Welcome to the division worksheets page at Math-Drills.com! Please give us your undivided attention while we introduce this page. Our worksheets for division help you to teach students the very important concept of division. If students have a good recall of multiplication facts, the division facts should be a breeze to teach. If you want your students to experience success in learning division, please make sure they know their multiplication facts to 81, how to multiply by 0 and how to multiply by 10. If they don't know these things, this is going to take a lot longer.

On this page you will find many Division Worksheets including division facts and long division with and without remainders. We start off with some division facts which as you know are just the multiplication facts expressed in a different way. The main difference is that you can't divide by 0 and get a real number. If you really want your students to impress, say at their dinner table when their parents ask them what they learned today, you can teach them that division by zero is undefined.

The rest of the page is devoted to long division which for some reason is disliked among some members of the population. Long division is most difficult when students don't know their multiplication facts, so make sure they know them first. Oh, we already said that. What about a long division algorithm... maybe the one you or your parents or your grandparents learned? We adamantly say, yes! The reason that you and your ancestors used it is because it is an efficient and beautiful algorithm that will allow you to solve some of the most difficult division problems that even base ten blocks couldn't touch. It works equally well for decimals and whole numbers. Long division really isn't that hard.

## Division Facts Worksheets

Division facts worksheets including division tables, division facts and worksheets with individual division facts.

### Division facts tables

Manipulatives can help students "get" the concept of division. For example, students could regroup base ten blocks into units, then divide the units into piles. For example, 81 ÷ 9 would end up being 9 piles of 9 units.

Division is essentially asing the question, "How many _____'s are in _____?" For the question, 81 ÷ 9, the prompt would sound like, "How many 9's are in 81?" This prompt will benefit students in later math studies when there are more complex concepts such as dividing decimals or fractions. "How many thirds are in four?" or even better,, How many third cups are in four cups?" If necessary, get out the measuring cups.

