Real-World Equations

Grade 6 · algebra · 95 practice problems · read aloud

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Real-World Equations: Making Math Make Sense 🌍

What Are Real-World Equations?

An equation is like a balanced scale—what's on the left of the equals sign (=) has the same value as what's on the right. We use equations to solve problems from everyday life, like figuring out how much pizza to order or how much money you'll have left after buying a video game. They turn word problems into math we can solve!

How to Solve Real-World Problems: Your Step-by-Step Guide

  1. Step 1: Understand - Read the problem carefully. What is it asking you to find?
  2. Step 2: Define the Variable - Choose a letter (like n or x) to represent what you're trying to find.
  3. Step 3: Write the Equation - Translate the words into a math sentence using your variable.
  4. Step 4: Solve - Work through the steps to find the value of your variable.
  5. Step 5: Check - Plug your answer back into the original problem. Does it make sense?

Visual Examples

Example 1: The Pizza Party

You have $30 to spend on pizzas. Each pizza costs $10. How many pizzas can you buy?

  1. We are finding the number of pizzas. Let p = number of pizzas.
  2. Equation: 10p = 30 (Cost per pizza × number of pizzas = Total money)
  3. Solve: 10p ÷ 10 = 30 ÷ 10 → p = 3
  4. Check: 3 pizzas × $10 = $30. ✔️ That makes sense!

Example 2: Saving for a Game

You already have $25. You need a total of $60 to buy a new game. How much more money do you need?

  1. We are finding the money needed. Let m = money needed.
  2. Equation: 25 + m = 60 (Money you have + money needed = total cost)
  3. Solve: 25 + m - 25 = 60 - 25 → m = 35
  4. Check: $25 + $35 = $60. ✔️ Correct!

Common Mistakes to Avoid 🚫

  • Mistake: Not defining the variable. Fix: Always start by writing "Let x = ..." so you know what you're solving for.
  • Mistake: Flipping the equation incorrectly. Fix: The equals sign means "is the same as." "You have 5 more than me" is you = me + 5, not me = you + 5.
  • Mistake: Forgetting to check the answer. Fix: Always ask yourself, "Does this answer make sense in the real world?"

Tips & Tricks

  • 🔄 Inverse Operations are Key: Use the opposite operation to solve. Addition undoes subtraction. Multiplication undoes division.
  • 📝 Underline Key Info: When reading a problem, underline the numbers and the question being asked.
  • 🤔 Estimate First: Before solving, guess what a reasonable answer might be. This helps you catch big mistakes later!

How to Practice

To get better at writing and solving equations, try these ideas:

  • Create Your Own Problems: Look around you and make up equations about your snacks, allowance, or video game scores.
  • Use Online Games: Websites like Khan Academy and Prodigy have fun, interactive practice.
  • Practice with a Partner: Give a friend a word problem and see if they can write the correct equation for it.

Practice problems

6 of the 95, worked through step by step — try them before opening the answer.

1 3/4 × 2/3 ÷ 1/2 = ?

Hint: When multiplying fractions, multiply numerators and denominators separately. When dividing, multiply by the reciprocal of the divisor.

Show the answer

Answer: 1

  1. Understand the order of operations** Multiplication and division have the same priority, so we work left to right. First compute: 3/4 × 2/3 Multiply numerators: 3 × 2 = 6 Multiply denominators: 4 × 3 = 12 So 3/4 × 2/3 = 6/12 Simplify 6/12: divide numerator and denominator by 6 → 1/2 Now the expression is: 1/2 ÷ 1/2 --- **
  2. Division of fractions** Dividing by 1/2 means multiplying by its reciprocal (2/1). So: 1/2 ÷ 1/2 = 1/2 × 2/1 --- **
  3. Multiply** Multiply numerators: 1 × 2 = 2 Multiply denominators: 2 × 1 = 2 So: 2/2 = 1 --- **Final Answer:** 1

Let's solve step by step. We have: 3/4 × 2/3 ÷ 1/2 --- **

2 (-12) × 3 + 15 ÷ (-5) = ?

Hint: Remember to follow the order of operations (PEMDAS/BODMAS) and pay close attention to the signs when multiplying and dividing negative numbers.

Show the answer

Answer: -39

  1. Identify the order of operations (PEMDAS/BODMAS)** Multiplication and division come before addition. So first compute: (-12) × 3 and 15 ÷ (-5) --- **
  2. Perform multiplication** (-12) × 3 = -36 --- **
  3. Perform division** 15 ÷ (-5) = -3 --- **
  4. Rewrite the expression with results** Now we have: -36 + (-3) --- **
  5. Perform addition** Adding a negative is the same as subtracting: -36 + (-3) = -36 - 3 = -39 --- **Final Answer:** -39

Let's solve step by step. We have: (-12) × 3 + 15 ÷ (-5) --- **

3 (-15) × 4 - 24 ÷ (-6) = ?

Hint: Remember to follow the order of operations and pay attention to the signs when multiplying and dividing negative numbers.

Show the answer

Answer: -56

  1. First, perform the multiplication: (-15) × 4 = -60
  2. Next, perform the division: 24 ÷ (-6) = -4
  3. Now substitute the results: -60 - (-4)
  4. Subtracting a negative is the same as adding: -60 + 4
  5. Add the numbers: -60 + 4 = -56

The answer is -56.

4 (-15) × 4 ÷ (-6) + 3² = ?

Hint: Remember to follow the order of operations (PEMDAS) and pay attention to negative signs when multiplying and dividing.

Show the answer

Answer: 19

  1. Calculate (-15) × 4 = -60
  2. Calculate -60 ÷ (-6) = 10 (dividing two negatives gives a positive)
  3. Calculate 3² = 9
  4. Add the results: 10 + 9 = 19

The answer is 19.

5 (-15) × 4 ÷ (-6) + 2³ = ?

Hint: Remember to follow the order of operations (PEMDAS) and pay attention to negative signs when multiplying and dividing.

Show the answer

Answer: 18

  1. Calculate the exponent first: 2³ = 2 × 2 × 2 = 8
  2. Multiply: (-15) × 4 = -60
  3. Divide: -60 ÷ (-6) = 10 (dividing two negatives gives a positive)
  4. Add: 10 + 8 = 18

The answer is 18.

6 (-15) × 4 - 24 ÷ (-3) = ?

Hint: Remember to follow the order of operations (PEMDAS) and pay attention to the signs when multiplying and dividing negative numbers.

Show the answer

Answer: -52

  1. First, handle the multiplication: (-15) × 4 = -60
  2. Next, handle the division: 24 ÷ (-3) = -8
  3. Now substitute back into the expression: -60 - (-8)
  4. Subtracting a negative is the same as adding: -60 + 8
  5. Combine the numbers: -60 + 8 = -52

The answer is -52.

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