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Z.1 Identify the equations

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What are equations?

Equations are mathematical statements that show two expressions are equal. They use an equal sign (=) to connect both sides.

Examples:
  • 3 + 4 = 7
  • 12 – 5 = 7
  • 2 × 5 = 10
Note

An equation always has two sides that balance. Both sides must represent the same value.

How to identify an equation

An equation has numbers, operations (like +, −, ×, ÷), and an equal sign (=). If there is no equal sign, it is not an equation.

Examples:
  • 7 + 8 = 15 → This is an equation.
  • 4 × 3 = 11 → This is an equation, but it is not true.
  • 9 − 2 → This is an expression, not an equation, because there is no equal sign.
Note

Always look for the equal sign (=) to decide if something is an equation.

Solving equations with a missing number

Sometimes an equation has a missing number, shown with a box (□) or a letter. To solve, find the number that makes both sides equal.

Examples:
  • 6 + □ = 10 → □ = 4
  • 15 − x = 9 → x = 6
  • 3 × n = 12 → n = 4
Note

Check your answer by putting the number back into the equation to see if both sides are equal.

Writing equations from word problems

Equations can represent real-world situations. Translate the problem into numbers, operations, and an equal sign.

Examples:
  • Maria has 5 apples. She buys 3 more. How many apples does she have? → 5 + 3 = 8
  • A box holds 4 toys. How many toys are in 3 boxes? → 3 × 4 = 12
  • Sam had 12 pencils. He gave away some and now has 7. How many did he give away? → 12 − □ = 7
Note

Underline key numbers in the problem to help write your equation correctly.

Checking your equations

After solving, always check your work. Both sides of the equation must have the same value to be correct.

Examples:
  • 8 + 6 = 14 → Check: 8 + 6 = 14 ✓
  • 20 ÷ 5 = 4 → Check: 20 ÷ 5 = 4 ✓
  • 9 − 3 = 5 → Check: 9 − 3 = 6 ✗
Note

Checking helps you catch mistakes and build confidence in your answers.