Long Division

Grade 4 · Math · Study Guide

Learn step-by-step how to divide large numbers using the long division process.

Long division is a method for dividing large numbers by breaking the problem into a series of smaller steps. It can feel tricky at first, but once you know the steps, it becomes like following a recipe.

The four steps of long division repeat until you've divided the entire number: Divide, Multiply, Subtract, Bring down. A helpful way to remember this is the phrase "Does McDonald's Sell Burgers" — Divide, Multiply, Subtract, Bring down.

Here's how it works: start by looking at the first digit (or digits) of the number being divided (the dividend). Ask how many times the divisor fits into that number. Write that number above the division bar — that's part of your quotient. Multiply the divisor by that number, write the product below, then subtract. Bring down the next digit and repeat the process.

Sometimes numbers don't divide evenly. Whatever is left over at the end is called the remainder, and it is written as "R" after the quotient. For example, 25 ÷ 4 = 6 R1, because 4 goes into 25 six times (4 × 6 = 24), and 25 − 24 = 1 left over.

Practicing long division builds your number sense and prepares you for fractions and algebra later on.

Key terms

Dividend
The number being divided (the big number inside the division bracket).
Divisor
The number you are dividing by (the number outside the bracket).
Quotient
The answer to a division problem, written above the division bar.
Remainder
The amount left over after dividing as evenly as possible.
Long Division
A step-by-step method to divide large numbers using Divide, Multiply, Subtract, Bring down.

Flashcards

Dividend
The number you are dividing — it goes inside the division bracket.
Divisor
The number you divide by — it goes outside the bracket.
Quotient
The answer to a division problem.
Remainder
What is left over after dividing as evenly as possible.
Long Division Steps
Divide, Multiply, Subtract, Bring down — repeat until done.
Estimate
Making a smart guess about how many times the divisor fits into part of the dividend.
Check Your Work
Multiply your quotient by the divisor, then add the remainder — you should get the dividend back.

Questions

  1. What is 96 ÷ 4?

    1. 22
    2. 24
    3. 26
    4. 28
    Show answer

    Answer: 24

    96 ÷ 4 = 24. You can check: 4 × 24 = 96.

  2. In the problem 75 ÷ 5, the number 5 is called the dividend.

    Show answer

    Answer: False

    In 75 ÷ 5, the number 75 is the dividend (the number being divided). The number 5 is the divisor.

  3. What is the remainder when 29 is divided by 6?

    1. 3
    2. 4
    3. 5
    4. 2
    Show answer

    Answer: 5

    6 goes into 29 four times (6 × 4 = 24). 29 − 24 = 5, so the remainder is 5.

  4. In long division, after you subtract, you ___ down the next digit.

    Show answer

    Answer: bring

    After subtracting, you bring down the next digit of the dividend to continue dividing.

  5. What is 84 ÷ 7?

    1. 10
    2. 11
    3. 12
    4. 13
    Show answer

    Answer: 12

    84 ÷ 7 = 12. Check: 7 × 12 = 84.

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