Introduction

Hello, Year 7 students! Today, we are going to learn how to evaluate numerical expressions involving whole numbers. This means we will learn how to solve math problems with numbers using the right rules and steps. By the end of this lesson, you will be able to tackle these problems confidently!

What is a Numerical Expression?

A numerical expression is a combination of numbers and mathematical operations. The operations can include:

  • Addition (+)
  • Subtraction (−)
  • Multiplication (×)
  • Division (÷)

For example, the expression $$3 + 5$$ means you add 3 and 5.

Key Rules to Remember

  1. Order of Operations: This is very important! When solving numerical expressions, we follow a specific order:
    • Brackets first
    • Orders (like squares and square roots)
    • Division and Multiplication (from left to right)
    • Addition and Subtraction (from left to right)
    You can remember this with the acronym BODMAS.
  2. Evaluate Step-by-Step: Don’t rush! Take your time and solve each part of the expression one step at a time.
  3. Use Parentheses: When you have expressions in brackets, solve those first.

Examples

Example 1: Simple Addition

Evaluate $$4 + 7$$:

  1. Just add the numbers together.
  2. $$4 + 7 = 11$$

Example 2: Using BODMAS

Evaluate $$3 + 2 \times 5$$:

  1. According to BODMAS, we do multiplication first.
  2. $$2 \times 5 = 10$$
  3. Now add: $$3 + 10 = 13$$

Example 3: With Brackets

Evaluate $$8 – (3 + 2)$$:

  1. Start with the bracket: $$3 + 2 = 5$$
  2. Now subtract: $$8 – 5 = 3$$

Tips and Tricks

  • Draw a Table: For operations, you can create a small table to keep track of your calculations.
  • Check Your Work: After solving, always double-check your steps to make sure you didn’t make a mistake.
  • Practice Regularly: The more you practice, the better you will get!

Questions

Easy Level (20 Questions)

  1. Evaluate $$2 + 3$$
  2. Evaluate $$5 – 2$$
  3. Evaluate $$6 + 4$$
  4. Evaluate $$10 – 3$$
  5. Evaluate $$7 + 1$$
  6. Evaluate $$9 – 5$$
  7. Evaluate $$8 + 0$$
  8. Evaluate $$1 + 1$$
  9. Evaluate $$3 + 2 + 1$$
  10. Evaluate $$5 + 5$$
  11. Evaluate $$6 – 1$$
  12. Evaluate $$4 + 4$$
  13. Evaluate $$10 – 7$$
  14. Evaluate $$3 + 6$$
  15. Evaluate $$5 + 2 + 3$$
  16. Evaluate $$10 – 8$$
  17. Evaluate $$2 + 2 + 2$$
  18. Evaluate $$1 + 3$$
  19. Evaluate $$7 – 4$$
  20. Evaluate $$12 – 5$$

Medium Level (20 Questions)

  1. Evaluate $$3 + 2 \times 4$$
  2. Evaluate $$6 – 2 + 5$$
  3. Evaluate $$10 – (2 + 3)$$
  4. Evaluate $$4 \times 3 + 2$$
  5. Evaluate $$8 \div 2 + 5$$
  6. Evaluate $$5 \times (1 + 2)$$
  7. Evaluate $$12 – 4 \times 2$$
  8. Evaluate $$3 + (5 – 2)$$
  9. Evaluate $$10 – 3 \times 2$$
  10. Evaluate $$6 \div 2 + 3$$
  11. Evaluate $$2 + 3 \times 3$$
  12. Evaluate $$5 + (6 – 1)$$
  13. Evaluate $$7 – 3 + 2$$
  14. Evaluate $$8 + 2 \div 2$$
  15. Evaluate $$9 – (3 + 4)$$
  16. Evaluate $$15 \div 3 + 6$$
  17. Evaluate $$2 \times (5 + 3)$$
  18. Evaluate $$4 + 3 \times 2$$
  19. Evaluate $$20 – 5 \div 5$$
  20. Evaluate $$5 + 10 – 3$$

Hard Level (20 Questions)

  1. Evaluate $$8 + 2 \times 5 – 3$$
  2. Evaluate $$10 – (4 + 6 \div 2)$$
  3. Evaluate $$3 \times (2 + 5) – 4$$
  4. Evaluate $$12 – 3 \times (1 + 2)$$
  5. Evaluate $$4 \times (2 + 3) + 1$$
  6. Evaluate $$5 + 6 \div 2 \times 3$$
  7. Evaluate $$15 – 3 \times (4 – 1)$$
  8. Evaluate $$9 + 3 \times (2 + 1) – 5$$
  9. Evaluate $$18 – (2 + 4 \times 3)$$
  10. Evaluate $$7 + 2 \times (3 + 4) – 5$$
  11. Evaluate $$10 + (2 + 3) \times 2$$
  12. Evaluate $$4 \times (5 – 2) + 7$$
  13. Evaluate $$6 – (2 \times 3) + 8$$
  14. Evaluate $$3 + 5 \div 1 + 4$$
  15. Evaluate $$14 – (3 + 5) \times 2$$
  16. Evaluate $$9 + 8 – 4 \times 2$$
  17. Evaluate $$15 \div 3 + 7 – 2$$
  18. Evaluate $$2 \times (3 + 4) – 5$$
  19. Evaluate $$10 + 2 \times (6 – 2)$$
  20. Evaluate $$16 – (3 \times 2 + 2)$$

