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math problem solving examples grade 6

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Grade 6 Maths word Problems With Answers

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.

Answers to the Above Questions

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Grade 6 math word problem worksheets with answers - estimation word problems for 6th Grade

Grade 6 Math Word Problem Worksheets with Answers

Estimation word problems for 6th grade.

Grade 6 math word problem worksheets with answers - Estimation word problems for 6th Grade are made of the following Math skills for kids: estimate to solve word problems, multi steps word problems, identifying word problems with extra or missing information, distance direction to starting point word problems, using logical reasoning to find the order, guest and check word problems. All these exercises have been created to generate interest and eagerness for more math word problems operations.

FREE WORKSHEETS

Grade 6 math word problem worksheets with answers - solving multi step word problems

6 th GRADE MATH PRINTABLES

Best of free 6 th grade math worksheets categories.

Multiplication

FREE 6 th GRADE ONLINE PRACTICE

sixth grade math practice online with solutions

6 th GRADE MATH ONLINE PRACTICE

See all 6 th Grade skills (1000+ math exercices online)

Important facts about word problems solving and estimation for Grade 6

In a significant way, our super amazing problem solving and estimation worksheets will help your young math learners to quickly understand the relevance of estimation skills in math concepts and real life.

It should be noted that, not only are these problem solving and estimation skills a key part in math concepts, but are equally an important approach to boast your kid’s mental math skills, logical and creative thinking abilities.

How can estimation skills enhance kid’s accuracy and experts in math?

If your kids can vividly estimate reasonably, then there’ll be no doubt that their accuracy in math will increase, thus math experts.

Moreover, with estimation skills, they can quickly determine whether their answer is within a reasonable range or not.

Given that estimation skill enhances kid’s mental math competency, your 6 th grader will be able to arrive at reasonable or concrete answers within a twinkle of an eye.

Most importantly, these problem solving and estimation skills will not only strengthen kid’s skills on basic math operations, but will prepare them for areas of advanced math, such as probability, statistics, geometry and algebra. At this point, they will be required to apply logical reasoning and estimation skills.

How is estimation skill relevant in our daily lives?

Whether at home, in the market, on the street or among friends, our activities will always be surrounded around estimation. This is true as we keep on using the phrase “Let’s say…….”.

So, problem solving and estimation skills will help your kids to easily;

Vital strategies, best for solving estimation word problems for 6 th grade

Our grade 6 math word problem worksheets with answers are a perfect example for kids to grab vital strategies, best for solving estimation word problems for 6 th grade .

What then are those peculiar strategies to consider when faced with situations of problem solving and estimation?

Most at times, math word problems require a step-by-step solving procedure. This is relevant to our multi steps word problems exercise. But before we begin solving these word problems, we need to;

Finally, check the reasonableness of your answer by comparing it with the one you estimated above.

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Proportions word problems

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Math worksheets: Proportions word problems

Below are grade 6 math worksheets with proportions word problems.

math problem solving examples grade 6

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GRADE 6 MATH WORD PROBLEMS WITH ANSWERS

Problem 1 :

A train travels 18 km/hr. How many meters will it travel in 12 minutes.

(A) 3600         (B) 4200          (C) 5100

Speed of the train  =  18 km/hr 

Speed of train in m/sec  =  18  ⋅ ( 5/18)

  =  5 m/sec

12 minutes  =  12 (60)

=  720 seconds

Distance covered in 720 seconds  =  time taken (Speed)

  =  720(5)

  =  3600 m

So, the distance covered is 3600 m.

Problem 2 :

The average age of 30 kids is 9 years. If the age of teacher is included, the average age becomes 10 years. What is the age of teacher?

(A) 26            (B) 58            (C) 40

The average age of 30 kids is 9 years

Let x be the age of teacher 

Average age  =  Sum of  ages/Total number of ages

9  =  sum of ages of 30 kids/30

Sum of ages of 30 kids  =  30  ⋅  9

  =  270

Sum of ages of kids and teacher  =  270 + x

Average age of kids and teacher   =  (270 + x)/31

10  =  (270 + x)/31

10 (31)  =  270 + x

310  =  270 + x

x  =  310 - 270

x  =  40

So, the required age is 40 years.

Problem 3 :

If the height of a cylinder is 7 cm and the radius is 3 cm, then the surface area of the cylinder is ?

