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**Free Math Worksheets for Grade 6**

These worksheets provide additional calculation practice for nearly all sixth grade math topics, following the Common Core standards and Math Mammoth grade 6 curriculum. Use them as you need!

The worksheets are generated automatically each time you click on the links below. You can print them directly from your browser window, but first check how it looks like in the "Print Preview".

If the worksheet does not fit the page in the Print Preview, adjust your margins, header, and footer in the Page Setup settings of the browser. Or, adjust the "scale" to 90% or less in the Print Preview. Some browsers may have "Print to fit" option, which will automatically scale the worksheet to be so small as to fit the printable area.

The problem sheets are randomly generated, so you can get a new, different one just by hitting the refresh button on your browser (or F5).

They all come with an answer key; however, you need to click to the answer key page *immediately* after generating a worksheet, because the answer key also is generated 'on the fly', and won't exist later on, should you come looking for it later.

In sixth grade, students will start the study of beginning algebra (order of operations, expressions, and equations). They learn about ratios & percent and start using integers. Students also review long division, factoring, fraction arithmetic, and decimal arithmetic.In geometry, the focus is on the area of triangles and polygons and the volume of rectangular prisms. Other topics include rounding, exponents, GCF, LCM, and measuring units. Please note that these free worksheets do not cover all 6th grade topics; most notably, they do not include problem solving.

*Jump to:*Multiplication and division |

### Multiplication and Division and Some Review

**Long multiplication**

Multiply a 4-digit number by a 2-digit number

Multiply a 5-digit number by a 2-digit number

Multiply a 3-digit number by a 3-digit number

Multiply a 4-digit number by a 3-digit number

Multiply a 4-digit number by a 4-digit number

**Long division**

1-digit divisor, 5-digit dividend, no remainder

1-digit divisor, 5-digit dividend, with remainder

1-digit divisor, 6-digit dividend, no remainder

1-digit divisor, 6-digit dividend, with remainder

1-digit divisor, 7-digit dividend, no remainder

1-digit divisor, 7-digit dividend, with remainder

2-digit divisor, 5-digit dividend, no remainder

2-digit divisor, 5-digit dividend, with remainder

2-digit divisor, 6-digit dividend, no remainder

2-digit divisor, 6-digit dividend, with remainder

2-digit divisor, 7-digit dividend, no remainder

2-digit divisor, 7-digit dividend, with remainder

3-digit divisor, 6-digit dividend, with remainder

3-digit divisor, 7-digit dividend, no remainder

3-digit divisor, 7-digit dividend, with remainder

If you wish for a smaller font size, more problems, more or less space, and so
on, you can *
generate the worksheets yourself!*

Multiply decimals, writing the numbers under each other (0-2 decimal
digits)

Divide a whole number or a decimal by a whole number, need to add zeros to
the dividend

Convert a fraction to a decimal using long division, rounding the answers to three decimals

**Convert measuring units using long division & multiplication**

Convert between inches & feet

Convert between inches, feet, and yards

Convert between ounces & pounds

**Primary Grade Challenge Math** by Edward Zaccaro

A good book on problem solving with very varied word problems and strategies on how to solve problems. Includes chapters on: Sequences, Problem-solving, Money, Percents, Algebraic Thinking, Negative Numbers, Logic, Ratios, Probability, Measurements, Fractions, Division. Each chapter’s questions are broken down into four levels: easy, somewhat challenging, challenging, and very challenging.

### Exponents

Easy exponents

Challenge exponents

Write using exponents

### Place value/Rounding

Write a number in expanded form (up to 9 digits)

Write a number in expanded form (up to 12 digits)

Write a number given in expanded form in normal form (up to 9 digits), the parts are scrambled

Write a number given in expanded form in normal form (up to 12 digits), the parts are scrambled

Write a decimal number given in expanded form in normal form (up to 6 decimal digits), the parts are scrambled

Mixed rounding problems 1 - rounding to the underlined digit, up to rounding to the nearest million

Mixed rounding problems 2 - round to the underlined digit, up to rounding to the nearest trillion