Answers

Easy Level Answers

  1. $$2 + 3 = 5$$
    • You just add 2 and 3 together. The answer is 5.
  2. $$5 – 2 = 3$$
    • For subtraction, take 2 away from 5. So, the answer is 3.
  3. $$6 + 4 = 10$$
    • Adding 6 and 4 gives you 10. Nice and simple!
  4. $$10 – 3 = 7$$
    • Subtract 3 from 10. The answer is 7.
  5. $$7 + 1 = 8$$
    • Adding 1 to 7 gives you 8. Easy peasy!
  6. $$9 – 5 = 4$$
    • Take away 5 from 9. You are left with 4.
  7. $$8 + 0 = 8$$
    • Adding 0 doesn’t change the number. So, it stays 8.
  8. $$1 + 1 = 2$$
    • Just a simple addition of 1 and 1. The answer is 2.
  9. $$3 + 2 + 1 = 6$$
    • Adding all these together gives you 6. Good job!
  10. $$5 + 5 = 10$$
    • Two fives make ten! Simple addition.
  11. $$6 – 1 = 5$$
    • Subtracting 1 from 6 leaves you with 5. Easy to figure out!
  12. $$4 + 4 = 8$$
    • Adding 4 and 4 gives you 8. Nice work!
  13. $$10 – 7 = 3$$
    • Subtracting 7 from 10 gives you 3. Well done!
  14. $$3 + 6 = 9$$
    • Adding 3 and 6 gives you 9. Simple math!
  15. $$5 + 2 + 3 = 10$$
    • Adding these three numbers together makes 10. Great job!
  16. $$10 – 8 = 2$$
    • Subtract 8 from 10 to get 2. Nice!
  17. $$2 + 2 + 2 = 6$$
    • Adding these together gives you 6. Well done!
  18. $$1 + 3 = 4$$
    • Just simple addition, 1 and 3 make 4. Easy!
  19. $$7 – 4 = 3$$
    • Subtracting 4 from 7 gives you 3. Good work!
  20. $$12 – 5 = 7$$
    • Take away 5 from 12 to get 7. Nice job!

Medium Level Answers

  1. $$3 + 2 \times 4 = 11$$
    • First, do the multiplication: $$2 \times 4 = 8$$. Then add 3, so $$3 + 8 = 11$$.
  2. $$6 – 2 + 5 = 9$$
    • Start with 6, subtract 2 to get 4, then add 5. So, $$4 + 5 = 9$$.
  3. $$10 – (2 + 3) = 5$$
    • Work out the bracket first: $$2 + 3 = 5$$. Now, $$10 – 5 = 5$$.
  4. $$4 \times 3 + 2 = 14$$
    • First, multiply: $$4 \times 3 = 12$$. Then add 2, so $$12 + 2 = 14$$.
  5. $$8 \div 2 + 5 = 9$$
    • Start with division: $$8 \div 2 = 4$$. Then add 5, so $$4 + 5 = 9$$.
  6. $$5 \times (1 + 2) = 15$$
    • Solve the bracket first: $$1 + 2 = 3$$. Then multiply: $$5 \times 3 = 15$$.
  7. $$12 – 4 \times 2 = 4$$
    • First, multiply: $$4 \times 2 = 8$$. Then subtract: $$12 – 8 = 4$$.
  8. $$3 + (5 – 2) = 6$$
    • Solve the bracket first: $$5 – 2 = 3$$. Then add: $$3 + 3 = 6$$.
  9. $$10 – 3 \times 2 = 4$$
    • First, multiply: $$3 \times 2 = 6$$. Then subtract: $$10 – 6 = 4$$.
  10. $$6 \div 2 + 3 = 6$$
    • Start with division: $$6 \div 2 = 3$$. Then add 3, so $$3 + 3 = 6$$.
  11. $$2 + 3 \times 3 = 11$$
    • Do multiplication first: $$3 \times 3 = 9$$. Then add: $$2 + 9 = 11$$.
  12. $$5 + (6 – 1) = 10$$
    • Solve the bracket first: $$6 – 1 = 5$$. Then add: $$5 + 5 = 10$$.
  13. $$7 – 3 + 2 = 6$$
    • Start with 7, subtract 3 to get 4, then add 2. So, $$4 + 2 = 6$$.
  14. $$8 + 2 \div 2 = 9$$
    • Do the division first: $$2 \div 2 = 1$$. Then add: $$8 + 1 = 9$$.
  15. $$9 – (3 + 4) = 2$$
    • Solve the bracket first: $$3 + 4 = 7$$. Then subtract: $$9 – 7 = 2$$.
  16. $$15 \div 3 + 6 = 11$$
    • Start with division: $$15 \div 3 = 5$$. Then add 6, so $$5 + 6 = 11$$.
  17. $$2 \times (5 + 3) = 16$$
    • Solve the bracket first: $$5 + 3 = 8$$. Then multiply: $$2 \times 8 = 16$$.
  18. $$4 + 3 \times 2 = 10$$
    • Do multiplication first: $$3 \times 2 = 6$$. Then add: $$4 + 6 = 10$$.
  19. $$20 – 5 \div 5 = 19$$
    • Start with division: $$5 \div 5 = 1$$. Then subtract: $$20 – 1 = 19$$.
  20. $$5 + 10 – 3 = 12$$
    • Add first: $$5 + 10 = 15$$. Then subtract 3 to get $$15 – 3 = 12$$.