**Horizontal division facts** worksheets

**25**Horizontal Division Facts with Dividends to

**36**Horizontal Division Facts with Dividends to

**49**Horizontal Division Facts with Dividends to

**64**Horizontal Division Facts with Dividends to

**81**Horizontal Division Facts with Dividends to

**100**Horizontal Division Facts with Dividends to

**121**Horizontal Division Facts with Dividends to

**144**Horizontal Division Facts with Dividends to

**169**Horizontal Division Facts with Dividends to

**196**Horizontal Division Facts with Dividends to

**225**

**Vertical division facts** worksheets

**Dividends to 25**With Division Sign Vertical Division Facts

**Dividends to 36**With Division Sign Vertical Division Facts

**Dividends to 49**With Division Sign Vertical Division Facts

**Dividends to 64**With Division Sign Vertical Division Facts

**Dividends to 81**With Division Sign Large Print Vertical Division Facts

**Dividends to 81**With Division Sign Vertical Division Facts

**Dividends to 100**With Division Sign Vertical Division Facts

**Dividends to 121**With Division Sign Vertical Division Facts

**Dividends to 144**With Division Sign Vertical Division Facts

**Dividends to 169**With Division Sign Vertical Division Facts

**Dividends to 196**With Division Sign Vertical Division Facts

**Dividends to 225**With Division Sign Vertical Division Facts

**Dividends to 25**With Long Division Symbol (50 per page) Vertical Division Facts

**Dividends to 36**With Long Division Symbol (50 per page) Vertical Division Facts

**Dividends to 49**With Long Division Symbol (50 per page) Vertical Division Facts

**Dividends to 64**With Long Division Symbol (50 per page) Vertical Division Facts

**Dividends to 81**With Long Division Symbol (50 per page) Vertical Division Facts

**Dividends to 100**With Long Division Symbol (50 per page) Vertical Division Facts

**Dividends to 121**With Long Division Symbol (50 per page) Vertical Division Facts

**Dividends to 144**With Long Division Symbol (50 per page) Vertical Division Facts

**Dividends to 169**With Long Division Symbol (50 per page) Vertical Division Facts

**Dividends to 196**With Long Division Symbol (50 per page) Vertical Division Facts

**Dividends to 225**With Long Division Symbol (50 per page)

**Horizontal Division facts** worksheets with **focus facts** and **quotients from 1 to 9**

**Divisor of 1**(Quotient 1-9) Division Facts with a

**Divisor of 2**(Quotient 1-9) Division Facts with a

**Divisor of 3**(Quotient 1-9) Division Facts with a

**Divisor of 4**(Quotient 1-9) Division Facts with a

**Divisor of 5**(Quotient 1-9) Division Facts with a

**Divisor of 6**(Quotient 1-9) Division Facts with a

**Divisor of 7**(Quotient 1-9) Division Facts with a

**Divisor of 8**(Quotient 1-9) Division Facts with a

**Divisor of 9**(Quotient 1-9)

**Horizontal Division facts** worksheets with **focus facts** and **quotients from 1 to 12**

**Divisor of 1**(Quotient 1-12) Division Facts with a

**Divisor of 2**(Quotient 1-12) Division Facts with a

**Divisor of 3**(Quotient 1-12) Division Facts with a

**Divisor of 4**(Quotient 1-12) Division Facts with a

**Divisor of 5**(Quotient 1-12) Division Facts with a

**Divisor of 6**(Quotient 1-12) Division Facts with a

**Divisor of 7**(Quotient 1-12) Division Facts with a

**Divisor of 8**(Quotient 1-12) Division Facts with a

**Divisor of 9**(Quotient 1-12) Division Facts with a

**Divisor of 10**(Quotient 1-12) Division Facts with a

**Divisor of 11**(Quotient 1-12) Division Facts with a

**Divisor of 12**(Quotient 1-12)

**Division facts** worksheets with **combinations of focus facts**

## Long Division Worksheets

Long division worksheets for practicing various long division strategies including questions with no remainders, remainders and decimal quotients.

Need an easier way to divide large numbers? Try this method using powers of ten. To successfully use this method, students need to be able to multiply by powers of ten and to subtract. Students subtract the dividend multiplied by decreasing powers of ten until they have zero or a remainder. Example: 1458 ÷ 54. Note 54 × **1** = 54, 54 × **10** = 540 (nothing greater is needed). 1458 - 540 - 540 = 378. Note that 540 was subtracted twice, so the number of times that 54 "goes into" 1458 so far is 20 times. Continuing, 378 - 54 - 54 - 54 - 54 - 54 - 54 - 54 = 0. Since 54 was subtracted seven times, the quotient increases by seven for a total of 27. In other words, 54 "goes into" 1458, 27 times.

We might also mention that this method can be even more sophisticated by using multiples of powers of ten. In the above example, using 54 × 5 = 270 would have helped to get to the quotient quicker.

**Long division** worksheets with **no remainders**

### **European Long division** worksheets **with no remainders**

Have you ever thought that you could help a student understand things better and get a more precise answer while still using remainders? It's quite easy really. Remainders are usually given out of context, including on the answer keys below. A remainder is really a numerator in a fractional quotient. For example 19 ÷ 3 is 6 with a remainder of 1 which is more precisely 6 1/3. Using fractional quotients means your students will always find the exact answer to all long division questions, and in many cases the answer will actually be more precise (e.g. compare 6 1/3 with 6.3333....).

**Long division** worksheets **with remainders**

**Long division** worksheets with **decimal quotients**

### **European long division** worksheets **with remainders**

### **European long division** worksheets **with decimal quotients**

### Long Division **with Remainders** worksheets with the **steps shown** on the answer key

We thought it might be helpful to include some long division worksheets with the steps shown. The answer keys for these division worksheets use the standard algorithm that you might learn if you went to an English speaking school. Learning this algorithm by itself is sometimes not enough as it may not lead to a good conceptual understanding. One tool that helps students learn the standard algorithm and develop an understanding of division is a set of base ten blocks. By teaching students division with base ten blocks first then progressing to the standard algorithm, students will gain a conceptual understanding plus have the use of an efficient algorithm for long division. Students who have both of these things will naturally experience more success in their future mathematical studies.

