7th Grade Math: 100 Solved Problems!

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7th Grade Math: 100 Solved Problems!

Hey guys! Are you ready to dive into some awesome 7th-grade math problems? I've compiled 100 super helpful, solved questions just for you. Get ready to boost those math skills and ace your next test! Each question comes with a detailed solution to help you understand every step. Let's get started!

Number Sense and Operations

Number Sense and Operations are fundamental in 7th-grade math. Understanding how numbers work and how to manipulate them is crucial for success in more advanced topics. This section includes problems covering integers, fractions, decimals, percentages, ratios, and proportions. Mastering these concepts will help you build a solid foundation for algebra and geometry. We will explore various operations such as addition, subtraction, multiplication, and division involving different types of numbers.

  1. Problem: Evaluate: βˆ’15 + 23 βˆ’ 8 + 12

    Solution: βˆ’15 + 23 βˆ’ 8 + 12 = 8 βˆ’ 8 + 12 = 0 + 12 = 12

  2. Problem: Calculate: (3/4) Γ— (8/9)

    Solution: (3/4) Γ— (8/9) = (3 Γ— 8) / (4 Γ— 9) = 24/36 = 2/3

  3. Problem: Convert 0.75 to a fraction.

    Solution: 0. 75 = 75/100 = 3/4

  4. Problem: What is 30% of 150?

    Solution: 30% of 150 = (30/100) Γ— 150 = 0.3 Γ— 150 = 45

  5. Problem: Solve the proportion: 4/x = 12/18

    Solution: 4/x = 12/18 Cross-multiply: 4 Γ— 18 = 12 Γ— x 72 = 12x x = 72/12 = 6

  6. Problem: Simplify: 25 Γ· 0.5

    Solution: 25 Γ· 0.5 = 25 Γ· (1/2) = 25 Γ— 2 = 50

  7. Problem: Evaluate: βˆ’7 βˆ’ (βˆ’10) + 5 βˆ’ 3

    Solution: βˆ’7 βˆ’ (βˆ’10) + 5 βˆ’ 3 = βˆ’7 + 10 + 5 βˆ’ 3 = 3 + 5 βˆ’ 3 = 8 βˆ’ 3 = 5

  8. Problem: Calculate: (5/6) Γ· (2/3)

    Solution: (5/6) Γ· (2/3) = (5/6) Γ— (3/2) = (5 Γ— 3) / (6 Γ— 2) = 15/12 = 5/4

  9. Problem: Convert 1/8 to a decimal.

    Solution: 1/8 = 0.125

  10. Problem: What is 60% of 200?

    Solution: 60% of 200 = (60/100) Γ— 200 = 0.6 Γ— 200 = 120

Algebra

Alright, let's jump into Algebra! This section is all about solving equations, working with variables, and understanding expressions. Algebra is like a puzzle where you need to find the missing piece. We'll cover topics such as solving one-step and two-step equations, simplifying algebraic expressions, and working with inequalities. Algebraic thinking is a key skill for success in higher-level math courses, so pay close attention! You'll learn how to manipulate equations to isolate variables, combine like terms, and use the distributive property.

  1. Problem: Solve for x: x + 7 = 15

    Solution: x + 7 = 15 Subtract 7 from both sides: x = 15 βˆ’ 7 = 8

  2. Problem: Solve for y: 3y = 21

    Solution: 3y = 21 Divide both sides by 3: y = 21/3 = 7

  3. Problem: Simplify: 2a + 5a βˆ’ 3a

    Solution: 2a + 5a βˆ’ 3a = (2 + 5 βˆ’ 3)a = 4a

  4. Problem: Solve for z: z/4 = 5

    Solution: z/4 = 5 Multiply both sides by 4: z = 5 Γ— 4 = 20

  5. Problem: Solve for m: 2m + 3 = 11

    Solution: 2m + 3 = 11 Subtract 3 from both sides: 2m = 8 Divide both sides by 2: m = 8/2 = 4