### Algebra

**Order of operations**

Three operations, uses ÷ for division, no exponents

Four operations, uses ÷ for division, no exponents

Two or three operations, uses the fraction line for division, exponents included

Two, three, or four operations, uses the fraction line, exponents included

**Expressions**

Evaluate expressions: usually one operation, no negative numbers

Evaluate expressions: usually one operation, larger numbers, no negative numbers

Write a number expression from expression given in words: one operation

Write a number expression from expression given in words: two operations

Simplify expressions (by combining like terms; no negative numbers)

Multiply using the distributive property

**Equations**

One-step equations with whole numbers (no negative numbers involved)

One-step equations where you need to first simplify something on one side
(no negative numbers involved)

**Key to Algebra Workbooks**

Key to Algebra offers a unique, proven way to introduce algebra to your students. New concepts are explained in simple language, and examples are easy to follow. Word problems relate algebra to familiar situations, helping students to understand abstract concepts. Students develop understanding by solving equations and inequalities intuitively before formal solutions are introduced. Students begin their study of algebra in Books 1-4 using only integers. Books 5-7 introduce rational numbers and expressions. Books 8-10 extend coverage to the real number system.

### Fractions vs. Decimals

Decimals to fractions
or mixed numbers (tenths/hundredths/thousandths)

Decimals to fractions
or mixed numbers (up to millionths)

Mixed numbers to decimals (denominators 10, 100, and 1000)

Proper and improper fractions to decimals (denominators 10, 100, or 1000)

Proper fractions to decimals
(denominators powers of ten till 1,000,000)

Mixed numbers to decimals
(denominators powers of ten, till 1,000,000)

Fractions or mixed numbers to decimals (easy, varied denominators)

Fraction to decimals - need long division

Fractions to decimals - mixed practice

*Generate these yourself*

### Decimal Addition and Subtraction

Mental addition/subtraction with up to 2 decimal digits

Mental addition/subtraction - missing number

Decimal addition or subtraction with 1-3 decimal digits

Decimal addition or subtraction with 1-6 decimal digits

Decimal addition, four addends

Decimal subtraction, two subtrahends

*Generate decimal addition/subtraction sheets yourself*

**Key to Decimals Workbooks**

This is a workbook series by Key Curriculum Press that begins with basic concepts and operations on decimals. Then the books cover real-world uses of decimals in pricing, sports, metrics, calculators, and science.

The set includes books 1-4.

### Decimal Multiplication

**Mental multiplication**

Multiply a whole number and a decimal (1-3 decimal digits), easy

Same as above, but with a missing factor

Multiply a decimal by decimal mentally (up to 2 decimal digits times 2 decimal digits)

Multiply a decimal by decimal mentally (up to 3 decimal digits times 3 decimal digits)

Missing factor problems 1 (decimal by decimal, 1 or 2 decimals)

Missing factor problems 2 (decimal by decimal, 1-3 decimals)

Multiply by 10, 100, or 1000 (1-3 decimal digits)

Like above, but missing factor

Multiply decimals by 10, 100, 1000, 10000, or 100,000 (1-5 decimal digits)

Like above but missing factor

**Multiply in columns**

Multiply a decimal with 1-3 decimal digits by a whole number

Multiply a decimal with 1-2 decimal digits by another decimal with 1-2 decimal digits

Multiply a decimal with 1-3 decimal digits by another decimal with 1-3 decimal digits

### Decimal Division

**Mental division
**

Easy decimal division (dividend has 1-2 decimal digits, a whole number divisor)

Like above, but missing dividend or divisor

Divide decimals by decimals (Think of how many times the divisor fits into the quotient.)

Mixed multiplication and division problems 1 (1 decimal digit)

Divide whole numbers
and decimals by 10, 100, or 1000

Same as above, missing dividend or divisor

Multiply or divide decimals & whole numbers by 10, 100, and 1000

Divide whole numbers
and decimals by 10, 100, 1000, or 10,000

Divide whole numbers
and decimals by 10, 100, 1000, or 10,000 - missing dividend or divisor

**Key to Decimals Workbooks**

This is a workbook series by Key Curriculum Press that begins with basic concepts and operations on decimals. Then the books cover real-world uses of decimals in pricing, sports, metrics, calculators, and science.

The set includes books 1-4.