**2-Digit by 1-Digit**Long Division with Remainders with the Steps Shown on the Answer Key

**3-Digit by 1-Digit**Long Division with Remainders with the Steps Shown on the Answer Key

**4-Digit by 1-Digit**Long Division with Remainders with the Steps Shown on the Answer Key

**5-Digit by 1-Digit**Long Division with Remainders with the Steps Shown on the Answer Key

**6-Digit by 1-Digit**Long Division with Remainders with the Steps Shown on the Answer Key

**3-Digit by 2-Digit**Long Division with Remainders with the Steps Shown on the Answer Key

**4-Digit by 2-Digit**Long Division with Remainders with the Steps Shown on the Answer Key

**5-Digit by 2-Digit**Long Division with Remainders with the Steps Shown on the Answer Key

**6-Digit by 2-Digit**Long Division with Remainders with the Steps Shown on the Answer Key

**4-Digit by 3-Digit**Long Division with Remainders with the Steps Shown on the Answer Key

**5-Digit by 3-Digit**Long Division with Remainders with the Steps Shown on the Answer Key

**6-Digit by 3-Digit**Long Division with Remainders with the Steps Shown on the Answer Key

## Long Division on a Grid

### Long division with **grid assistance** and **NO remainders** worksheets

Some students find it difficult to get everything lined up when completing a long division algorithm, so these worksheets include a grid and wider spacing of the digits to help students get things in the right place. The answer keys include the typical steps that students would record while completing each problem; however, slight variations in implementation may occur. For example, some people don't bother with the subtraction signs,some might show steps subtracting zero, etc.