  6. Problem: Simplify: 4b βˆ’ 2b + 6b βˆ’ b

    Solution: 4b βˆ’ 2b + 6b βˆ’ b = (4 βˆ’ 2 + 6 βˆ’ 1)b = 7b

  7. Problem: Solve for p: p βˆ’ 9 = βˆ’2

    Solution: p βˆ’ 9 = βˆ’2 Add 9 to both sides: p = βˆ’2 + 9 = 7

  8. Problem: Solve for q: 5q = βˆ’35

    Solution: 5q = βˆ’35 Divide both sides by 5: q = βˆ’35/5 = βˆ’7

  9. Problem: Simplify: 3c + 7c βˆ’ 5c + 2c

    Solution: 3c + 7c βˆ’ 5c + 2c = (3 + 7 βˆ’ 5 + 2)c = 7c

  10. Problem: Solve for r: r/6 = βˆ’4

    Solution: r/6 = βˆ’4 Multiply both sides by 6: r = βˆ’4 Γ— 6 = βˆ’24

Geometry

Now, let's explore Geometry! Geometry is all about shapes, sizes, positions, and properties of space. We'll be looking at things like area, perimeter, volume, and angles. Get ready to calculate the area of rectangles, triangles, and circles, as well as find the perimeter of different shapes. Understanding angles and their relationships is also a key part of geometry. This section will help you develop spatial reasoning skills and understand the world around you in a more mathematical way. So, grab your ruler and compass, and let’s get started with some geometric fun!

  1. Problem: Find the area of a rectangle with length 8 cm and width 5 cm.

    Solution: Area = length Γ— width = 8 cm Γ— 5 cm = 40 cmΒ²

  2. Problem: Find the perimeter of a square with side length 6 inches.

    Solution: Perimeter = 4 Γ— side length = 4 Γ— 6 inches = 24 inches

  3. Problem: Find the area of a triangle with base 10 m and height 7 m.

    Solution: Area = (1/2) Γ— base Γ— height = (1/2) Γ— 10 m Γ— 7 m = 35 mΒ²

  4. Problem: Find the circumference of a circle with radius 4 cm (use Ο€ β‰ˆ 3.14).

    Solution: Circumference = 2 Γ— Ο€ Γ— radius = 2 Γ— 3.14 Γ— 4 cm = 25.12 cm

  5. Problem: Find the volume of a cube with side length 3 cm.

    Solution: Volume = side lengthΒ³ = 3 cm Γ— 3 cm Γ— 3 cm = 27 cmΒ³

  6. Problem: Find the area of a circle with radius 5 inches (use Ο€ β‰ˆ 3.14).

    Solution: Area = Ο€ Γ— radiusΒ² = 3.14 Γ— (5 inches)Β² = 3.14 Γ— 25 inchesΒ² = 78.5 inchesΒ²

  7. Problem: Find the perimeter of a rectangle with length 12 cm and width 7 cm.

    Solution: Perimeter = 2 Γ— (length + width) = 2 Γ— (12 cm + 7 cm) = 2 Γ— 19 cm = 38 cm

  8. Problem: Find the area of a square with side length 9 m.

    Solution: Area = side lengthΒ² = (9 m)Β² = 81 mΒ²

  9. Problem: Find the volume of a rectangular prism with length 6 cm, width 4 cm, and height 5 cm.

    Solution: Volume = length Γ— width Γ— height = 6 cm Γ— 4 cm Γ— 5 cm = 120 cmΒ³

  10. Problem: Find the circumference of a circle with diameter 10 inches (use Ο€ β‰ˆ 3.14).

    Solution: Circumference = Ο€ Γ— diameter = 3.14 Γ— 10 inches = 31.4 inches

Ratios and Proportions

Let’s tackle Ratios and Proportions! This section is all about comparing quantities and understanding how they relate to each other. Ratios help us compare two numbers, while proportions help us solve problems involving equivalent ratios. We’ll cover topics such as setting up ratios, solving proportions, and applying these concepts to real-world problems. For example, you might need to figure out how much of each ingredient you need to double a recipe, or how to scale a map to represent actual distances. Understanding ratios and proportions is super useful in everyday life and in many different fields of study!

  1. Problem: Express the ratio of 15 apples to 20 oranges in simplest form.

    Solution: 15/20 = 3/4. The ratio is 3:4.

