Grade 4 · Math · 2 minutes
Long division, step by step
Divide, multiply, subtract, bring down. Then repeat.
Key terms
- Dividend
- The number being shared or divided, written inside the division bracket.
- Divisor
- The number you divide by, written outside the bracket on the left.
- Quotient
- The answer to a division problem, written on top of the bracket.
- Remainder
- The amount left over when a number can't be divided equally.
- Bring down
- The fourth step of long division, where you drop the next digit down beside what is left, then repeat.
Transcript
You have eight hundred fifty two stickers to share equally among six friends. How many stickers does each friend get? That's a job for long division: four small steps, on repeat.
First, draw the division bracket. The number we're sharing, the dividend, goes inside. The six, the divisor, goes outside, on the left. The answer, the quotient, goes on top.
Start on the left: eight hundreds. Step one, divide. How many sixes fit in eight? Just one. Write it above the eight. That's one hundred each. Step two, multiply. One times six is six. Step three, subtract. Eight minus six is two. Two hundreds left over.
Step four, bring down the five. Two hundreds are the same as twenty tens. Add the five tens, and we have twenty five tens. Now repeat. How many sixes fit in twenty five? Four. Four times six is twenty four. Twenty five minus twenty four is one.
Bring down the two to make twelve ones. Six fits in twelve exactly two times. Two times six is twelve. Twelve minus twelve is zero. Nothing left over. Each friend gets one hundred forty two stickers!
Now a faster one. Ninety five divided by four. Four fits in nine two times. Two times four is eight. Nine minus eight is one. Bring down the five: fifteen. Four fits in fifteen three times. Three times four is twelve. Fifteen minus twelve is three. No more digits, so the answer is twenty three, remainder three.
Now multiply to check. Twenty three times four is ninety two. Add the remainder of three, and we're back at ninety five. It matches!
So, the four steps: divide, multiply, subtract, bring down. Then repeat. Need a memory trick? Use the first letters. Dragons munch spicy burritos.
Sources
Every fact in the video, and where it comes from.
- 1learning.ccsso.org/wp-content/uploads/2022/11/Math_Standards1.pdf
- CCSS 4.NBT.B.6 (Grade 4): "Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models." The standard does not name the standard algorithm; fluency with it is expected in Grade 6 (6.NS.B.2).
- 2thecorestandards.org/Math/Content/4/NBT/B/6
- Text of 4.NBT.B.6 (web page copy of the standard).
- 3mathsisfun.com/long_division.html
- Long division repeats four steps until there are no more digits to bring down: divide, multiply, subtract, bring down.
- Worked example 1: 852 ÷ 6 = 142. Hundreds: 8 ÷ 6 = 1, 1 × 6 = 6, 8 − 6 = 2. Tens: 2 hundreds = 20 tens, plus 5 tens = 25 tens; 25 ÷ 6 = 4, 4 × 6 = 24, 25 − 24 = 1. Ones: 1 ten = 10 ones, plus 2 = 12; 12 ÷ 6 = 2, 2 × 6 = 12, 12 − 12 = 0. Check: 142 × 6 = 852. (Arithmetic recomputed by hand and in code; the method follows the linked source.)
- Worked example 2: 95 ÷ 4 = 23 remainder 3. 9 ÷ 4 = 2, 2 × 4 = 8, 9 − 8 = 1; bring down 5 to make 15; 15 ÷ 4 = 3, 3 × 4 = 12, 15 − 12 = 3. Check: 23 × 4 = 92, 92 + 3 = 95; remainder 3 is less than divisor 4. (Arithmetic recomputed by hand and in code; the method follows the linked source.)
- 4mathwords.com/l/long_division.htm
- The dividend is the number being divided, the divisor is the number you divide by, the quotient is the answer, and the remainder is the amount left over, which is always less than the divisor.
- 5mathsisfun.com/numbers/division-remainder.html
- A division answer can be checked with multiplication: quotient times divisor, plus the remainder, equals the dividend (shown by example: "Check it by multiplying: 5 × 3 + 4 = 19").
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