What are Expressions?

Hello, Year 6! Today, we are going to learn about simplifying expressions. An expression is a combination of numbers, letters (which we call variables), and operation signs (like +, -, ×, ÷). For example, an expression could be ( 3x + 4 ).

Why Simplify Expressions?

When we simplify expressions, we make them easier to work with. Simplifying helps us solve problems faster and understand maths better!

Key Rules for Simplifying Expressions

  1. Combine Like Terms:
    • Like terms are terms that have the same variable and exponent. For example, ( 2x ) and ( 3x ) are like terms because they both have the variable ( x ).
    • To combine them, you simply add or subtract the numbers in front of the variable.
    • Example: 2x + 3x = (2 + 3)x = 5x
  2. Use the Distributive Property:
    • This means multiplying a single term by each term inside a bracket.
    • Example: 3(2 + x) = 3 \times 2 + 3 \times x = 6 + 3x
  3. Keep It Neat:
    • Always write your final answer in the simplest form.
    • Example: Instead of writing ( 4 + 2x + 3 ), you can combine ( 4 ) and ( 3 ) to write ( 7 + 2x ).

Tips and Tricks

  • Look for Patterns: When combining terms, try to group them together.
  • Double-Check Your Work: Always read through your simplified expression to ensure you didn’t miss anything.
  • Practice!: The more you practice simplifying expressions, the easier it will become.

Examples to Try

  1. Simplify ( 5a + 3a ).
  2. Simplify ( 7y – 2y + 4 ).
  3. Simplify ( 2(3 + 4x) ).

Questions for You

Easy Level Questions

  1. Simplify ( 2x + 3x ).
  2. Simplify ( 4y + 5y ).
  3. Simplify ( 6 + 2 + 3 ).
  4. Simplify ( 5a + 2a ).
  5. Simplify ( 3p + 4p ).
  6. Simplify ( 10 – 3 + 2 ).
  7. Simplify ( 2x + 5 – 3x ).
  8. Simplify ( 1 + 1 + 1 + 1 ).
  9. Simplify ( 6m + 3m ).
  10. Simplify ( 4x + 2 + 3x ).

Medium Level Questions

  1. Simplify ( 2(3x + 4) ).
  2. Simplify ( 5y + 3y – 2y ).
  3. Simplify ( 4 – (2x + 1) ).
  4. Simplify ( 3(2 + 5x) ).
  5. Simplify ( 5a + 2 – 3a + 7 ).
  6. Simplify ( 2x + 3y – 5 + x – 2y ).
  7. Simplify ( 4x + 5 – 3x + 2 ).
  8. Simplify ( 6(2 + y) ).
  9. Simplify ( 3(2x + 4) – 5x ).
  10. Simplify ( 7p – 2 – 3p + 4 ).

Hard Level Questions

  1. Simplify ( 4(2x + 3) + 3(3x – 2) ).
  2. Simplify ( 5y + 2(3y – 1) – 4y ).
  3. Simplify ( 6x – (2x + 3) + 7 ).
  4. Simplify ( 3(4x – 2) + 2(5 – x) ).
  5. Simplify ( 2(3a + 4) – 3(2a – 1) ).
  6. Simplify ( 5(x + 2) – 3(2x – 1) ).
  7. Simplify ( x + 5 – 3(2x – 4) ).
  8. Simplify ( 7(2 + x) – 4(1 + 3x) ).
  9. Simplify ( 6x + 5 – (3x + 4 – 2x) ).
  10. Simplify ( 2(3x – 5) + 4(x + 1) – 3x ).

Answers and Explanations

Easy Level Answers

  1. ( 5x )
  2. ( 9y )
  3. ( 11 )
  4. ( 7a )
  5. ( 7p )
  6. ( 9 )
  7. ( -x + 5 )
  8. ( 4 )
  9. ( 9m )
  10. ( 7x + 2 )

Medium Level Answers

  1. ( 6 + 8x )
  2. ( 6y )
  3. ( 3 – 2x )
  4. ( 6 + 15x )
  5. ( 2a + 9 )
  6. ( -y + 2x – 5 )
  7. ( x + 7 )
  8. ( 12 + 6y )
  9. ( 6x + 12 – 5x = x + 12 )
  10. ( 4p + 2 )

Hard Level Answers

  1. ( 24x + 6 )
  2. ( 6y + 2 )
  3. ( 4x + 4 )
  4. ( 6x + 10 )
  5. ( a + 11 )
  6. ( -x + 10 )
  7. ( -5x + 23 )
  8. ( 14 – x )
  9. ( 3x + 5 )
  10. ( 4x – 6 )

Remember, practice makes perfect! Keep working on simplifying expressions, and soon it will feel like second nature. Happy learning!