25 Math Problems for 6th Graders with Answers and Explanations
Welcome to a collection of 25 math problems specifically designed for 6th graders. These problems cover various mathematical concepts, including fractions, decimals, geometry, and more. Each question is labeled with its corresponding math subcategory and difficulty level, ranging from easy to hard. To assist you in your learning journey, we have provided detailed step-by-step explanations for each problem. Let's get started and boost our mathematical skills!
Problem 1: Multiplying Fractions (Arithmetic) - Easy
Simplify the product: (1/3) × (4/5).
Solution:
Step 1: Multiply the numerators: 1 × 4 = 4.
Step 2: Multiply the denominators: 3 × 5 = 15.
Step 3: Simplify the fraction if possible: 4/15.
Answer: The product of (1/3) and (4/5) is 4/15.
Problem 2: Converting Decimals to Fractions (Arithmetic) - Easy
Express 0.6 as a fraction in simplest form.
Solution:
Step 1: Write the decimal as a fraction: 0.6 = 6/10.
Step 2: Simplify the fraction: 6/10 = 3/5.
Answer: 0.6 is equivalent to 3/5 in simplest form.
Problem 3: Perimeter of a Rectangle (Geometry) - Easy
Find the perimeter of a rectangle with length 8 cm and width 5 cm.
Solution:
Step 1: Use the formula for the perimeter of a rectangle: Perimeter = 2(length + width).
Step 2: Substitute the given values: Perimeter = 2(8 cm + 5 cm).
Step 3: Calculate: Perimeter = 2(13 cm).
Step 4: Multiply: Perimeter = 26 cm.
Answer: The perimeter of the rectangle is 26 cm.
Problem 4: Dividing Decimals (Arithmetic) - Easy
Divide 3.2 by 0.4.
Solution:
Step 1: Set up the division: 3.2 ÷ 0.4.
Step 2: Multiply both numbers by 10 to move the decimal point: 32 ÷ 4.
Step 3: Divide: 32 ÷ 4 = 8.
Answer: 3.2 divided by 0.4 is equal to 8.
Problem 5: Area of a Triangle (Geometry) - Easy
Find the area of a triangle with base length 6 cm and height 4 cm.
Solution:
Step 1: Use the formula for the area of a triangle: Area = (1/2) × base × height.
Step 2: Substitute the given values: Area = (1/2) × 6 cm × 4 cm.
Step 3: Multiply: Area = 3 cm² × 4 cm.
Step 4: Calculate: Area = 12 cm².
Answer: The area of the triangle is 12 cm².
Problem 6: Subtracting Integers (Arithmetic) - Medium
Evaluate the expression: (-8) - (-3).
Solution:
Step 1: Simplify the expression using the rules of subtracting integers: (-8) + 3.
Step 2: Add the numbers: -5.
Answer: The value of the expression is -5.
Problem 7: Converting Fractions to Decimals (Arithmetic) - Medium
Convert 3/4 into a decimal.
Solution:
Step 1: Divide the numerator by the denominator: 3 ÷ 4 = 0.75.
Answer: 3/4 is equivalent to 0.75 as a decimal.
Problem 8: Volume of a Cube (Geometry) - Medium
Find the volume of a cube with edge length 5 cm.
Solution:
Step 1: Use the formula for the volume of a cube: Volume = edge length³.
Step 2: Substitute the given value: Volume = 5 cm × 5 cm × 5 cm.
Step 3: Calculate: Volume = 125 cm³.
Answer: The volume of the cube is 125 cm³.
Problem 9: Solving Equations with Fractions (Algebra) - Medium
Solve the equation: (2/3)x = 8.
Solution:
Step 1: Multiply both sides of the equation by the reciprocal of the fraction: x = 8 × (3/2).
Step 2: Simplify: x = 12.
Answer: The solution to the equation is x = 12.
Problem 10: Ordering Decimals (Arithmetic) - Medium
Arrange the following decimals in ascending order: 0.23, 0.35, 0.19, 0.42.
Solution:
Step 1: Compare the decimals from left to right:
0.19, 0.23, 0.35, 0.42.
Step 2: The ascending order is: 0.19, 0.23, 0.35, 0.42.
Answer: The decimals arranged in ascending order are 0.19, 0.23, 0.35, 0.42.
Problem 11: Solving Proportions (Arithmetic) - Medium
Solve the proportion: 2/5 = x/15.