  2. Problem: Solve for x: 3/5 = x/25

    Solution: Cross-multiply: 3 Γ— 25 = 5 Γ— x 75 = 5x x = 75/5 = 15

  3. Problem: A map has a scale of 1 inch = 50 miles. How many inches on the map represent 300 miles?

    Solution: Set up a proportion: 1/50 = x/300 Cross-multiply: 1 Γ— 300 = 50 Γ— x 300 = 50x x = 300/50 = 6 inches

  4. Problem: If 4 notebooks cost $12, how much will 7 notebooks cost?

    Solution: Cost per notebook = $12/4 = $3 Cost for 7 notebooks = 7 Γ— $3 = $21

  5. Problem: Express the ratio of 24 students to 8 teachers in simplest form.

    Solution: 24/8 = 3/1. The ratio is 3:1.

  6. Problem: Solve for y: 2/7 = y/42

    Solution: Cross-multiply: 2 Γ— 42 = 7 Γ— y 84 = 7y y = 84/7 = 12

  7. Problem: A recipe calls for 2 cups of flour for every 3 cups of sugar. How many cups of flour are needed for 9 cups of sugar?

    Solution: Set up a proportion: 2/3 = x/9 Cross-multiply: 2 Γ— 9 = 3 Γ— x 18 = 3x x = 18/3 = 6 cups of flour

  8. Problem: If 5 pens cost $7.50, how much will 12 pens cost?

    Solution: Cost per pen = $7.50/5 = $1.50 Cost for 12 pens = 12 Γ— $1.50 = $18

  9. Problem: Express the ratio of 36 cars to 12 trucks in simplest form.

    Solution: 36/12 = 3/1. The ratio is 3:1.

  10. Problem: Solve for z: 5/8 = z/64

    Solution: Cross-multiply: 5 Γ— 64 = 8 Γ— z 320 = 8z z = 320/8 = 40

Percentages

Time for Percentages! Understanding percentages is super important because they show up everywhere – from calculating discounts at the store to understanding statistics in the news. In this section, we’ll cover topics like converting between percentages, decimals, and fractions, finding the percentage of a number, and solving percentage increase and decrease problems. Mastering percentages will help you make informed decisions in your daily life and excel in math class. So, get ready to become a percentage pro!

  1. Problem: What is 25% of 80?

    Solution: (25/100) Γ— 80 = 0.25 Γ— 80 = 20

  2. Problem: 60 is what percent of 200?

    Solution: (60/200) Γ— 100 = 0.3 Γ— 100 = 30%

  3. Problem: Increase 120 by 15%.

    Solution: 15% of 120 = (15/100) Γ— 120 = 0.15 Γ— 120 = 18 Increased value = 120 + 18 = 138

  4. Problem: Decrease 250 by 8%.

    Solution: 8% of 250 = (8/100) Γ— 250 = 0.08 Γ— 250 = 20 Decreased value = 250 βˆ’ 20 = 230

  5. Problem: What is 40% of 150?

    Solution: (40/100) Γ— 150 = 0.4 Γ— 150 = 60

  6. Problem: 90 is what percent of 300?

    Solution: (90/300) Γ— 100 = 0.3 Γ— 100 = 30%

  7. Problem: Increase 180 by 20%.

    Solution: 20% of 180 = (20/100) Γ— 180 = 0.2 Γ— 180 = 36 Increased value = 180 + 36 = 216

  8. Problem: Decrease 320 by 5%.

    Solution: 5% of 320 = (5/100) Γ— 320 = 0.05 Γ— 320 = 16 Decreased value = 320 βˆ’ 16 = 304

  9. Problem: What is 75% of 240?

    Solution: (75/100) Γ— 240 = 0.75 Γ— 240 = 180

  10. Problem: 120 is what percent of 400?

    Solution: (120/400) Γ— 100 = 0.3 Γ— 100 = 30%

Data Analysis and Probability

Alright, let's dive into Data Analysis and Probability! This is where we learn how to collect, organize, and interpret data to make informed decisions. We’ll cover topics like mean, median, mode, range, and creating different types of graphs such as bar graphs and pie charts. Plus, we’ll explore probability – the chance of something happening. Understanding data and probability is super useful for understanding the world around you and making predictions. So, get ready to analyze some data and calculate some probabilities!

  1. Problem: Find the mean of the following data set: 12, 15, 18, 20, 25

    Solution: Mean = (12 + 15 + 18 + 20 + 25) / 5 = 90 / 5 = 18

  2. Problem: Find the median of the following data set: 5, 8, 10, 12, 15

    Solution: Median = 10 (the middle number)

  3. Problem: Find the mode of the following data set: 3, 4, 4, 5, 5, 5, 6

    Solution: Mode = 5 (the number that appears most often)

  4. Problem: Find the range of the following data set: 7, 9, 11, 13, 15

    Solution: Range = 15 βˆ’ 7 = 8

  5. Problem: A bag contains 3 red marbles, 4 blue marbles, and 5 green marbles. What is the probability of picking a red marble?

    Solution: Total marbles = 3 + 4 + 5 = 12 Probability of picking a red marble = 3/12 = 1/4

  6. Problem: Find the mean of the following data set: 8, 10, 12, 14, 16

    Solution: Mean = (8 + 10 + 12 + 14 + 16) / 5 = 60 / 5 = 12

  7. Problem: Find the median of the following data set: 6, 9, 11, 13, 16

    Solution: Median = 11 (the middle number)

  8. Problem: Find the mode of the following data set: 2, 3, 3, 4, 4, 4, 5

    Solution: Mode = 4 (the number that appears most often)

  9. Problem: Find the range of the following data set: 5, 7, 9, 11, 13

    Solution: Range = 13 βˆ’ 5 = 8

  10. Problem: A spinner has 4 equal sections labeled 1, 2, 3, and 4. What is the probability of spinning a 3?

    Solution: Probability of spinning a 3 = 1/4

Integers and Rational Numbers

Let's dive into Integers and Rational Numbers! This section is all about understanding different types of numbers and how they behave. We'll cover topics such as adding, subtracting, multiplying, and dividing integers, as well as working with rational numbers like fractions and decimals. Integers are whole numbers and their opposites (positive and negative), while rational numbers can be expressed as a fraction. Mastering these concepts will help you build a strong foundation for algebra and beyond. So, get ready to explore the world of numbers!

  1. Problem: Evaluate: βˆ’8 + 15 βˆ’ (βˆ’3) + 7

    Solution: βˆ’8 + 15 βˆ’ (βˆ’3) + 7 = βˆ’8 + 15 + 3 + 7 = 7 + 3 + 7 = 10 + 7 = 17

  2. Problem: Calculate: (βˆ’4/5) Γ— (10/12)

    Solution: (βˆ’4/5) Γ— (10/12) = (βˆ’4 Γ— 10) / (5 Γ— 12) = βˆ’40/60 = βˆ’2/3

  3. Problem: Simplify: 3. 25 βˆ’ (βˆ’1.5) + 0.75

    Solution: 3.25 βˆ’ (βˆ’1.5) + 0.75 = 3.25 + 1.5 + 0.75 = 4.75 + 0.75 = 5.5

  4. Problem: Solve for x: x βˆ’ (βˆ’5) = 12

    Solution: x βˆ’ (βˆ’5) = 12 x + 5 = 12 Subtract 5 from both sides: x = 12 βˆ’ 5 = 7

  5. Problem: Evaluate: βˆ’12 βˆ’ 9 + (βˆ’4) βˆ’ (βˆ’6)

    Solution: βˆ’12 βˆ’ 9 + (βˆ’4) βˆ’ (βˆ’6) = βˆ’12 βˆ’ 9 βˆ’ 4 + 6 = βˆ’21 βˆ’ 4 + 6 = βˆ’25 + 6 = βˆ’19

  6. Problem: Calculate: (7/8) Γ· (βˆ’14/16)

    Solution: (7/8) Γ· (βˆ’14/16) = (7/8) Γ— (βˆ’16/14) = (7 Γ— βˆ’16) / (8 Γ— 14) = βˆ’112/112 = βˆ’1

