6th Grade Math Answer Key

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Free Math Worksheets for Class 6

This is a comprehensive collection of complimentary printable math worksheets for sixth form, organized past topics such as multiplication, partitioning, 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 plan, but go especially well with IXL's sixth grade math curriculum.

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

In sixth grade, students will starting time the study of beginning algebra (order of operations, expressions, and equations). They learn virtually ratios & pct and start using integers. Students too review long division, factoring, fraction arithmetics, 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. Delight note that these free worksheets do non cover all sixth grade topics; most notably, they do not include problem solving.

Multiplication and Partition 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 iii-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 rest
1-digit divisor, 6-digit dividend, no remainder
ane-digit divisor, half-dozen-digit dividend, with residual
one-digit divisor, 7-digit dividend, no remainder
one-digit divisor, vii-digit dividend, with remainder

2-digit divisor, 5-digit dividend, no remainder
ii-digit divisor, 5-digit dividend, with remainder
2-digit divisor, 6-digit dividend, no remainder
ii-digit divisor, 6-digit dividend, with remainder
2-digit divisor, vii-digit dividend, no remainder
two-digit divisor, 7-digit dividend, with residual

3-digit divisor, six-digit dividend, no remainder
iii-digit divisor, six-digit dividend, with rest
3-digit divisor, 7-digit dividend, no remainder
three-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 segmentation & multiplication

Catechumen between inches & feet
Convert between inches, feet, and yards
Convert between ounces & pounds

Primary Grade Challenge Math cover

Primary Form Claiming Math past Edward Zaccaro

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

Exponents

Piece of cake exponents
Challenge exponents
Write using exponents

Identify 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 grade in normal form (up to 9 digits), the parts are scrambled
Write a number given in expanded form in normal form (upwards to 12 digits), the parts are scrambled
Write a decimal number given in expanded form in normal class (upwardly to 6 decimal digits), the parts are scrambled

Mixed rounding issues 1 - rounding to the underlined digit, upwards to rounding to the nearest million
Mixed rounding bug 2 - round to the underlined digit, up to rounding to the nearest trillion

Algebra

Lodge of operations

3 operations, uses ÷ for division, no exponents
Four operations, uses ÷ for division, no exponents
Two or three operations, uses the fraction line for partition, no exponents
2 or 3 operations, uses the fraction line for sectionalisation, exponents included
Two, iii, or four operations, uses the fraction line, exponents included

Expressions

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

Write a number expression from expression given in words: one functioning
Write a number expression from expression given in words: ii operations

Simplify expressions (past combining like terms; no negative numbers)
Multiply using the distributive property
Gene the expressions

Equations

I-step equations with whole numbers (no negative numbers involved)
1-footstep equations where you demand to showtime simplify something on one side
(no negative numbers involved)

Key to Algebra workbook series

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 piece of cake to follow. Word bug relate algebra to familiar situations, helping students to understand abstract concepts. Students develop understanding by solving equations and inequalities intuitively earlier formal solutions are introduced. Students begin their study of algebra in Books one-4 using merely integers. Books 5-seven innovate rational numbers and expressions. Books eight-10 extend coverage to the real number system.

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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 g)
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 add-on/subtraction with up to 2 decimal digits
Mental improver/subtraction - missing number

Decimal improver or subtraction with ane-three decimal digits
Decimal add-on or subtraction with one-6 decimal digits
Decimal addition, iv addends
Decimal subtraction, two subtrahends

Key to Decimals workbook series

Primal to Decimals Workbooks

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

The set includes books 1-iv.

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Decimal Multiplication

Mental multiplication

Multiply a whole number and a decimal (1-3 decimal digits), easy
Aforementioned as in a higher place, but with a missing cistron
Multiply a decimal by decimal mentally (upwardly to ii decimal digits times 2 decimal digits)
Multiply a decimal by decimal mentally (upwardly to iii decimal digits times three decimal digits)
Missing factor problems 1 (decimal by decimal, 1 or 2 decimals)
Missing cistron problems 2 (decimal by decimal, 1-3 decimals)

Multiply decimals by 10, 100, or grand (1-iii decimal digits)
Multiply decimals by x, 100, or 1000; missing factor
Multiply decimals by power of 10 (1-5 decimal digits)
Multiply decimals by ability of 10; missing factor

Multiply in columns

Multiply a decimal with ane-3 decimal digits by a whole number
Multiply a decimal with ane-2 decimal digits by another decimal with 1-2 decimal digits
Multiply a decimal with 1-3 decimal digits by another decimal with i-3 decimal digits

Decimal Division

Mental division

Easy decimal sectionalisation (dividend has i-ii 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 issues 1 (i decimal digit)

Carve up whole numbers and decimals past 10, 100, or grand
Same every bit 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 segmentation

Divide decimals by whole numbers, 1-digit divisor
Carve up decimals past whole numbers, 2-digit divisor

Divide a decimal by a whole number, add together zeros to dividend if necessary
Divide a decimal by a whole number, add zeros to dividend if necessary, more than difficult
Separate whole numbers, requite answer to 3 decimal digits

Divide decimals by decimals 1: Dividend less than 10; divisor 1-ii digits
Divide decimals by decimals two: Dividend varies more; divisor i-2 digits
Divide decimals past decimals iii: the divisor has one-3 decimal digits
Divide decimals past decimals, generic

Measuring units

Customary system

Convert measuring units using long partitioning & multiplication (newspaper & pencil) or mental math

Convert between inches & feet
Convert betwixt inches, feet, and yards

Convert between ounces & pounds
Convert between tons & pounds

Convert betwixt cups, pints, and quarts
Convert between cups, pints, quarts, and gallons
Convert between ounces, cups, and quarts