Solution:
Step 1: Cross-multiply: 2 × 15 = 5x.
Step 2: Calculate: 30 = 5x.
Step 3: Divide by 5: x = 30/5.
Step 4: Simplify: x = 6.
Answer: The solution to the proportion is x = 6.
Problem 12: Operations with Mixed Numbers (Arithmetic) - Medium
Perform the operation: (2 1/2) + (1 3/4).
Solution:
Step 1: Convert the mixed numbers to improper fractions:
(2 1/2) = (5/2),
(1 3/4) = (7/4).
Step 2: Find a common denominator: The least common multiple of 2 and 4 is 4.
Step 3: Rewrite the fractions with a denominator of 4:
(5/2) = (10/4),
(7/4) = (7/4).
Step 4: Add the fractions: (10/4) + (7/4) = 17/4.
Step 5: Simplify the fraction, if possible: 17/4 = 4 1/4.
Answer: (2 1/2) + (1 3/4) = 4 1/4.
Problem 13: Finding Percentages (Arithmetic) - Medium
What is 20% of 80?
Solution:
Step 1: Convert the percentage to a decimal: 20% = 0.20.
Step 2: Multiply: 0.20 × 80 = 16.
Answer: 20% of 80 is 16.
Problem 14: Surface Area of a Rectangular Prism (Geometry) - Medium
Find the surface area of a rectangular prism with length 9 cm, width 6 cm, and height 4 cm.
Solution:
Step 1: Calculate the area of each face:
Face 1: Area = length × width = 9 cm × 6 cm = 54 cm².
Face 2: Area = length × width = 9 cm × 6 cm = 54 cm².
Face 3: Area = width × height = 6 cm × 4 cm = 24 cm².
Face 4: Area = width × height = 6 cm × 4 cm = 24 cm².
Face 5: Area = length × height = 9 cm × 4 cm = 36 cm².
Face 6: Area = length × height = 9 cm × 4 cm = 36 cm².
Step 2: Sum up the areas of all the faces: 54 cm² + 54 cm² + 24 cm² + 24 cm² + 36 cm² + 36 cm² = 228 cm².
Answer: The surface area of the rectangular prism is 228 cm².
Problem 15: Multiplying Decimals (Arithmetic) - Medium
Multiply 0.7 by 0.3.
Solution:
Step 1: Multiply the decimals: 0.7 × 0.3 = 0.21.
Answer: 0.7 multiplied by 0.3 equals 0.21.
Problem 16: Probability (Statistics) - Easy
A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If you randomly select a marble, what is the probability of selecting a red marble?
Solution:
Step 1: Determine the total number of marbles in the bag: 5 + 3 + 2 = 10.
Step 2: Calculate the probability: Number of red marbles / Total number of marbles = 5/10 = 1/2.
Answer: The probability of randomly selecting a red marble is 1/2.
Problem 17: Solving Equations with Variables on Both Sides (Algebra) - Medium
Solve the equation: 3x - 5 = 2x + 7.
Solution:
Step 1: Subtract 2x from both sides: 3x - 2x - 5 = 2x - 2x + 7.
Step 2: Simplify: x - 5 = 7.
Step 3: Add 5 to both sides: x - 5 + 5 = 7 + 5.
Step 4: Simplify: x = 12.
Answer: The solution to the equation is x = 12.
Problem 18: Area of a Circle (Geometry) - Easy
Find the area of a circle with a radius of 3 cm. (Use π ≈ 3.14)
Solution:
Step 1: Use the formula for the area of a circle: Area = πr².
Step 2: Substitute the given value: Area = 3.14 × (3 cm)².
Step 3: Simplify: Area = 3.14 × 9 cm².
Step 4: Multiply: Area = 28.26 cm².
Answer: The area of the circle is 28.26 cm².
Problem 19: Adding and Subtracting Fractions (Arithmetic) - Medium
Evaluate the expression: (2/3) + (1/4) - (1/6).
Solution:
Step 1: Find a common denominator: The least common multiple of 3, 4, and 6 is 12.
Step 2: Rewrite each fraction with a denominator of 12:
(2/3) = (8/12),
(1/4) = (3/12),
(1/6) = (2/12).
Step 3: Add and subtract the fractions: (8/12) + (3/12) - (2/12) = 9/12.
Step 4: Simplify the fraction, if possible: 9/12 = 3/4.
Answer: The simplified expression is 3/4.
Problem 20: Finding Percentages of a Whole (Arithmetic) - Easy
If 40% of a number is 32, what is the number?
Solution:
Step 1: Set up a proportion: 40% = 32 / x.
Step 2: Cross-multiply: 40x = 32.
Step 3: Divide by 40: x = 32 / 40.
Step 4: Simplify: x = 4 / 5.
Answer: The number is 4/5 or 0.8.
Problem 21: Geometry: Identifying Geometric Shapes - Easy
Which of the following shapes has four sides of equal length?
a) Rectangle
b) Square
c) Triangle
d) Circle
Solution:
b) Square
Answer: The shape that has four sides of equal length is a square.
Problem 22: Solving Proportions with Variables (Algebra) - Medium
Solve the proportion: x/5 = 3/10.
Solution:
Step 1: Cross-multiply: 10x = 15.
Step 2: Divide by 10: x = 15/10.
Step 3: Simplify: x = 3/2 or 1.5.
Answer: The solution to the proportion is x = 3/2 or 1.5.
Problem 23: Dividing Fractions (Arithmetic) - Medium
Divide (2/3) by (1/4).
Solution:
Step 1: Take the reciprocal of the second fraction: (2/3) ÷ (1/4) = (2/3) × (4/1).
Step 2: Multiply the fractions: (2/3) × (4/1) = 8/3.
Answer: (2/3) divided by (1/4) is equal to 8/3.
Problem 24: Prime and Composite Numbers (Number Theory) - Easy
Identify whether the number 17 is prime or composite.
Solution:
Step 1: Determine if the number has any factors other than 1 and itself.
Step 2: Since 17 is only divisible by 1 and 17, it is a prime number.
Answer: The number 17 is a prime number.
Problem 25: Order of Operations with Parentheses (Arithmetic) - Medium
Evaluate the expression: 3 × (2 + 4) - 8 ÷ 2.
Solution:
Step 1: Perform the operations inside the parentheses: 3 × 6 - 8 ÷ 2.
Step 2: Divide: 3 × 6 - 4.
Step 3: Multiply: 18 - 4.
Step 4: Subtract: 14.
Answer: The value of the expression is 14.
Congratulations on completing the 25 math problems for 6th graders! By practicing and understanding the step-by-step solutions, you have enhanced your mathematical skills. Keep exploring and applying these concepts to excel in math. Remember, practice makes perfect, so continue to challenge yourself and enjoy the wonders of mathematics!
Problem 1: Multiplying Fractions (Arithmetic) - Easy
Simplify the product: (1/3) × (4/5).
Solution:
Step 1: Multiply the numerators: 1 × 4 = 4.
Step 2: Multiply the denominators: 3 × 5 = 15.
Step 3: Simplify the fraction if possible: 4/15.
Answer: The product of (1/3) and (4/5) is 4/15.
Problem 2: Converting Decimals to Fractions (Arithmetic) - Easy
Express 0.6 as a fraction in simplest form.
Solution:
Step 1: Write the decimal as a fraction: 0.6 = 6/10.
Step 2: Simplify the fraction: 6/10 = 3/5.
Answer: 0.6 is equivalent to 3/5 in simplest form.
Problem 3: Perimeter of a Rectangle (Geometry) - Easy
Find the perimeter of a rectangle with length 8 cm and width 5 cm.
Solution:
Step 1: Use the formula for the perimeter of a rectangle: Perimeter = 2(length + width).
Step 2: Substitute the given values: Perimeter = 2(8 cm + 5 cm).
Step 3: Calculate: Perimeter = 2(13 cm).
Step 4: Multiply: Perimeter = 26 cm.
Answer: The perimeter of the rectangle is 26 cm.
Problem 4: Dividing Decimals (Arithmetic) - Easy
Divide 3.2 by 0.4.
Solution:
Step 1: Set up the division: 3.2 ÷ 0.4.
Step 2: Multiply both numbers by 10 to move the decimal point: 32 ÷ 4.
Step 3: Divide: 32 ÷ 4 = 8.
Answer: 3.2 divided by 0.4 is equal to 8.
Problem 5: Area of a Triangle (Geometry) - Easy
Find the area of a triangle with base length 6 cm and height 4 cm.
Solution:
Step 1: Use the formula for the area of a triangle: Area = (1/2) × base × height.
Step 2: Substitute the given values: Area = (1/2) × 6 cm × 4 cm.
Step 3: Multiply: Area = 3 cm² × 4 cm.
Step 4: Calculate: Area = 12 cm².
Answer: The area of the triangle is 12 cm².
Problem 6: Subtracting Integers (Arithmetic) - Medium
Evaluate the expression: (-8) - (-3).
Solution:
Step 1: Simplify the expression using the rules of subtracting integers: (-8) + 3.
Step 2: Add the numbers: -5.
Answer: The value of the expression is -5.
Problem 7: Converting Fractions to Decimals (Arithmetic) - Medium
Convert 3/4 into a decimal.
Solution:
Step 1: Divide the numerator by the denominator: 3 ÷ 4 = 0.75.
Answer: 3/4 is equivalent to 0.75 as a decimal.
Problem 8: Volume of a Cube (Geometry) - Medium
Find the volume of a cube with edge length 5 cm.
Solution:
Step 1: Use the formula for the volume of a cube: Volume = edge length³.
Step 2: Substitute the given value: Volume = 5 cm × 5 cm × 5 cm.
Step 3: Calculate: Volume = 125 cm³.
Answer: The volume of the cube is 125 cm³.
Problem 9: Solving Equations with Fractions (Algebra) - Medium
Solve the equation: (2/3)x = 8.
Solution:
Step 1: Multiply both sides of the equation by the reciprocal of the fraction: x = 8 × (3/2).
Step 2: Simplify: x = 12.
Answer: The solution to the equation is x = 12.
Problem 10: Ordering Decimals (Arithmetic) - Medium
Arrange the following decimals in ascending order: 0.23, 0.35, 0.19, 0.42.
Solution:
Step 1: Compare the decimals from left to right:
0.19, 0.23, 0.35, 0.42.
Step 2: The ascending order is: 0.19, 0.23, 0.35, 0.42.
Answer: The decimals arranged in ascending order are 0.19, 0.23, 0.35, 0.42.
Problem 11: Solving Proportions (Arithmetic) - Medium
Solve the proportion: 2/5 = x/15.
Solution:
Step 1: Cross-multiply: 2 × 15 = 5x.
Step 2: Calculate: 30 = 5x.
Step 3: Divide by 5: x = 30/5.
Step 4: Simplify: x = 6.
Answer: The solution to the proportion is x = 6.
Problem 12: Operations with Mixed Numbers (Arithmetic) - Medium
Perform the operation: (2 1/2) + (1 3/4).
Solution:
Step 1: Convert the mixed numbers to improper fractions:
(2 1/2) = (5/2),
(1 3/4) = (7/4).
Step 2: Find a common denominator: The least common multiple of 2 and 4 is 4.
Step 3: Rewrite the fractions with a denominator of 4:
(5/2) = (10/4),
(7/4) = (7/4).
Step 4: Add the fractions: (10/4) + (7/4) = 17/4.
Step 5: Simplify the fraction, if possible: 17/4 = 4 1/4.
Answer: (2 1/2) + (1 3/4) = 4 1/4.
Problem 13: Finding Percentages (Arithmetic) - Medium
What is 20% of 80?
Solution:
Step 1: Convert the percentage to a decimal: 20% = 0.20.
Step 2: Multiply: 0.20 × 80 = 16.
Answer: 20% of 80 is 16.
Problem 14: Surface Area of a Rectangular Prism (Geometry) - Medium
Find the surface area of a rectangular prism with length 9 cm, width 6 cm, and height 4 cm.
Solution:
Step 1: Calculate the area of each face:
Face 1: Area = length × width = 9 cm × 6 cm = 54 cm².
Face 2: Area = length × width = 9 cm × 6 cm = 54 cm².
Face 3: Area = width × height = 6 cm × 4 cm = 24 cm².
Face 4: Area = width × height = 6 cm × 4 cm = 24 cm².
Face 5: Area = length × height = 9 cm × 4 cm = 36 cm².
Face 6: Area = length × height = 9 cm × 4 cm = 36 cm².
Step 2: Sum up the areas of all the faces: 54 cm² + 54 cm² + 24 cm² + 24 cm² + 36 cm² + 36 cm² = 228 cm².
Answer: The surface area of the rectangular prism is 228 cm².
Problem 15: Multiplying Decimals (Arithmetic) - Medium
Multiply 0.7 by 0.3.
Solution:
Step 1: Multiply the decimals: 0.7 × 0.3 = 0.21.
Answer: 0.7 multiplied by 0.3 equals 0.21.
