Free Math Worksheets for Grade 6

This is a comprehensive collection of free printable math worksheets for sixth grade, organized by topics such as multiplication, division, exponents, place value, algebraic thinking, decimals, measurement units, ratio, percent, prime factorization, GCF, LCM, fractions, integers, and geometry. They are randomly generated, printable from your browser, and include the answer key. The worksheets support any sixth grade math program, but go especially well with IXL's 6th grade math curriculum.

The worksheets are randomly generated each time you click on the links below. You can also get a new, different one just by refreshing the page in your browser (press F5).

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, adjust the margins, header, and footer in the Page Setup settings of your browser. Another option is to adjust the "scale" to 95% or 90% in the Print Preview. Some browsers and printers have "Print to fit" option, which will automatically scale the worksheet to fit the printable area.

All worksheets come with an answer key placed on the 2nd page of the file.

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.

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, no 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


• 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, 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
• Factor the expressions

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.

=> Learn more

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

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

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.

=> Learn more

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 decimals by 10, 100, or 1000 (1-3 decimal digits)
• Multiply decimals by 10, 100, or 1000; missing factor
• Multiply decimals by power of 10 (1-5 decimal digits)
• Multiply decimals by power of 10; 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

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

Measuring units

Customary system

Convert measuring units 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

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

Ratio

• Write a ratio and simplify it
• Ratio word problems

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 what percentage a number is of another
• Find percentages of number OR find what percentage a number is of another - easy
  
• Find percentages of number OR find what percentage a number is of another - use a calculator

Prime factorization, 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

Fraction multiplication

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

• Fraction times a whole number
• 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)

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

Fractions vs. Decimals

• Decimals to fractions or mixed numbers (up to 3 decimals)
• Decimals to fractions or mixed numbers (up to 6 decimals)


• Mixed numbers to decimals (up to 3 decimals)
• Proper and improper fractions to decimals (up to 3 decimals)


• Proper fractions to decimals (up to 6 decimals)
• Mixed numbers to decimals (up to 6 decimals)


• Fractions or mixed numbers to decimals (easy, varied denominators)
• Fraction to decimals - need long division
• Fractions to decimals - mixed practice

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 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 (print in landscape)
• Simple missing addend problems
• More complex missing addend problems (print in landscape)


• 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

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 1: easy
• 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

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)

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

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

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: