Division
Lessons in this chapter
About Division
Division is the hardest arithmetic chapter of 4th grade, and it is the first time kids divide numbers too large to recall from a times table.
Divide Tens, Hundreds, and Thousands by Single-Digit Numbers and Estimate Quotients starts where the facts still reach. 2,400 ÷ 6 is 24 ÷ 6 with the place value carried, and estimating first is what stops an answer coming out ten times too large.
Identify Terms in a Division Sentence names dividend, divisor and quotient. The names matter because division is not commutative: 12 ÷ 3 and 3 ÷ 12 are different, and having words for the roles stops them being swapped.
Divide Using Partial Quotients is the method worth dwelling on. Instead of one tightly prescribed procedure, a child subtracts convenient multiples of the divisor and adds up how many they took. It is slower than long division and far easier to understand, and it leads to the same answer.
Divide Numbers up to 4-digits by single digit numbers, Relate Multiplication and Division and Solve Multi-Step Problems on Division finish the chapter, with multiplication as the check at every step.
All six lessons open as 4th grade math worksheets in the page. Divide Using Partial Quotients, Divide Numbers up to 4-digits by single digit numbers and Solve Multi-Step Problems on Division give division problems for fourth graders to work one at a time, scored as you answer. They are free to try, with no login needed for your first 3.
Frequently asked questions
Divide Tens, Hundreds, and Thousands by Single-Digit Numbers and Estimate Quotients starts where the times tables still reach, and Identify Terms in a Division Sentence names dividend, divisor and quotient. Divide Using Partial Quotients then gives the method worth dwelling on, before Divide Numbers up to 4-digits by single digit numbers, Relate Multiplication and Division and Solve Multi-Step Problems on Division finish the chapter. It sits in Number and Operations in Base Ten (4.NBT), with the multi-step problems in Operations and Algebraic Thinking (4.OA).
In 48 ÷ 6 = 8, the 48 is the dividend, the 6 is the divisor, and the 8 is the quotient. Naming them matters because the order cannot be swapped.
Subtracting convenient multiples of the divisor from the dividend and adding up how many you took. It is slower than long division and much easier to follow, and it gives the same answer.
Use the fact you know: 24 ÷ 6 is 4, so 2,400 ÷ 6 is 400. The place value carries straight through.
Because division errors tend to be out by a factor of ten. An estimate makes that obvious immediately, where a wrong digit otherwise looks plausible.
It checks it. Multiplying the quotient by the divisor should return the dividend, which catches most errors without redoing the division.