All customary units except miles - mixed do
All customary units except miles - mixed practice - a challenge

Convert using a figurer, with decimals

Catechumen betwixt inches, feet, and yards - apply a computer
Catechumen between miles, yards, and anxiety ane - employ a calculator
Convert betwixt miles, yards, and feet 2 - utilise a calculator
Catechumen between tons, pounds, and ounces with decimals - apply a calculator
Convert between various customary units with decimals - utilize a computer

Metric system

Convert between mm, cm and thou - using decimals
Catechumen betwixt mm, cm, chiliad, and km - using decimals
Convert between ml & l and g & kg - using decimals

All metric units mentioned in a higher place - mixed practice - using decimals

Metric system: convert between the units of length (mm, cm, dm, m, dam, hm, km)
Metric arrangement: convert between the units of weight (mg, cg, dg, g, dag, hg, kg)
Metric system: convert between the units of book (ml, cl, dl, Fifty, dal, hl, kl)

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

Ratio

Write a ratio and simplify information technology
Ratio give-and-take issues

Per centum

Alter decimals to percents and vice versa
Every bit above, simply allow more than 100%
Find percentages of numbers - easy, percents are multiples of ten
Easy practice with percentages over 100%

Detect percentages of numbers - easy, percents are multiples of 10
Find percentages of numbers - medium, percents are multiples of five
Find percentages of numbers - use a calculator

Find what percentage a number is of some other
Find percentages of number OR find what pct a number is of another - like shooting fish in a barrel
Find percentages of number OR find what percentage a number is of some other - use a calculator

Prime factorization, GCF, and LCM

Gene numbers within 0-100 to prime number factors
Cistron numbers within ii-500 to prime number factors

Discover the greatest common gene of two numbers (piece of cake, numbers within one-fifty)
Discover the greatest mutual factor of two numbers (numbers within 1-100)
Discover the greatest common factor of 3 numbers betwixt i and 100

Find the to the lowest degree common multiple of 2 numbers between 2 and 30
Find the least common multiple of two numbers between ii and 50
Find the least common multiple of 3 numbers between 2 and 30

Fraction improver and subtraction

Add & subtract different fractions - proper fractions, denominators two-12
Add & subtract unlike fractions - denominators 2-12
Add & subtract dissimilar fractions - larger denominators
Add & decrease iii unlike fractions - proper fractions, denominators two-8
Add & subtract 4 unlike fractions - proper fractions, denominators 2-eight
Add & subtract 3 dissimilar fractions, denominators 2-12

Add & decrease 2 mixed numbers - denominators 2-12
Add together & decrease two mixed numbers - larger denominators
Add together & 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 earlier you multiply.

Fraction times a whole number
Fraction multiplication 1 - three fractions, denominators two-12
Fraction multiplication ii - 3 fractions, denominators ii-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 (3 numbers; fractions, mixed numbers, or whole numbers)

A whole number times a fraction - missing factor
A fraction times a fraction - missing cistron

Fraction division

Carve up 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 (past 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 and 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 (upward 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 (upwardly to iii decimals)

Proper fractions to decimals (up to 6 decimals)
Mixed numbers to decimals (upwardly to vi decimals)

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

Integers

Coordinate grid

Plot points & shapes or tell coordinates of points 1
Plot points & shapes or tell coordinates of points ii (scaling on the filigree is from -20 to xx)

Move a shape either in 1 or two directions (up/downwards/left/right)
Reflect shapes in ten- or y-centrality
Mixture of issues: motility shapes or reverberate them

Addition & subtraction

Add-on and subtraction of integers are beyond the Common Core Standards for grade 6 simply some curricula or standards may include them in 6th class.

Unproblematic addition of integers inside -10 to x
Simple addition of integers within -30 to 30
Simple add-on of integers, 3 addends
Uncomplicated addition of integers, four addends (print in landscape)
Simple missing addend problems
More than complex missing addend problems (impress in landscape)

Integer subtraction inside -ten and x
Integer subtraction within -xxx and thirty
Missing minuend and subtrahend problems

Mixed addition and subtraction problems (within -xx and 20)
Claiming: mixed addition and subtraction problems: missing numbers

Multiplication & Partition

Multiplication and division of integers are across the Common Core Standards for class half dozen just the worksheets links are included here for abyss sake, as some curricula or standards may include them in sixth grade.

Integer multiplication 1: easy
Integer multiplication 2: medium

Simple missing factor problems
Integer multiplication, whole tens

Simple division of integers
Elementary division of integers, missing dividend or divisor

Mixed multiplication and division problems

Geometry

Surface area - these worksheets are done in the coordinate grid.

Notice the expanse of correct triangles
Find the area of right triangles, parallelograms, and trapezoids

Notice the area of triangles and quadrilaterals
Find the expanse of quadrilaterals, pentagons, and hexagons

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

Volume & surface area

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

Observe 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 border lengths (easy: halves, thirds, and fourths; the whole number part is max two)
Find the book 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 surface area of rectangular prisms (using decimals)

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

Optional topics

Proportions

Like shooting fish in a barrel proportions (can be solved by thinking of equivalent fractions) - but whole numbers
Proportions (answers to be rounded to 1 decimal)
Proportions - using decimals
Uncomplicated proportion discussion problems
Discussion problems like above, only using decimal numbers

Circle

Detect the circumference when either radius or diameter is given
Find the expanse of the circumvolve when either radius or bore is given
Challenge: calculate diameter/radius/area when circumference is given

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