Problem 16: Probability (Statistics) - Easy
A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If you randomly select a marble, what is the probability of selecting a red marble?
Solution:
Step 1: Determine the total number of marbles in the bag: 5 + 3 + 2 = 10.
Step 2: Calculate the probability: Number of red marbles / Total number of marbles = 5/10 = 1/2.
Answer: The probability of randomly selecting a red marble is 1/2.
Problem 17: Solving Equations with Variables on Both Sides (Algebra) - Medium
Solve the equation: 3x - 5 = 2x + 7.
Solution:
Step 1: Subtract 2x from both sides: 3x - 2x - 5 = 2x - 2x + 7.
Step 2: Simplify: x - 5 = 7.
Step 3: Add 5 to both sides: x - 5 + 5 = 7 + 5.
Step 4: Simplify: x = 12.
Answer: The solution to the equation is x = 12.
Problem 18: Area of a Circle (Geometry) - Easy
Find the area of a circle with a radius of 3 cm. (Use π ≈ 3.14)
Solution:
Step 1: Use the formula for the area of a circle: Area = πr².
Step 2: Substitute the given value: Area = 3.14 × (3 cm)².
Step 3: Simplify: Area = 3.14 × 9 cm².
Step 4: Multiply: Area = 28.26 cm².
Answer: The area of the circle is 28.26 cm².
Problem 19: Adding and Subtracting Fractions (Arithmetic) - Medium
Evaluate the expression: (2/3) + (1/4) - (1/6).
Solution:
Step 1: Find a common denominator: The least common multiple of 3, 4, and 6 is 12.
Step 2: Rewrite each fraction with a denominator of 12:
(2/3) = (8/12),
(1/4) = (3/12),
(1/6) = (2/12).
Step 3: Add and subtract the fractions: (8/12) + (3/12) - (2/12) = 9/12.
Step 4: Simplify the fraction, if possible: 9/12 = 3/4.
Answer: The simplified expression is 3/4.
Problem 20: Finding Percentages of a Whole (Arithmetic) - Easy
If 40% of a number is 32, what is the number?
Solution:
Step 1: Set up a proportion: 40% = 32 / x.
Step 2: Cross-multiply: 40x = 32.
Step 3: Divide by 40: x = 32 / 40.
Step 4: Simplify: x = 4 / 5.
Answer: The number is 4/5 or 0.8.
Problem 21: Geometry: Identifying Geometric Shapes - Easy
Which of the following shapes has four sides of equal length?
a) Rectangle
b) Square
c) Triangle
d) Circle
Solution:
b) Square
Answer: The shape that has four sides of equal length is a square.
Problem 22: Solving Proportions with Variables (Algebra) - Medium
Solve the proportion: x/5 = 3/10.
Solution:
Step 1: Cross-multiply: 10x = 15.
Step 2: Divide by 10: x = 15/10.
Step 3: Simplify: x = 3/2 or 1.5.
Answer: The solution to the proportion is x = 3/2 or 1.5.
Problem 23: Dividing Fractions (Arithmetic) - Medium
Divide (2/3) by (1/4).
Solution:
Step 1: Take the reciprocal of the second fraction: (2/3) ÷ (1/4) = (2/3) × (4/1).
Step 2: Multiply the fractions: (2/3) × (4/1) = 8/3.
Answer: (2/3) divided by (1/4) is equal to 8/3.
Problem 24: Prime and Composite Numbers (Number Theory) - Easy
Identify whether the number 17 is prime or composite.
Solution:
Step 1: Determine if the number has any factors other than 1 and itself.
Step 2: Since 17 is only divisible by 1 and 17, it is a prime number.
Answer: The number 17 is a prime number.
Problem 25: Order of Operations with Parentheses (Arithmetic) - Medium
Evaluate the expression: 3 × (2 + 4) - 8 ÷ 2.
Solution:
Step 1: Perform the operations inside the parentheses: 3 × 6 - 8 ÷ 2.
Step 2: Divide: 3 × 6 - 4.
Step 3: Multiply: 18 - 4.
Step 4: Subtract: 14.
Answer: The value of the expression is 14.
Congratulations on completing the 25 math problems for 6th graders! By practicing and understanding the step-by-step solutions, you have enhanced your mathematical skills. Keep exploring and applying these concepts to excel in math. Remember, practice makes perfect, so continue to challenge yourself and enjoy the wonders of mathematics!