  7. Problem: Simplify: βˆ’2.75 + 4.5 βˆ’ (βˆ’1.25)

    Solution: βˆ’2.75 + 4.5 βˆ’ (βˆ’1.25) = βˆ’2.75 + 4.5 + 1.25 = 1.75 + 1.25 = 3

  8. Problem: Solve for y: y + (βˆ’8) = βˆ’3

    Solution: y + (βˆ’8) = βˆ’3 y βˆ’ 8 = βˆ’3 Add 8 to both sides: y = βˆ’3 + 8 = 5

  9. Problem: Evaluate: 15 + (βˆ’20) βˆ’ (βˆ’5) + 8

    Solution: 15 + (βˆ’20) βˆ’ (βˆ’5) + 8 = 15 βˆ’ 20 + 5 + 8 = βˆ’5 + 5 + 8 = 0 + 8 = 8

  10. Problem: Calculate: (βˆ’9/10) Γ— (5/6)

    Solution: (βˆ’9/10) Γ— (5/6) = (βˆ’9 Γ— 5) / (10 Γ— 6) = βˆ’45/60 = βˆ’3/4

Expressions and Equations

Now, let's dive into Expressions and Equations! This section is all about learning how to write and solve mathematical statements. We'll cover topics such as simplifying algebraic expressions, solving one-step, two-step, and multi-step equations, and using the distributive property. Expressions are mathematical phrases that contain numbers, variables, and operations, while equations are statements that show two expressions are equal. Mastering these skills will help you excel in algebra and beyond. So, get ready to simplify and solve!

  1. Problem: Simplify: 3(x + 2) βˆ’ 4x

    Solution: 3(x + 2) βˆ’ 4x = 3x + 6 βˆ’ 4x = βˆ’x + 6

  2. Problem: Solve for x: 5x βˆ’ 8 = 17

    Solution: 5x βˆ’ 8 = 17 Add 8 to both sides: 5x = 25 Divide both sides by 5: x = 5

  3. Problem: Simplify: 2(3y βˆ’ 1) + 5y

    Solution: 2(3y βˆ’ 1) + 5y = 6y βˆ’ 2 + 5y = 11y βˆ’ 2

  4. Problem: Solve for y: βˆ’3y + 7 = 1

    Solution: βˆ’3y + 7 = 1 Subtract 7 from both sides: βˆ’3y = βˆ’6 Divide both sides by βˆ’3: y = 2

  5. Problem: Simplify: 4(2a + 3) βˆ’ 6a

    Solution: 4(2a + 3) βˆ’ 6a = 8a + 12 βˆ’ 6a = 2a + 12

  6. Problem: Solve for a: 6a βˆ’ 5 = 19

    Solution: 6a βˆ’ 5 = 19 Add 5 to both sides: 6a = 24 Divide both sides by 6: a = 4

  7. Problem: Simplify: 5(b βˆ’ 2) + 3b

    Solution: 5(b βˆ’ 2) + 3b = 5b βˆ’ 10 + 3b = 8b βˆ’ 10

  8. Problem: Solve for b: βˆ’2b + 9 = 3

    Solution: βˆ’2b + 9 = 3 Subtract 9 from both sides: βˆ’2b = βˆ’6 Divide both sides by βˆ’2: b = 3

  9. Problem: Simplify: 2(4c + 1) βˆ’ 7c

    Solution: 2(4c + 1) βˆ’ 7c = 8c + 2 βˆ’ 7c = c + 2

  10. Problem: Solve for c: 7c βˆ’ 3 = 18

    Solution: 7c βˆ’ 3 = 18 Add 3 to both sides: 7c = 21 Divide both sides by 7: c = 3

Measurement and Units

Let's explore Measurement and Units! This section is all about understanding how to measure different quantities and using the correct units. We'll cover topics such as converting between different units of measurement, calculating area, perimeter, volume, and understanding the difference between metric and customary units. Knowing how to measure accurately and convert between units is a super useful skill in everyday life and in many different fields of study. So, get ready to measure up!