**Long division**

Divide decimals by whole numbers, 1-digit divisor

Divide decimals by whole numbers, 2-digit divisor

Divide a decimal by a whole number, add zeros to dividend if necessary

Divide a decimal by a whole number, add zeros to dividend if necessary, more difficult

Divide whole numbers, give answer to 3 decimal digits

Divide decimals by decimals 1: Dividend less than 10; divisor 1-2 digits

Divide decimals by decimals 2: Dividend varies more; divisor 1-2 digits

Divide decimals by decimals 3: the divisor has 1-3 decimal digits

Divide decimals by decimals, generic

*Generate decimal multiplication or division worksheets yourself*

### Measuring units

**Customary system**

*Convert using long division & multiplication (paper & pencil) or mental
math*

Convert between inches & feet

Convert between inches, feet, and yards

Convert between ounces & pounds

Convert between tons & pounds

Convert between cups, pints, and quarts

Convert between cups, pints, quarts, and gallons

Convert between ounces, cups, and quarts

All customary units except miles - mixed practice

All customary units except miles - mixed practice - a challenge

**Convert using a calculator, with decimals**

Convert between inches, feet, and yards - use a calculator

Convert between miles, yards, and feet 1 - use a calculator

Convert between miles, yards, and feet 2 - use a calculator

Convert between tons, pounds, and ounces with decimals - use a calculator

Convert between various customary units with decimals - use a calculator

**Key to Measurements Workbooks**

*Key to Measurement* workbooks include a variety of hands-on experiences related to the customary units of measurement. Group projects are included in addition to numerous individual activities. In Book 1, students learn how a linear measurement system is developed and then do activities related to measuring length. Book 2 focuses on length, perimeter, and area measures. In Book 3, the concept of area is further developed, and students are introduced to volume. Book 4 covers a variety of topics. Students experiment with weighing objects and measuring capacity, and they also learn about temperature and time.

**Metric system**

Convert between mm, cm and m - using decimals

Convert between mm, cm, m, and km - using decimals

Convert between ml & l and g & kg - using decimals

All metric units mentioned above - mixed practice - using decimals

Metric system: convert between the units of length (mm, cm, dm, m, dam, hm, km)

Metric system: convert between the units of weight (mg, cg, dg, g, dag, hg, kg)

Metric system: convert between the units of volume (ml, cl, dl, L, dal, hl, kl)

Metric system: convert between the units of length, weight, and volume

*You can use the measuring worksheets generator to generate more different kinds of measuring unit worksheets.*

### Ratio

Write a ratio and simplify it

Ratio word problems

**Brain Quest Workbook: Grade 6**

The book boasts 300 pages jam-packed with curriculum-based activities and exercises in every subject, with a focus on math and language arts. Original full-color illustrations throughout give the book a bright, lively style that will appeal to older kids. It is engaging, user-friendly, and written to make schoolwork fun. Sixth graders will delve into research and analysis, metaphor and meaning, ratios and proportions, expressions and equations, and geometry. The workbook covers spelling and vocabulary, writing, social studies, science, and more.

### Percent

Change decimals to percents and vice versa

As above, but allow more than 100%

Find percentages of numbers - easy, percents are multiples of ten

Easy practice with percentages over 100%

Find percentages of numbers - easy, percents are multiples of ten

Find percentages of numbers - medium, percents are multiples of five

Find percentages of numbers - use a calculator

Find how many percent a number is of another

Find percentages of number OR find how many percent a number is of another - easy

Find percentages of number OR find how many percent a number is of another - use a calculator

**Key to Percents Workbooks**

Key to Percents first emphasizes mental computation and estimation skills--since most work with percents is done without pencil and paper. Then students are taught to solve percent problems using equal fractions and decimal multiplication. Finally, percents are used to solve word problems in a variety of applications. Key to Percents assumes only a knowledge of fraction and decimal computation. Book 1 covers Percent Concepts. Book 2 covers Percents and Fractions. Book 3 covers Percents and Decimals.