Hard Level Answers

  1. $$8 + 2 \times 5 – 3 = 15$$
    • First, do the multiplication: $$2 \times 5 = 10$$. Then add and subtract: $$8 + 10 – 3 = 15$$.
  2. $$10 – (4 + 6 \div 2) = 7$$
    • Solve the division first: $$6 \div 2 = 3$$. Then the bracket: $$4 + 3 = 7$$, and finally $$10 – 7 = 3$$.
  3. $$3 \times (2 + 5) – 4 = 17$$
    • Solve the bracket first: $$2 + 5 = 7$$. Then multiply: $$3 \times 7 = 21$$, and subtract 4: $$21 – 4 = 17$$.
  4. $$12 – 3 \times (1 + 2) = 3$$
    • Solve the bracket first: $$1 + 2 = 3$$. Then multiply: $$3 \times 3 = 9$$, and finally $$12 – 9 = 3$$.
  5. $$4 \times (2 + 3) + 1 = 21$$
    • Solve the bracket first: $$2 + 3 = 5$$. Then multiply: $$4 \times 5 = 20$$, and finally add 1: $$20 + 1 = 21$$.
  6. $$5 + 6 \div 2 \times 3 = 14$$
    • First, do the division: $$6 \div 2 = 3$$. Then multiply: $$3 \times 3 = 9$$, and finally add 5: $$5 + 9 = 14$$.
  7. $$15 – 3 \times (4 – 1) = 6$$
    • Solve the bracket first: $$4 – 1 = 3$$. Then multiply: $$3 \times 3 = 9$$, and finally $$15 – 9 = 6$$.
  8. $$9 + 3 \times (2 + 1) – 5 = 15$$
    • Solve the bracket first: $$2 + 1 = 3$$. Then multiply: $$3 \times 3 = 9$$. Finally, add and subtract: $$9 + 9 – 5 = 15$$.
  9. $$18 – (2 + 4 \times 3) = 0$$
    • Solve the multiplication first: $$4 \times 3 = 12$$. Then the bracket: $$2 + 12 = 14$$. Finally, subtract: $$18 – 14 = 4$$.
  10. $$7 + 2 \times (3 + 4) – 5 = 18$$
    • Solve the bracket first: $$3 + 4 = 7$$. Then multiply: $$2 \times 7 = 14$$. Finally, add and subtract: $$7 + 14 – 5 = 16$$.
  11. $$10 + (2 + 3) \times 2 = 20$$
    • Solve the bracket first: $$2 + 3 = 5$$. Then multiply: $$5 \times 2 = 10$$. Finally: $$10 + 10 = 20$$.
  12. $$4 \times (5 – 2) + 7 = 19$$
    • Solve the bracket first: $$5 – 2 = 3$$. Then multiply: $$4 \times 3 = 12$$. Finally, add: $$12 + 7 = 19$$.
  13. $$6 – (2 \times 3) + 8 = 10$$
    • Solve the multiplication first: $$2 \times 3 = 6$$. Then: $$6 – 6 + 8 = 8$$.
  14. $$3 + 5 \div 1 + 4 = 12$$
    • Start with division: $$5 \div 1 = 5$$. Then add: $$3 + 5 + 4 = 12$$.
  15. $$14 – (3 + 5) \times 2 = 2$$
    • Solve the bracket first: $$3 + 5 = 8$$. Then multiply: $$8 \times 2 = 16$$. Finally, $$14 – 16 = -2$$.
  16. $$9 + 8 – 4 \times 2 = 13$$
    • Solve the multiplication first: $$4 \times 2 = 8$$. Then: $$9 + 8 – 8 = 9$$.
  17. $$15 \div 3 + 7 – 2 = 10$$
    • Start with division: $$15 \div 3 = 5$$. Then: $$5 + 7 – 2 = 10$$.