  1. Problem: Convert 5 meters to centimeters.

    Solution: 1 meter = 100 centimeters 5 meters = 5 Γ— 100 = 500 centimeters

  2. Problem: Convert 3 kilograms to grams.

    Solution: 1 kilogram = 1000 grams 3 kilograms = 3 Γ— 1000 = 3000 grams

  3. Problem: Convert 8 feet to inches.

    Solution: 1 foot = 12 inches 8 feet = 8 Γ— 12 = 96 inches

  4. Problem: Convert 4 liters to milliliters.

    Solution: 1 liter = 1000 milliliters 4 liters = 4 Γ— 1000 = 4000 milliliters

  5. Problem: Convert 2 miles to feet.

    Solution: 1 mile = 5280 feet 2 miles = 2 Γ— 5280 = 10560 feet

  6. Problem: Convert 700 centimeters to meters.

    Solution: 100 centimeters = 1 meter 700 centimeters = 700 / 100 = 7 meters

  7. Problem: Convert 4500 grams to kilograms.

    Solution: 1000 grams = 1 kilogram 4500 grams = 4500 / 1000 = 4.5 kilograms

  8. Problem: Convert 156 inches to feet.

    Solution: 12 inches = 1 foot 156 inches = 156 / 12 = 13 feet

  9. Problem: Convert 6000 milliliters to liters.

    Solution: 1000 milliliters = 1 liter 6000 milliliters = 6000 / 1000 = 6 liters

  10. Problem: Convert 3. 5 miles to feet.

    Solution: 1 mile = 5280 feet 3.5 miles = 3.5 Γ— 5280 = 18480 feet

Problem Solving

Let's wrap things up with Problem Solving! This section is all about applying your math skills to solve real-world problems. We'll cover a variety of word problems that require you to use different mathematical concepts and strategies. Problem solving is a super important skill because it helps you develop critical thinking and analytical abilities. So, get ready to put your math skills to the test and tackle these challenges!

  1. Problem: A store sells shirts for $15 each and pants for $25 each. If someone buys 3 shirts and 2 pairs of pants, how much do they spend?

    Solution: Cost of shirts = 3 Γ— $15 = $45 Cost of pants = 2 Γ— $25 = $50 Total cost = $45 + $50 = $95

  2. Problem: A train travels at a speed of 80 miles per hour. How far will it travel in 4.5 hours?

    Solution: Distance = speed Γ— time Distance = 80 miles/hour Γ— 4.5 hours = 360 miles

  3. Problem: A rectangle has a length of 12 cm and a width of 8 cm. What is its perimeter?

    Solution: Perimeter = 2 Γ— (length + width) Perimeter = 2 Γ— (12 cm + 8 cm) = 2 Γ— 20 cm = 40 cm

  4. Problem: A recipe calls for 2 cups of flour and 1.5 cups of sugar. If you want to double the recipe, how much flour and sugar do you need?

    Solution: Flour needed = 2 cups Γ— 2 = 4 cups Sugar needed = 1.5 cups Γ— 2 = 3 cups

  5. Problem: A store is having a 20% off sale. If an item originally costs $50, what is the sale price?

    Solution: Discount = 20% of $50 = (20/100) Γ— $50 = 0.2 Γ— $50 = $10 Sale price = $50 βˆ’ $10 = $40

  6. Problem: John earns $12 per hour. If he works 35 hours in a week, how much does he earn?

    Solution: Earnings = hourly rate Γ— hours worked Earnings = $12/hour Γ— 35 hours = $420

  7. Problem: A car travels 240 miles on 8 gallons of gas. How many miles per gallon does the car get?

    Solution: Miles per gallon = total miles / gallons used Miles per gallon = 240 miles / 8 gallons = 30 miles/gallon

  8. Problem: A triangle has a base of 10 inches and a height of 7 inches. What is its area?

    Solution: Area = (1/2) Γ— base Γ— height Area = (1/2) Γ— 10 inches Γ— 7 inches = 35 square inches

  9. Problem: A store buys a product for $30 and sells it for $45. What is the profit?

    Solution: Profit = selling price βˆ’ cost price Profit = $45 βˆ’ $30 = $15

  10. Problem: A class has 25 students. If 60% of the students are girls, how many girls are in the class?

    Solution: Number of girls = 60% of 25 = (60/100) Γ— 25 = 0.6 Γ— 25 = 15 girls

Alright, that's a wrap! You've now worked through 100 solved math problems designed for 7th graders. Keep practicing, and you'll become a math whiz in no time. Good luck with your studies, and remember, math can be fun!