(A) 150          (B) 132          (B) 143

Height of the cylinder  =  7 cm

Radius of the cylinder  =  3 cm

Curved surface area of cylinder  =  2 Π r h

  =  2  ⋅  (22/7)  ⋅  7  ⋅  3

  =  2  ⋅   22  ⋅  3

  =  44  ⋅  3

 =  132 cm 2

So, the answer is 132 cm 2

Problem 4 :

Jack purchases a calculator for $350 and sells for $420.Then the percentage of profit is

(A) 10%           (B) 20%             (C) 50%

Cost price of a calculator  =  $350

Selling price of the calculator  =  $420

Profit  =  Selling price - Cost price

  =  420 - 350

  =  70

profit percentage  =  (profit/cost price)  ⋅  100

  =  (70/350) ⋅ 100

  =  (1/5) ⋅ 100

  =  20%

So, the answer is 20%

Problem 5 :

The average of 6 numbers is 8. What is the 7th number, so that its average will become 10 ?

(A) 15        (B) 22        (C) 12

The average of 6 numbers is 8

Average  =  Sum of numbers/Number of terms

8  =  Sum of 6 numbers/6

6(8)  =  Sum of 6 numbers

Sum of 6 numbers  =  48

If 7th term is added with this total, its average will become 10

Let x be the 7th term

(48 + x)/7  =  10

48 + x  =  70

x  =  70 - 48

x  =  22   

So, the answer is 22.

Problem 6 :

Find the number of prime factors of 6 10  × 7 17  × 55 27

(A) 100            (B) 91          (C) 64

  =  6  10  × 7  17  × 55 27

  =  (2 x 3)  10  × 7  17  × (5 x 11) 27

  =  2 10  x 3 10  × 7  17  × 5 27  x 11 27

Total number of prime factors  =  10 + 10 + 17 + 27 + 27

  =  91

So, the answer is 91.

Problem 7 :

If 12 man can do a piece of work in 36 days. Within how many days 18 men can do the same work ?

(A) 27        (B) 24          (C) 22

Work done  =  Number of days  ⋅ number of men

  =  36 ⋅ 12

  =  432  ---(1)

Work done  =  Number of days ⋅ 18  ----(2)

432  =   Number of days ⋅ 18

Number of days  =  432 / 18

Number of days  =  24

So, the required number of days is 24.

Problem 8 :

A man traveled from the village to the post office at the rate of 25 kmph and walked back at the rate of 4 kmph. If the entire journey took 5 hours 48 minutes, determine the distance of the post office from that village.

(A) 20           (B) 13         (C) 20

The distance covered in both cases are same.

Time  =  Distance / Speed

T 1   =  Distance / 25

T 2   =  Distance / 4

5 hours 48 minutes  =  5   4/5  hours

29/5  =  (Distance / 25) + (Distance / 4)

29/5  =  (4 Distance + 25 Distance) / 100

  (29/5)  ⋅ (100/29)   =  Distance 

  Distance  =  20 km

Problem 9 :

The sum of reciprocal of (3/2) and the reciprocal of 3 is

(A) 2           (B) 1            (C) 5

Reciprocal of 3/2 is 2/3

reciprocal of 3 is 1/3

Sum of these two numbers  =  (2/3) + (1/3)

  =  (2 + 1)/3

  =  3/3

  =  1

So, the correct answer for this question is 1

Problem 10 :

It is 9 hours now in a 12 hour clock. What will be the time after 18 hours ?

(A) 2           (B) 4          (C) 3

Now, the time is 9 hours. We want to know the time after 18 hours.

To get answer for our question, we have to do the following steps.

Add 18 to 9

Divide the result by the divisor 12

Take the remainder

9 + 18  =  27

When 27 is divided by 12, the remainder is 3

The time after 18 hours will be 3 hours.  So the answer is 3 hours.

math problem solving examples grade 6

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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

math problem solving examples grade 6

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

math problem solving examples grade 6

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

math problem solving examples grade 6

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 . 

math problem solving examples grade 6

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6th Grade Math Word Problems (Percentages)

Related Pages Word Problems Solved The Singapore Math Way 2-Step Word Problems And Bar Models Singapore Mental Math Strategies Singapore Math More Numbers Lessons

In this lesson, we will learn how to solve percent word problems

Using Bar Models

Percent Word Problem using Models

Example: 15% of the number of people who attended a concert arrived late. If 30 people arrived late, find the number of people who attended the concert.