**3-Digit by 1-Digit**Long Division with

**Grid Assistance and Prompts**and NO Remainders

**3-Digit by 2-Digit**Long Division with

**Grid Assistance and Prompts**and NO Remainders

**4-Digit by 1-Digit**Long Division with

**Grid Assistance and Prompts**and NO Remainders

**4-Digit by 2-Digit**Long Division with

**Grid Assistance and Prompts**and NO Remainders

**5-Digit by 1-Digit**Long Division with

**Grid Assistance and Prompts**and NO Remainders

**5-Digit by 2-Digit**Long Division with

**Grid Assistance and Prompts**and NO Remainders

**6-Digit by 1-Digit**Long Division with

**Grid Assistance and Prompts**and NO Remainders

**6-Digit by 2-Digit**Long Division with

**Grid Assistance and Prompts**and NO Remainders

**3-Digit by 1-Digit**Long Division with

**Grid Assistance**and NO Remainders

**3-Digit by 2-Digit**Long Division with

**Grid Assistance**and NO Remainders

**4-Digit by 1-Digit**Long Division with

**Grid Assistance**and NO Remainders

**4-Digit by 2-Digit**Long Division with

**Grid Assistance**and NO Remainders

**5-Digit by 1-Digit**Long Division with

**Grid Assistance**and NO Remainders

**5-Digit by 2-Digit**Long Division with

**Grid Assistance**and NO Remainders

**6-Digit by 1-Digit**Long Division with

**Grid Assistance**and NO Remainders

**6-Digit by 2-Digit**Long Division with

**Grid Assistance**and NO Remainders

### Long division with **grid assistance** and **SOME remainders** worksheets

**3-Digit by 1-Digit**Long Division with

**Grid Assistance and Prompts**and some Remainders

**3-Digit by 2-Digit**Long Division with

**Grid Assistance and Prompts**and some Remainders

**4-Digit by 1-Digit**Long Division with

**Grid Assistance and Prompts**and some Remainders

**4-Digit by 2-Digit**Long Division with

**Grid Assistance and Prompts**and some Remainders

**5-Digit by 1-Digit**Long Division with

**Grid Assistance and Prompts**and some Remainders

**5-Digit by 2-Digit**Long Division with

**Grid Assistance and Prompts**and some Remainders

**6-Digit by 1-Digit**Long Division with

**Grid Assistance and Prompts**and some Remainders

**6-Digit by 2-Digit**Long Division with

**Grid Assistance and Prompts**and some Remainders

**3-Digit by 1-Digit**Long Division with

**Grid Assistance**and some Remainders

**3-Digit by 2-Digit**Long Division with

**Grid Assistance**and some Remainders

**4-Digit by 1-Digit**Long Division with

**Grid Assistance**and some Remainders

**4-Digit by 2-Digit**Long Division with

**Grid Assistance**and some Remainders

**5-Digit by 1-Digit**Long Division with

**Grid Assistance**and some Remainders

**5-Digit by 2-Digit**Long Division with

**Grid Assistance**and some Remainders

**6-Digit by 1-Digit**Long Division with

**Grid Assistance**and some Remainders

**6-Digit by 2-Digit**Long Division with

**Grid Assistance**and some Remainders

## Divisibility Rules

Worksheets for practicing divisibility rules including a variety of small and large numbers and focusing on various divisors.

Divisibility by 2, 5 and 10

A number is divisible by 2 if the final digit (the digit in the ones place) is even. Numbers ending in 0, 2, 4, 6, or 8 therefore are divisible by 2. A number is divisible by 5 if the final digit is a 0 or a 5. A number is divisible by 10 if the final digit is a 0.

Divisibility by 3, 6 and 9

A number is divisible by 3 if the sum of its digits is divisible by 3. For example, 285 is divisible by 3 because 2 + 8 + 5 = 15 is divisible by 3. A number is divisible by 6 if it is divisible by both 3 and 2 (see above rules). A number is divisible by 9 if the sum of its digits is divisible by 9. For examples, 285 is not divisible by 9 because 2 + 8 + 5 = 15 is not divisible by 9.

Divisibility by 4, 7 and 8

A number is divisible by 4 if the last two digits of the number are divisible by 4. For 7, there are a couple of strategies to use. Please see Divisibility Tricks for Learning Math or Divisibility Rules and Prime Factorization for more information. A number is divisible by 8 if the last three digits are divisible by 8. This is the standard rule which can be a little sketchy for larger numbers, like who knows if 680 is divisible by 8? Because of this, we offer our Math-Drills.com solution which requires a little arithmetic, but can be accomplished quite easily with a little practice. As you know 8 is 2 to the third power, so we thought if you could divide the last three digits of a number by 2 three times, it would be divisible by 8. 680 ÷ 2 ÷ 2 ÷ 2 = 340 ÷ 2 ÷ 2 = 170 ÷ 2 = 85. We have a winner! 680 is indeed divisible by 8.

**Divisibility rules** for **2-digit** numbers

**Divisibility rules** for **3-digit** numbers

**Divisibility rules** for **4-digit** numbers

## Dividing in Other Number Systems

Dividing numbers in number systems other than decimal numbers including binary, quaternary, octal, duodecimal and hexadecimal numbers.

### Dividing in **other base number systems**

**Binary**Numbers (Base 2) Dividing

**Ternary**Numbers (Base 3) Dividing

**Quaternary**Numbers (Base 4) Dividing

**Quinary**Numbers (Base 5) Dividing

**Senary**Numbers (Base 6) Dividing

**Octal**Numbers (Base 8) Dividing

**Duodecimal**Numbers (Base 12) Dividing

**Hexadecimal**Numbers (Base 16) Dividing

**Vigesimal**Numbers (Base 20) Dividing

**Hexatrigesimal**Numbers (Base 36) Dividing

**Various**Numbers (Various Bases)