Divide 974 by 5

Long Division with Three-Digit Dividends

5974

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Let's start by dividing the leftmost digit in the dividend
00:08 Write the result without the remainder above
00:12 Now multiply the result by the divisor
00:16 Subtract the product from the number
00:22 Now bring down the next digit and use the same steps
00:25 Divide
00:29 Write the result without the remainder above, pay attention to positioning
00:32 Multiply the result and subtract
00:39 Now bring down the next digit and use the same steps
00:43 Divide
00:47 Write the result without the remainder above, pay attention to positioning
00:50 Multiply the result and subtract
00:58 We got a remainder of 4
01:02 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

5974

2

Step-by-step solution

To solve this problem using long division, follow these steps:

  • Step 1: Start with the first digit of the dividend.
  • The dividend is 974, and the divisor is 5.
    Take the first digit of the dividend, which is 9. Divide 9 by 5 to get 1 because 5 goes into 9 once.

  • Step 2: Subtract and bring down the next digit.
  • Multiply the divisor (5) by the quotient digit (1): 5×1=55 \times 1 = 5.
    Subtract this from 9 to get a remainder of 4: 95=49 - 5 = 4.
    Bring down the next digit from the dividend (7), making the new number 47.

  • Step 3: Repeat the division process.
  • Now divide 47 by 5. 5 goes into 47 nine times, so the next digit of the quotient is 9.
    Multiply the divisor (5) by this quotient digit (9): 5×9=455 \times 9 = 45.
    Subtract this from 47 to get a remainder of 2: 4745=247 - 45 = 2.
    Bring down the final digit (4), making the new number 24.

  • Step 4: Divide the last number.
  • Finally, divide 24 by 5. 5 goes into 24 four times. The last digit of the quotient is 4.
    Multiply the divisor (5) by 4: 5×4=205 \times 4 = 20.
    Subtract this from 24 to get a final remainder of 4: 2420=424 - 20 = 4.

Thus, the result of 974 divided by 5 is a quotient of 194194 with a remainder of 44.

The correct choice is therefore Choice 4: 194194 with a remainder of 44.

3

Final Answer

194 194 with a remainder of 4

Key Points to Remember

Essential concepts to master this topic
  • Division Steps: Divide each digit position systematically from left to right
  • Technique: Multiply quotient digit by divisor: 5×9=45 5 \times 9 = 45 , then subtract
  • Check: Multiply quotient by divisor and add remainder: 194×5+4=974 194 \times 5 + 4 = 974

Common Mistakes

Avoid these frequent errors
  • Forgetting to bring down the next digit after subtraction
    Don't subtract and then try to divide the remainder alone = incomplete division! This skips digits and gives a quotient that's too small. Always bring down the next digit from the dividend before continuing to the next division step.

Practice Quiz

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216

FAQ

Everything you need to know about this question

What if the first digit is smaller than the divisor?

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If 5 won't go into 9, you'd take the first two digits (like 97) and divide by 5. The quotient would then be a 2-digit number instead of 3-digit.

How do I know when to stop dividing?

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Stop when you've brought down all digits from the original number (974). The final remainder should be smaller than the divisor - here, remainder 4 is less than divisor 5.

Can I check my answer without doing the whole multiplication?

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Yes! Use the division relationship: Dividend = Quotient × Divisor + Remainder. So 974=194×5+4 974 = 194 \times 5 + 4 should be true.

What if I get a different remainder than the choices show?

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Double-check your subtraction at each step! The most common error is subtracting incorrectly when bringing down digits. Work slowly and verify each calculation.

Why does 5 go into 47 exactly 9 times?

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Because 5×9=45 5 \times 9 = 45 , which is the largest multiple of 5 that doesn't exceed 47. The next multiple 5×10=50 5 \times 10 = 50 would be too big!

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