5th Grade Dividing by Two-Digit Divisors Lesson: Notes and Examples (Free PDF)

5th grade long division lesson – Maths PDF

Cover of the book Grade 5 Math Lessons (PDF)

Download as a PDFThe Grade 5 math lessons bookPrintable PDFSee the book ›

Sommaire

This 5th grade long division lesson covers dividing by two-digit divisors (Common Core 5.NBT.B.6), with a free PDF to print.

Key takeaway: This lesson helps fifth grade students divide whole numbers with up to four digits by two digit divisors.

Topic: Dividing by Two-Digit Divisors (5th grade)
Content: One-page lesson with a definition, a worked example and key facts
Standards: 5.NBT.B.6
Answers: Explanations included
Format: Free printable PDF, US Letter, black and white

To divide a whole number by a two-digit number, subtract easy multiples of the divisor from the dividend and add up how many you used. These are partial quotients. Estimate first with compatible numbers, keep going until what is left is smaller than the divisor, and write that leftover as the remainder.

This lesson helps fifth grade students divide whole numbers with up to four digits by two digit divisors. It builds from basic facts and multiples of ten to partial quotients and area models, so each step has a reason.

Students learn to estimate with compatible numbers, break a dividend into easy parts, and add the partial quotients. They also learn to write remainders and to decide what a remainder means in a story. Also, plan about 25 minutes. Work each example on paper, and write the multiples of the divisor in a small list first.

Grade 5 · Common Core State Standards: 5.NBT.B.6

Key facts in this 5th grade long division lesson

Key facts

The dividend is divided by the divisor to give the quotient.
Partial quotients break the answer into easy pieces that add up to the quotient.
An area model shows the dividend as an area with the divisor as one side.
Then, a remainder is always smaller than the divisor.
Check by multiplying the quotient by the divisor and adding the remainder.

What are the parts of a division problem?

In \(1{,}872\div24=78\), 1,872 is the dividend, 24 is the divisor and 78 is the quotient. If the dividend cannot be split evenly, the amount left over is the remainder. The remainder is always less than the divisor.

How do you divide with partial quotients?

Partial quotients let you subtract easy multiples of the divisor. Divide \(1{,}872\div24\).

Pick an easy multiple that fits: \(24\times50=1{,}200\). Subtract: \(1872-1200=672\).
Pick another: \(24\times20=480\). Subtract: \(672-480=192\).
Pick another: \(24\times8=192\). Subtract: \(192-192=0\).
Add the partial quotients: \(50+20+8=78\).

The quotient is 78.

Subtract friendly multiples of 24 until nothing is left.

How does an area model show division?

Think of 1,872 as the area of a rectangle. One side is 24. The other side is the quotient. You build the area in parts: 1,200, 480 and 192. The widths of the parts are 50, 20 and 8, which add to 78.

50 + 20 + 8 = 78 is the missing width.

How do you estimate a quotient?

Round the divisor to a friendly number. Then choose a dividend close to the real one that you can divide easily. These are called compatible numbers. For \(2{,}534\div37\), use \(2{,}400\div40=60\). The real quotient should be close to 60. Good compatible dividends are multiples of the rounded divisor, such as 2,400, 2,800 or 3,200 when the divisor is about 40.

The estimate is about 60.

What do you do with a remainder?

Keep dividing until what is left is less than the divisor. For \(2{,}534\div37\): take out 60 groups (\(37\times60=2{,}220\)), leaving 314. Take out 8 more groups (\(37\times8=296\)), leaving 18. The answer is 68 R 18. Check: \(37\times68+18=2{,}534\). In a word problem, think about what the remainder means.

Multiply, then add the remainder.

The meaning depends on the question. If 250 students ride buses that hold 48, five full buses leave 10 students behind, so you need 6 buses. If you put 500 stickers on album pages with 35 on each page, the 10 stickers that are left are simply left over.

5th grade long division lesson: questions and answers

What are partial quotients?

Partial quotients are the parts of the answer that you find one at a time. You subtract friendly multiples of the divisor, like 24 × 50, and then add the multipliers. For 1,872 ÷ 24 they are 50, 20 and 8, which add to 78.

How do I know when to stop dividing?

Stop when what is left is smaller than the divisor. If the leftover is 0, the division is exact. If the leftover is not 0, it is the remainder.

How do I check a division answer?

Multiply the quotient by the divisor and add the remainder. You should get the dividend. For \(475\div22=21\text{ R }13\), \(22\times21+13=475\).

What do I do with a remainder in a word problem?

Read the question. Sometimes you ignore the remainder, sometimes you round the answer up, and sometimes the remainder is the answer. For 250 students and buses that hold 48, you need 6 buses because 5 buses leave 10 students behind.

How do I estimate a quotient?

Use compatible numbers: round the divisor and change the dividend to a nearby number that divides easily. For \(3{,}185\div49\) use \(3{,}000\div50=60\).

Common mistakes with this 5th grade long division lesson

Students pick a partial quotient that is too small and stop early. Also, keep subtracting until the leftover is smaller than the divisor.
Students lose a place when they bring down digits. Instead, line up each digit of the quotient above its place in the dividend.
Students forget to check with multiplication. Also, multiply the quotient by the divisor and add the remainder to confirm.

How to study this chapter

Write the first nine multiples of the divisor before you start. Then, a list makes each partial quotient quick to choose.
Estimate with compatible numbers first. Finally, for a divisor near 30, think of a nearby multiple of 30.
Parents can ask the child to explain why the leftover must be smaller than the divisor. Repeat this habit on every problem for the best results.

Download the 5th grade long division lesson as a PDF with the button below and keep it with your notes.