 358 = 358 2 × 358 = 716 3 × 358 = 1074 4 × 358 = 1432 5 × 358 = 1790 6 × 358 = 2148 7 × 358 = 2506 8 × 358 = 2864 9 × 358 = 3222

Step 7 With a target of 2858, the closest we can get is 2506 by multiplying 358 by 7. Write the 2506 below the 2858 as shown.	2 1 4 7  rem 352 358 7 6 8 9 7 8 7 1 6 5 2 9 3 5 8 1 7 1 7 1 4 3 2 2 8 5 8 2 5 0 6
358 × table 1 × 358 = 358 2 × 358 = 716 3 × 358 = 1074 4 × 358 = 1432 5 × 358 = 1790 6 × 358 = 2148 7 × 358 = 2506 8 × 358 = 2864 9 × 358 = 3222

Step 8 Finally, subtract 2506 from 2858 giving 352. Since there are no other digits to bring down, 352 is therefore also the remainder for the whole sum. So 768978 ÷ 358 = 2147 rem 352	2 1 4 7  rem 352 358 7 6 8 9 7 8 7 1 6 5 2 9 3 5 8 1 7 1 7 1 4 3 2 2 8 5 8 2 5 0 6 3 5 2
358 × table 1 × 358 = 358 2 × 358 = 716 3 × 358 = 1074 4 × 358 = 1432 5 × 358 = 1790 6 × 358 = 2148 7 × 358 = 2506 8 × 358 = 2864 9 × 358 = 3222