# 6th Grade Algebra Homework Help

### Solved Examples

Question 1: Simplify 572 ÷ 2 $\times$ 4.9
Solution:

Given, 572 ÷ 2 $\times$ 4.9

Step 1:
572 ÷ 2  = 286

Step 2:
286 $\times$ 4.9 = 1401.4

$\Rightarrow$ 572 ÷ 2 $\times$ 4.9 = 1401.4

Question 2: Find the value of  'a'.

12p - 18a = 6p, for p = 1

Solution:

Given, 12p - 18a = 6p

Step 1:
Solve for a,

Subtract 12p from both sides

$\Rightarrow$ 12p - 18a -12p = 6p - 12p

$\Rightarrow$ -18a = - 6p

Divide each side by -18

$\Rightarrow$ a = $\frac{6}{18}$p = $\frac{1}{3}$p

Step 2:
Put p = 1

$\Rightarrow$ a = $\frac{1}{3}$ $\times$ 1

$\Rightarrow$ a = $\frac{1}{3}$

Question 3: Find the least common multiple of 12, 16 and 24.
Solution:

Prime Factors of 12 = 2 $\times$ 2 $\times$ 3

Prime Factors of 16 = 2 $\times$ 2 $\times$ 2 $\times$ 2

Prime Factors of 24 = 2 $\times$ 2 $\times$ 2 $\times$ 3

$\Rightarrow$ LCM(12, 16, 24) = 2 $\times$ 2 $\times$ 2 $\times$ 2 $\times$ 3 = 48

Question 4: A certain map uses a scale of 1 inch equals 35 miles. How many miles are represented by 15 inches on this map?
Solution:

Given
1 inch = 35 miles

$\Rightarrow$ 15 inches = 35 $\times$ 15

3 5
x 1 5
--------------
1 7 5
+ 3 5 x
--------------
5 2 5
--------------

Hence, 525 miles are represented by 15 inches on map.

## Math Practice

Students should practice Math topics of class 6 in a precise manner by following some solved examples. TutorVista provides several solved examples of tough Math problems and students need to follow these and understand the entire process in a step-by-step manner. They can also take live Math help with virtual tutors to improve their performance in exams.

Some practice problems designed for 6th grade Math are as follows:

### Practice Problems

Question 1: Find the least common multiple of 15, 35 and 75.

Question 2: Find the value of 'm'. If 20y + 12m = 5y for y = 1

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## 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 grade 6 math program, but have been specifically designed to match Math Mammoth grade 6 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

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

#### 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.

### 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

Equations

#### 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

#### 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 in columns

### 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

### 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

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

### Fraction multiplication

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

### Integers

Coordinate grid

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.

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.

### Geometry

Area - these worksheets are done in the coordinate grid.

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.

## Optional topics

### Circle

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: