Long Division

To check your long-division answer, use this formula:

$$ \text{Quotient} \times \text{Divisor} + \text{Remainder} = \text{Dividend} $$

For example, you solved:

$$ 364 \div 30 = 12\ \text{R}\ 4$$

Let’s identify each part:

• Dividend = 364 → the number being divided
• Divisor = 30 → the number you’re dividing by
• Quotient = 12 → how many whole times 30 fits into 364
• Remainder = 4 → what’s left over

Substitute the numbers:

$$ 12 \times 30 + 4 = 360 + 4 = 364$$

It matches the original number (364), so the division is correct! ✅

Let’s use long division to divide 1615 by 7.

• Set it up:
  • 1615 is the dividend (the number being divided).
  • 7 is the divisor (the number you’re dividing by).
• Divide the first digits:
  • 7 goes into 16 two times.
  • Write 2 above the 6 in the quotient area.
  • Multiply: 2 × 7 = 14
  • Subtract: 16 − 14 = 2
• Bring down the next digit (1):
  • Now you have 21
  • 7 goes into 21 three times.
  • Write 3 in the quotient
  • Multiply: 3 × 7 = 21
  • Subtract: 21 − 21 = 0
• Bring down the last digit (5):
  • Now you have 5
  • 7 goes into 5 zero times.
  • Write 0 in the quotient
  • Subtract: 5 − 0 = 5

• Result:

  • There are no more digits to bring down, so the quotient is 230, and the remainder is 5.
  • So:  1615 ÷ 7 = 230 R 5

To double-check that your calculation is correct, use this formula:

$$ \text{Quotient} \times \text{Divisor} + \text{Remainder} = \text{Dividend} $$

$$ 230 \times 7 + 5 = 1610 + 5 = 1615$$

It matches the original number (1615), so the division is correct! ✅