From the above model, we see that 15% → 30 people 1% → 30 ÷ 15 = 2 people 100% → 100 × 2 = 200 people 200 people attended the concert.

Examples of solving percent problems with bar models

Marilyn saves 30% of the money she earns each month. She earns $350 each month. How much does she save?

At the Natural History Museum, 40% of the visitors are children. There are 36 children at the museum. How many visitors altogether are at the museum?

Bill bought cards to celebrate Pi day. He sends 60% of his cards to friends. He sent 42 cards to friends. How many cards did he buy altogether?

Bruce cookies 80% of the pancakes at the pancake breakfast last weekend. They made 1120 pancakes. How many pancakes did Bruce cook?

The following video shows examples of finding total price with sales tax and an example of finding cost after discount using bar models.

Alejandro bought a television set for $900 and paid a sales tax of 8%. How much did he pay for the television set?

Alice saved for a new bike. The bike was on sale for a discount of 35%. The original cost of the bike was $270. How much did she pay for the bike?

Using Grid Method

Setting up the Percent Problem Describes how to set up a percent problem using the grid method. Uses examples with the total given and looking for the parts.

Example: There are 250 chairs in a room a) If 150 chairs are full, what % are full? b) What % are empty?

Multiple Step Percent Problems Part 1 Examples of how to solve percent word problems with the grid method.

Example 1: A stereo listed for $350 is on sale for 20% off the list price. The sales tax is 6%. What price does a customer pay for the stereo if she buys it on sale?

Example 2: Stacey just received her annual cost-of-living raise. She previously earned $1450 a month. Her new salary is $1508. What is the rate of increase?

Example 3: At a playoff game, paid attendance was 39,900. The total attendance was 42,000. What percent of those attending had free tickets?

Solving Percentage Word Problems Using Proportions

Practice solving percentage word problems by setting up a proportion and solving.

Example: A poll was conducted by a local newspaper asking if the governor was doing a good job. 6,000 people were polled. If 2,400 said they approved of the job the governor was doing, what percent of the people polled disapproved?

Percent Word Problems: Percentage Problems Shows how to solve “percent of” word problems using proportions.

Percent Word Problems: Sales and Discount Solving percent word problems that involve finding a sale price given original price and discount, finding an original price given sale price and discount, and finding sale price given profit.

Example 1: A laptop that normally costs $600 is offered at a discount of 35%. What is the new sale price?

Example 2: A pair of shoes is marked down 20% during a sale and costs $60. What was the original price?

Percent Word Problems: Profit Solving percent word problems that involve finding the percentage profit.

Example 1: The total cost of producing a tablet is $150. If the manufacturer wants to make a 20% profit, at what price must they sell the tablet?

Example 2: Kevin bought a concert ticket for $50 and sold it for $54. What was the percentage profit?

Percent Word Problems: Percent Increase and Decrease Solving percent word problems that involve percent increase and decrease.

Example 1: 15 fans attended a band’s first concert. 18 fans attended their second concert. What was the percent increase in the number of fans from the first concert to second?

Example 2: Last year, a football team won 15 games. This year, the team won 20% fewer games. How many games did the team win this year?

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Math Problem Solving Worksheets For Grade 6 Solving Algebraic Equations, Algebra Equations, Maths Algebra, Exponents, Integers, Grade 6 Math Worksheets, Worksheets For Kids, Quotes For Students, Quotes For Kids

Math Problem Solving Worksheets For Grade 6 | Free Worksheets Samples

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    Grade 6 math word problem worksheets with answers - Estimation word problems for 6th Grade are made of the following Math skills for kids: estimate to solve

  4. Proportions word problems

    Grade 6 math worksheets on solving proportions word problems. Free pdf worksheets from K5 Learning's online reading and math program.

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    daily life. Math Word Problems Made Easy: Grade 6 is designed to help you help students sharpen their problem-solving abilities (and share a.

  6. Grade 6 Math Word Problems with Answers

    GRADE 6 MATH WORD PROBLEMS WITH ANSWERS ... Problem 1 : A train travels 18 km/hr. How many meters will it travel in 12 minutes. ... So, the distance covered is 3600

  7. Realistic Math Problems Help 6th-graders Solve Real-Life Questions

    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

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