Math word Problems With Answers for Grade 6
Grade 6 maths word problems with answers are presented. Some of these problems are challenging and need more time to solve. Also detailed solutions and full explanations are included.
- Two numbers N and 16 have LCM = 48 and GCF = 8. Find N.
- If the area of a circle is 81pi square feet, find its circumference.
- Find the greatest common factor of 24, 40 and 60.
- In a given school, there are 240 boys and 260 girls. a) What is the ratio of the number of girls to the number of boys? b) What is the ratio of the number of boys to the total number of pupils in the school?
- If Tim had lunch at $50.50 and he gave 20% tip, how much did he spend?
- Find k if 64 ÷ k = 4.
- Little John had $8.50. He spent $1.25 on sweets and gave to his two friends $1.20 each. How much money was left?
- What is x if x + 2y = 10 and y = 3?
- A telephone company charges initially $0.50 and then $0.11 for every minute. Write an expression that gives the cost of a call that lasts N minutes.
- A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 180 kilometers?
- A machine fills 150 bottles of water every 8 minutes. How many minutes it takes this machine to fill 675 bottles?
- A car travels at a speed of 65 miles per hour. How far will it travel in 5 hours?
- A small square of side 2x is cut from the corner of a rectangle with a width of 10 centimeters and length of 20 centimeters. Write an expression in terms of x for the area of the remaining shape.
- A rectangle A with length 10 centimeters and width 5 centimeters is similar to another rectangle B whose length is 30 centimeters. Find the area of rectangle B.
- A school has 10 classes with the same number of students in each class. One day, the weather was bad and many students were absent. 5 classes were half full, 3 classes were 3/4 full and 2 classes were 1/8 empty. A total of 70 students were absent. How many students are in this school when no students are absent?
- The perimeter of square A is 3 times the perimeter of square B. What is the ratio of the area of square A to the area of square B.
- John gave half of his stamps to Jim. Jim gave gave half of his stamps to Carla. Carla gave 1/4 of the stamps given to her to Thomas and kept the remaining 12. How many stamps did John start with?
- Two balls A and B rotate along a circular track. Ball A makes 4 full rotations in 120 seconds. Ball B makes 3 full rotation in 60 seconds. If they start rotating now from the same point, when will they be at the same starting point again?
- A segment is 3 units long. It is divided into 9 parts. What fraction of a unit are 2 parts of the segment?
- A car is traveling 75 kilometers per hour. How many meters does the car travel in one minute?
- Carla is 5 years old and Jim is 13 years younger than Peter. One year ago, Peter's age was twice the sum of Carla's & Jim's age. Find the present age of each one of them.
- Linda spent 3/4 of her savings on furniture. She then spent 1/2 of her remaining savings on a fridge. If the fridge cost her $150, what were her original savings?
- The distance bewteen Harry and Kate is 2500 meters. Kate and Harry start walking toward one another and Kate' dog start running back and forth between Harry and Kate at a speed of 120 meters per minute. Harry walks at the speed of 40 meters per minute while Kate walks at the speed of 60 meters per minute. What distance will the dog have travelled when Harry and Kate meet each other?
Answers to the Above Questions
- a) 13:12 b)12:25
- 0.50 + N * 0.11
- 4.5 gallons
- 450 centimeters squared
- 108 cubic centimeters
- 1250 meters/minute
- Carla:5 years, Jim: 6 years, Peter: 19 years.
- 3000 meters
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Students are entering a new section of math that consists of algebra, geometry, decimals, and more complicated division problems. When there is not a parent or teacher around, students have access to on-demand videos for their sixth-grade mathematical lessons. Our video tutorials are taught by math teachers who go through the problem solving process.
- The key to learning math is repetition, and our math teachers go through multiple examples.
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- Students learn money, ratios, decimals, graphing, and other concepts from the 6th grade curriculum.
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6th Grade Math Worksheets
Count on our printable 6th grade math worksheets with answer keys for a thorough practice. With strands drawn from vital math topics like ratio, multiplication, division, fractions, common factors and multiples, rational numbers, algebraic expressions, integers, one-step equations, ordered pairs in the four quadrants, and geometry skills like determining area, surface area, and volume, organizing numerical data as dot plots, histograms and box plots, finding mean, median, and quartiles of datasets, these pdfs become your often go-to place. Grab your ticket to a great start with our free math worksheets for grade 6 students!
Select Grade 6 Math Worksheets by Topic
Explore 4,600+ Sixth Grade Math Worksheets
Division | 4-Digit by 2-Digit and 3-Digit
Divide a 4-digit number by a 2-digit or 3-digit number, starting from the largest place value and dividing your way down to the last digit to find the quotient and remainder (if any).
- Download the set
Drawing Shapes to Represent the Ratio
Jazz up your ratio skills with our 6th grade math worksheet pdfs. Direct students to visually represent the terms of each ratio by sketching the specified number of shapes.
Multiplying Two Fractions by Cross Cancelling
Breaking down the numerator and denominator into prime factors, cross-cancelling the common factors, and multiplying the uncancelled parts of the fraction are all grade 6 learners are expected to do!
Expressing Decimals in Words | Up to Millionths
Let your understanding of decimal place value soar to new heights as you dive into these printable 6th grade math worksheets and express decimals up to millionths in words and vice versa.
Finding the GCF of Two Numbers
Follow the step-by-step process of finding the GCF by listing out all the factors of each pair of 2-digit numbers, then compare the factors, figure out the common ones and the greatest among them is your answer.
Representation of Integers
Laying a strong foundation in integers becomes easy with a touch of real-world offered in these grade 6 math pdf worksheets, where each scenario should be represented with a positive or negative integer.
One-Step Equation: Addition and Subtraction | Integers
Rearrange the equation, making the variable the subject, and take the integer constant to the other side and change its sign, add or subtract to find the value of the unknown variable.
Identifying Ordered Pairs in All Quadrants
Get acquainted with the coordinate plane, the four quadrants, and the ordered pairs. Identify the point representing each ordered pair in Part A; and locate and write the x-y coordinates of each point in part B.
Determining the Area of a Square
Equip grade 6 children with these printable math worksheets, if practice in determining the area of a square is on your mind. Get students to square the fractional side lengths and compute the area.
Identifying Nets of 3D Shapes
Get 6th grade learners to imagine folding the 2D nets presented in this printable math worksheet along the edges and visualize the 3D shapes that can be constructed from them.
- Grab the Worksheet
Surface Area using Nets | Counting Squares
Whether it is refining or testing skills in counting the unit squares to determine the surface area of rectangular prisms, cubes or triangular prisms from their nets, these pdfs serve the purpose.
Five-Number Summary
Descriptively analyze each dataset, by rearranging the values in ascending order and figuring out the maximum and minimum values, and the lower or 1st, median or 2nd, and upper or 3rd quartiles.
Division of 5-Digit Numbers by 1-Digit and 2-Digit Divisors
Push boundaries and brush up your division skills with adequate practice provided by these exercises in dividing 5-digit numbers with single and double-digit divisors.
Ratio Word Problems | Part-to-Part
Put your analytical skills to test with our 6th grade math worksheet pdfs. Study the data given in the pictogram and answer the set of questions detecting the part-to-part ratio in each scenario.
Multiplying Mixed Numbers and Fractions
Effortlessly multiply mixed numbers and fractions by converting the mixed numbers to improper fractions, cross cancelling the common factors and then multiplying what's left over.
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6th Grade Math Worksheets Hub Page
Welcome to our 6th Grade Math Worksheets hub page.
This is a new hub page and currently under development - so there will be more 6th grade resources on the way soon!
Here you will find a wide range of free printable worksheets that follow the standards for 6th Grade .
Come and take a look at our adding subtracting fractions page, or our 6th grade math games page. Looking for some help with algebra? We have some basic algebra worksheets too.
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- This page contains links to other Math webpages where you will find a range of activities and resources.
- If you can't find what you are looking for, try searching the site using the Google search box at the top of each page.
6th Grade Math Learning
Here are the standards for the end of the year for 6th Grade.
- Find the greatest common factor of whole numbers up to 100.
- Find the least common multiple of two whole numbers up to 12.
- Recognise opposite signs of numbers (positive and negative) as being on opposite sides of 0 on a number line.
- Recognise that the opposite of the opposite of a number is the number itself e.g. -(-7) = 7
- Understand a rational number as a point on a number line.
- Find and position rational numbers on a range of number lines.
- Understand the absolute value of a number.
- Write, interpret and explain statements about rational numbers, such as -3°C > -7°C
- Write and evaluate expressions involving whole number exponents.
- Fluently divide multi-digit numbers.
- Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm.
- Find the percentage of a quantity as a rate per 100.
- Divide fractions by fractions using visual models.
- Solve problems involving dividing fractions by fractions.
- Understand the concept of ratio and use ratio language.
- Understand the concept of a unit rate a/b associated with a ratio a:b.
- Use ratio and rate reasoning to solve a range of problems.
- Write, read, and evaluate expressions in which letters stand for numbers
- Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient);
- Evaluate expressions at specific values of the variables of different formulas.
- Apply the properties of operations to generate equivalent expressions, e.g. 10 + 5y = 5(2 + y).
- Reason about and solve one-variable equations and inequalities.
- Write an inequality of the for x<c or x>c to represent a constraint or condition.
- Represent and analyze quantitative relationships between dependent and independent variables.
- Develop understanding of statistical variability
- Summarize and describe distributions
- Display numerical data in plots on a number line, including dot plots, histograms, and box plots
- Find the median and the mean of a set of data.
- Find the interquartile range and/or mean absolute deviation and describe patterns in data.
- Find the area of right triangles, other triangles, special quadrilaterals, and polygons.
- Find the volume of a right rectangular prism with fractional edge lengths
- Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms.
- Draw polygons in the coordinate plane given coordinates for the vertices.
- Use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate.
- Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane.
- Represent three-dimensional figures using nets made up of rectangles and triangles.
- Use the nets to find the surface area of these figures
6th Grade Math Worksheets
On this page you will find link to our range of math worksheets for 6th grade.
Quicklinks to 6th Grade ...
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Word Problems Zone
Fractions Percentages Ratio Zone
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There is a different grab pack for each grade.
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6th Grade Place Value Zone
Ordering numbers, including negative numbers, decimals to 3dp and rational numbers.
The sheets in this section involve negative numbers, decimals to 3 decimal places, and a range of rational numbers.
There are sheets with decimals up to 10, and also sheets with numbers from -10 to 10.
- Ordering Decimals to 3dp
- Ordering Negative Numbers -10 to 10
- Ordering and Comparing Rational Numbers
Rounding Decimals and Significant Figures
- Rounding Decimal Places Sheets to 2dp
- Rounding Decimals Worksheet Challenges
- Rounding Significant Figures Worksheets
6th Grade Number Sense Worksheets
Here you will find a range of 6th Grade Number Worksheets covering skills connected to Numbers and the Number System.
Using these sheets will help your child to:
- understand how to use inequalities including where you have two values
- understand how to use exponents (powers) of a number;
- find the greatest common factors of two numbers up to 100
- find the least common multiple of two numbers up to 12.
- extend their knowledge of prime and composite (non-prime) numbers up to 100;
- know and be able to use the PEMDAS (or PEDMAS) rule.
- understand and use absolute value
Inequalities
- Inequalities on a Number Line
- Writing Inequalities from Word Problems
Factors and Multiples 6th Grade Worksheets
- Greatest Common Factor Worksheets
- Least Common Multiple Worksheets
- Factor Tree Worksheets (easier)
- Prime Factorization Worksheets (harder)
PEMDAS and Order of Operations Worksheets
- PEMDAS Rule Support Page
- PEMDAS Problems Worksheets 5th Grade
- 6th Grade Order of Operations
- Absolute Value Worksheets
Roman Numerals Worksheets
- Roman Numerals worksheets
6th Grade Mental Math Quizzes
Here you will find a range of printable mental math 6th grade quizzes for your child to enjoy.
Each worksheet tests the children on a range of math topics from number facts and mental arithmetic to geometry, fraction and measures questions.
A great way to revise topics, or use as a weekly math quiz!
- Mental Math Worksheets 6th Grade
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4 Operations Zone
Decimal counting worksheets.
Using these sheets will support you child to:
- count on and back by multiples of 0.1;
- fill in the missing numbers in sequences;
- count on and back into negative numbers.
- find number bonds to 1;
- Counting By Decimals
- Decimal Number Bonds to 1
6th Grade Addition & Subtraction Worksheets
The following 6th grade math worksheets involve using addition and subtraction with a range of different number types.
- add and subtract decimals up to 3dp;
- add a columns of multi-digit numbers, including decimals.
- add and subtract positive and negative integers
The addition worksheet generator below will create a range of addition problems in columns, including decimals.
- Addition With Regrouping Worksheet Generator
- Subtraction With Regrouping Worksheet Generator
- Adding Positive and Negative Numbers (randomly generated)
- Subtracting Positive and Negative Numbers (randomly generated)
- Adding and Subtracting Negative Numbers (randomly generated)
6th Grade Multiplication Worksheets
Here you will find a range of Free Printable 5th Grade Multiplication Worksheets.
The following worksheets involve using the 6th Grade Math skills of multiplying multi-digit numbers, including decimals.
- extend their knowlege of multiplication to decimals;
- use their multiplication tables to answer related facts, including decimals;
- multiply a range of decimals by a whole number;
- multiply positive and negative numbers.
- Multiplying Decimals by Whole Numbers
- Negative Number Multiplication (randomly generated)
- Multiply and Divide Negative Numbers (randomly generated)
6th Grade Division Worksheets
Here you will find a range of Free Printable 6th Grade Division Worksheets.
The following worksheets involve using the 6th Grade Math skills of dividing multi-digit numbers, including decimals, and solving division problems.
Using these sheets will help your child learn to:
- divide multi-digit numbers by one and 2-digit numbers;
- divide decimals.
- Divisibility Rules Worksheets
- Decimal Division Facts
- Long Division of Decimal Numbers
- Dividing Negative Numbers (randomly generated)
6th Grade Math Problems
Here you will find our selection of free 6th grade math word problems.
Each sheet is availabel in both standard and metric units (where applicable).
Each sheet comes complete with a separate answer sheet.
All the problems are based around 'real life' such as the planets, heights of mountains, or length of rivers.
Using these sheet will help your child to:
- apply their addition, subtraction, multiplication and division skills;
- apply their knowledge of rounding and place value;
- solve a range of problems including "real life" problems and ratio problems.
- 6th Grade Percent Word Problems
- Fractions Worksheets
- Percentage Worksheets
- Ratio Worksheets
6th Grade Fraction Worksheets
Here you will find a range of free printable 6th Grade Fraction Worksheets.
At 6th Grade level, children are introduced to adding and subtracting fractions with different denominators. They know and can use equivalent fractions, and can multiply and divide fractions by whole numbers, as well as mixed numbers.
- add and subtract fractions and mixed numbers;
- understand how to multiply fractions by a whole number;
- understand how to multiply two fractions together, including mixed fractions;
- understand the relationship between fractions and division;
- know how to divide fractions and mixed fractions;
- convert decimals to fractions.
- Multiplying Fractions Worksheets
- Multiplying Mixed Fractions
- How to Divide Fractions
- Dividing Fractions by Whole numbers
- Divide Whole numbers by Fractions
- How to Divide Mixed Numbers
- Multiplying and Dividing Fractions (Randomly Generated)
- Add Subtract Multiply Divide Fractions (Randomly Generated)
- Free Printable Fraction Riddles (harder)
- Fractions Decimals Percents Worksheets
6th Grade Percentage Worksheets
Take a look at our percentage worksheets for finding the percentage of a number or money amount.
We have a range of percentage sheets from quite a basic level to much harder.
- Percentage of Numbers Worksheets
- Money Percentage Worksheets
- Basic Percentage Word Problems (easier)
- 6th Grade Percent Word Problems (harder)
6th Grade Ratio and Unit Rate Worksheets
These 5th grade ratio worksheets are a great way to introduce this concept.
We have a range of part to part ratio worksheets and slightly harder problem solving worksheets.
- Ratio Part to Part Worksheets
- Ratio and Proportion Worksheets
- The Definition of Unit Rate
- Unit Rate Problems 6th Grade
6th Grade Algebra Worksheets
If you are looking for some 6th grade algebra worksheets to use with your child to help them understand simple equations then try our selection of basic algebra worksheets.
There are a range of 6th grade math worksheets covering the following concepts:
- Generate the algebra - and write your own algebraic expressions;
- Calculate the algebra - work out the value of different expressions;
- Solve the algebra - find the value of the term in the equation.
- Use the distributive property to factorize and expand different expressions
- 6th Grade Distributive Property Worksheets
- Expressions and Equations 6th Grade
- Basic Algebra Worksheets (6th & 7th Grade)
Geometry & Measurement Zone
Quicklinks to ...
6th Grade Geometry Worksheets
Here is our range of 6th grade Geometry worksheets.
- Geometry Nets Information and Worksheets
- Parts of a Circle Worksheets
- Coordinate Plane Worksheets (All 4 Quadrants)
6th Grade Area & Perimeter Worksheets
- Area of Parallelogram Worksheets
- Area of Quadrilaterals
- Area of Right Triangle
- Square Inside a Circle Area Support Page
- Surface Area Worksheet 6th Grade
6th Grade Measurement Worksheets
- Metric Conversion Worksheets (4th to 6th Grade)
- Convert Customary Units of Length Worksheets (randomly generated)
- Convert Customary Units of Capacity Worksheets (randomly generated)
Data & Statistics Worksheets
Find links to our 6th grade Statistics worksheets below.
Using these 6th grade math worksheets will help you to:
- find the mean of up to 5 numbers;
- find a missing data point when the mean is given.
- find the median of a set of data.
- create and interpret line plots.
- create and interpret dot plots and box plots.
- Median Worksheets
- Mean Worksheets
- Mode and Range Worksheets
- Mean Median Mode and Range Worksheets
- Line Graphs 6th Grade Worksheets
- Dot Plot Worksheets
- Box Plot Worksheets
Fun Zone: Puzzles, Games and Riddles
- 6th Grade Math Games
Here you will find a range of free printable 6th Grade Math games.
All children like to play Math games, and you will find a good range of Grade 6 Math Games here for your child to play and enjoy.
The following games involve different 5th Grade Math activities which you and your child can enjoy together.
- Algebra Math Games
- 6th Grade Math Puzzles
Here you will find a range of printable 6th grade math puzzles for your child to enjoy.
The puzzles will help your child practice and apply their addition, subtraction, multiplication and division facts as well as developing their thinking and reasoning skills in a fun and engaging way.
Using these puzzles will help your child to:
- learn and practice their addition and subtraction facts, including fractions and decimals;
- develop their understanding of negative numbers;
- practice and apply multiplication and division facts;
- develop problem solving skills and reasoning.
6th Grade Math Quiz
Here is our collection of Math Quizzes for 6th grade.
Quizzes are a great way to practise math skills or to asses knowledge.
- 6th Grade Math Quiz page
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Realistic Math Problems Help 6th-graders Solve Real-Life Questions
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Solving math problems can intimidate sixth-graders but it shouldn't. Using a few simple formulas and a bit of logic can help students quickly calculate answers to seemingly intractable problems. Explain to students that you can find the rate (or speed) that someone is traveling if you know the distance and time that she traveled. Conversely, if you know the speed (rate) that a person is traveling as well as the distance, you can calculate the time he traveled. You simply use the basic formula: rate times the time equals distance, or r * t = d (where "*" is the symbol for multiplication.)
The free, printable worksheets below involve problems such as these, as well as other important problems, such as determining the largest common factor, calculating percentages, and more. The answers for each worksheet are provided in the next slide right after each worksheet. Have students work the problems, fill in their answers in the provided blank spaces, then explain how they would arrive at the solutions for questions where they are having difficulty. The worksheets provide a great and simple way to do quick formative assessments for an entire math class.
Worksheet No 1
Print PDF : Worksheet No 1
On this PDF, your students will solve problems such as: "Your brother traveled 117 miles in 2.25 hours to come home for school break. What’s the average speed that he was traveling?" and "You have 15 yards of ribbon for your gift boxes. Each box gets the same amount of ribbon. How much ribbon will each of your 20 gift boxes get?"
Worksheet No. 1 Solutions
Print Solutions PDF : Worksheet No. 1 Solutions
To solve the first equation on the worksheet, use the basic formula: rate times the time = distance, or r * t = d . In this case, r = the unknown variable, t = 2.25 hours, and d = 117 miles. Isolate the variable by dividing "r" from each side of the equation to yield the revised formula, r = t ÷ d . Plug in the numbers to get: r = 117 ÷ 2.25, yielding r = 52 mph .
For the second problem, you don't even need to use a formula—just basic math and some common sense. The problem involves simple division: 15 yards of ribbon divided by 20 boxes, can be shortened as 15 ÷ 20 = 0.75. So each box gets 0.75 yards of ribbon.
Worksheet No. 2
Print PDF : Worksheet No. 2
On worksheet No. 2, students solve problems that involve a little bit of logic and a knowledge of factors, such as: "I’m thinking of two numbers, 12 and another number. 12 and my other number have a greatest common factor of 6 and their least common multiple is 36. What’s the other number I’m thinking of?"
Other problems require only a basic knowledge of percentages, as well as how to convert percentages to decimals, such as: "Jasmine has 50 marbles in a bag. 20% of the marbles are blue. How many marbles are blue?"
Worksheet No. 2 Solution
Print PDF Solutions : Worksheet No. 2 Solution
For the first problem on this worksheet, you need to know that the factors of 12 are 1, 2, 3, 4, 6, and 12 ; and the multiples of 12 are 12, 24, 36 . (You stop at 36 because the problem says that this number is the least common multiple.) Let's pick 6 as a possible greatest common multiple because it's the largest factor of 12 other than 12. The multiples of 6 are 6, 12, 18, 24, 30, and 36 . Six can go into 36 six times (6 x 6), 12 can go into 36 three times (12 x 3), and 18 can go into 36 twice (18 x 2), but 24 cannot. Therefore the answer is 18, as 18 is the largest common multiple that can go into 36 .
For the second answer, the solution is simpler: First, convert 20% to a decimal to get 0.20. Then, multiply the number of marbles (50) by 0.20. You would set up the problem as follows: 0.20 x 50 marbles = 10 blue marbles .
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