### Factoring, GCF, and LCM

Factor numbers within 0-100 to prime factors

Factor numbers within 2-500 to prime factors

Find the greatest common factor of two numbers (easy, numbers within 1-50)

Find the greatest common factor of two numbers (numbers within 1-100)

Find the greatest common factor of 3 numbers between 1 and 100

Find the least common multiple of 2 numbers between 2 and 30

Find the least common multiple of 2 numbers between 2 and 50

Find the least common multiple of 3 numbers between 2 and 30

### Fraction addition and subtraction

Add & subtract unlike fractions - proper fractions, denominators 2-12

Add & subtract unlike fractions - denominators 2-12

Add & subtract unlike fractions - larger denominators

Add & subtract 3 unlike fractions - proper fractions, denominators 2-8

Add & subtract 4 unlike fractions - proper fractions, denominators 2-8

Add & subtract 3 unlike fractions, denominators 2-12

Add & subtract two mixed numbers - denominators 2-12

Add & subtract two mixed numbers - larger denominators

Add & subtract three mixed numbers - denominators 2-12

Add & subtract whole numbers, fractions, or mixed numbers - mixed practice; denominators 2-12

*Make more add/subtract sheets yourself*

### Fraction multiplication

*In all fraction multiplication and division problems, it helps to simplify before you multiply.*

Fraction multiplication 1 - 3 fractions, denominators 2-12

Fraction multiplication 2 - 3 fractions, denominators 2-20

Fraction multiplication 3 - 4 fractions, denominators 2-12

Mixed number times a fraction

Mixed number times a mixed number

Mixed multiplication practice 1 (two numbers; fractions, mixed numbers, or whole numbers)

Mixed multiplication practice 2 (three numbers; fractions, mixed numbers, or whole numbers)

A whole number times a fraction - missing factor

A fraction times a fraction - missing factor

### Fraction division

Divide a whole number, fraction, or mixed number by a fraction - mental math, as the answers are whole numbers

Fraction divided by a fraction

Mixed number divided by a mixed number

Mixed division practice (by fractions, mixed numbers, or whole numbers)

*Make more multiplication or division worksheets yourself*

**Key to Fractions Workbooks**

These workbooks by Key Curriculum Press feature a number of exercises to help your child learn about fractions. Book 1 teaches fraction concepts, Book 2 teaches multiplying and dividing, Book 3 teaches adding and subtracting, and Book 4 teaches mixed numbers. Each book has a practice test at the end.

### Convert fractions to mixed numbers and vv

Convert mixed numbers to fractions

Fractions to mixed numbers - easy

Fractions to mixed numbers - not so easy

### Simplify or equivalent fractions

Simplify fractions - easy

Simplify fractions - harder

Simplify fractions - a challenge

Equivalent fractions - easy

Equivalent fractions - harder

Equivalent fractions - hardest

*Generate these yourself*.

### Fractions vs. Decimals

Decimals to fractions or mixed numbers (tenths/hundredths/thousandths)

Decimals to fractions or mixed numbers (up to millionths)

Mixed numbers to decimals (denominators 10, 100, and 1000)

Proper and improper fractions to decimals (denominators 10, 100, or 1000)

Proper fractions to decimals (denominators powers of ten till 1,000,000)

Mixed numbers to decimals (denominators powers of ten, till 1,000,000)

Fractions or mixed numbers to decimals (easy, varied denominators)

Fraction to decimals - need long division

Fractions to decimals - mixed practice

*Generate these yourself*

**Key to Fractions Workbooks**

These workbooks by Key Curriculum Press feature a number of exercises to help your child learn about fractions. Book 1 teaches fraction concepts, Book 2 teaches multiplying and dividing, Book 3 teaches adding and subtracting, and Book 4 teaches mixed numbers. Each book has a practice test at the end.

### Integers

**Coordinate grid**

Plot points & shapes or tell coordinates of points
1

Plot points & shapes or tell coordinates of points
2

(scaling on the grid is from -20 to 20)

Move a shape either in 1 or 2 directions (up/down/left/right)

Reflect shapes in x- or y-axis

Mixture of problems: move shapes or reflect them

**Addition & subtraction**

*Addition and subtraction of integers are beyond the Common Core Standards for grade 6 but the worksheets links are included here for completeness sake, as some curricula or standards may include them in 6th grade.*

Simple addition of integers within -10 to 10

Simple addition of integers within -30 to 30

Simple addition of integers, three addends

Simple addition of integers, four addends

Simple missing addend problems

More complex missing addend problems

Integer subtraction within -10 and 10

Integer subtraction within -30 and 30

Missing minuend and subtrahend problems

Mixed addition and subtraction problems (within -20 and 20)

Challenge: mixed addition and subtraction problems: missing numbers

**Brain Quest Workbook: Grade 6**

The book boasts 300 pages jam-packed with curriculum-based activities and exercises in every subject, with a focus on math and language arts. Original full-color illustrations throughout give the book a bright, lively style that will appeal to older kids. It is engaging, user-friendly, and written to make schoolwork fun. Sixth graders will delve into research and analysis, metaphor and meaning, ratios and proportions, expressions and equations, and geometry. The workbook covers spelling and vocabulary, writing, social studies, science, and more.

**Multiplication & Division**

*Multiplication and division of integers are beyond the Common Core Standards for grade 6 but the worksheets links are included here for completeness sake, as some curricula or standards may include them in 6th grade.*

Integer multiplication 2: medium

Simple missing factor problems

Integer multiplication, whole tens

Simple division of integers

Simple division of integers, missing dividend or divisor

Mixed multiplication and division problems

You can create *integers worksheets yourself here!*

### Geometry

*Area **- these worksheets are done in the coordinate grid.*

Find the area of right triangles

Find the area of right triangles, parallelograms, and trapezoids

Find the area of triangles and quadrilaterals

Find the area of quadrilaterals, pentagons, and hexagons

Challenge: find the area of triangles & quadrilaterals (scaling on the grid is from -50 to 50)

*
Generate worksheets for the area of polygons yourself*

Volume & surface area

*Since these worksheets below contain images of variable sizes, please first check
how the worksheet looks like in print preview before printing. If it doesn't
fit, you can either print it scaled (such as at 90%), or make another one by
refreshing the worksheet page (F5) until you get one that fits.*

Find the volume of a rectangular prism with fractional edge lengths

(easy: halves, thirds, and fourths; the whole number part is max 1)

Find the volume of a rectangular prism with fractional edge lengths

(easy: halves, thirds, and fourths; the whole number part is max 2)

Find the volume of a rectangular prism with fractional edge lengths

(challenge: fractions up till sixths)

Find the volume or surface area of rectangular prisms (easy)

Find the volume or surface area of rectangular prisms (using decimals)

Problem solving: find the volume/surface area/edge length of cube when surface area or volume is given

*
Generate worksheets for volume & surface area of rectangular prisms yourself*

**Key to Geometry Workbooks**

Here is a non-intimidating way to prepare students for formal geometry. *Key to Geometry* workbooks introduce students to a wide range of geometric discoveries as they do step-by-step constructions. Using only a pencil, compass, and straightedge, students begin by drawing lines, bisecting angles, and reproducing segments. Later they do sophisticated constructions involving over a dozen steps-and are prompted to form their own generalizations. When they finish, students will have been introduced to 134 geometric terms and will be ready to tackle formal proofs.

## Optional topics

### Proportions

Easy proportions (can be solved by thinking of equivalent fractions) - only whole numbers

Proportions (answers to be rounded to 1 decimal)

Proportions - using decimals

Simple proportion word problems

Word problems like above, but using decimal numbers

### Circle

Find the circumference when either radius or diameter is given

Find the area of the circle when either radius or diameter is given

Challenge: calculate diameter/radius/area when circumference is given

**Brain Quest Workbook: Grade 6**

The book boasts 300 pages jam-packed with curriculum-based activities and exercises in every subject, with a focus on math and language arts. Original full-color illustrations throughout give the book a bright, lively style that will appeal to older kids. It is engaging, user-friendly, and written to make schoolwork fun. Sixth graders will delve into research and analysis, metaphor and meaning, ratios and proportions, expressions and equations, and geometry. The workbook covers spelling and vocabulary, writing, social studies, science, and more.

If you wish to have more control on the options such as number of problems or font size or spacing of problems, or range of numbers, just click on these links to use the worksheet generators yourself: