Unit 5 Basic Worksheet

Algebra Basics & Patterns - 25 Questions

Unit 5 Basic Worksheet

Algebra Basics & Patterns

Practice fundamental concepts of variables, expressions, one-step equations, and number patterns.

Question 1: If n = 5, what is n + 7?

Answer: 0

n + 7 = 5 + 7 = 12. Replace the variable with its value.

Question 2: Write an expression for 'a number plus 8': ___

Answer: n + 8

'A number plus 8' translates to n + 8, where n is the unknown number.

Question 3: If m = 3, what is 4 × m?

Answer: 0

4 × m = 4 × 3 = 12. In algebra, 4m means 4 times m.

Question 4: If y = 10, what is y - 4? ___

Answer: 6

y - 4 = 10 - 4 = 6. Substitute and calculate.

Question 5: In algebra, 3n means 3 times n.

Answer: True

True! When a number is next to a variable, it means multiplication: 3n = 3 × n.

Question 6: Solve: x + 5 = 12

Answer: 0

Subtract 5 from both sides: x = 12 - 5 = 7. Check: 7 + 5 = 12 ✓

Question 7: Solve: n - 8 = 15. n = ___

Answer: 23

Add 8 to both sides: n = 15 + 8 = 23. Check: 23 - 8 = 15 ✓

Question 8: Solve: 4m = 24

Answer: 0

Divide both sides by 4: m = 24 ÷ 4 = 6. Check: 4 × 6 = 24 ✓

Question 9: Solve: p ÷ 3 = 7. p = ___

Answer: 21

Multiply both sides by 3: p = 7 × 3 = 21. Check: 21 ÷ 3 = 7 ✓

Question 10: To solve x + 5 = 12, you should subtract 5 from both sides.

Answer: True

True! Subtraction is the inverse of addition, so subtract 5 to isolate x.

Question 11: What is the next number? 3, 6, 9, 12, ___

Answer: 0

The pattern adds 3 each time: 12 + 3 = 15.

Question 12: What is the rule for this pattern? 5, 10, 15, 20, 25 → Rule: ___

Answer: add 5

Each number increases by 5, so the rule is 'add 5'.

Question 13: Complete: 2, 4, 8, 16, ___

Answer: 0

Each number doubles (×2): 16 × 2 = 32.

Question 14: What comes next? 50, 45, 40, 35, ___

Answer: 30

The pattern subtracts 5 each time: 35 - 5 = 30.

Question 15: The pattern 7, 14, 21, 28 follows the rule 'multiply by 7'.

Answer: False

False! The rule is 'add 7' not 'multiply by 7'. Or you can say 'multiply position by 7'.

Question 16: Emma has x stickers. She gets 6 more. Write an expression for her total stickers.

Answer: x + 6

Starting with x stickers and getting 6 more: x + 6 stickers total.

Question 17: Jake buys b bananas at $2 each. Write an expression for the total cost in dollars.

Answer: 2b

If each banana costs $2 and he buys b bananas: 2 × b = 2b dollars.

Question 18: If k = 12, what is k ÷ 4? ___

Answer: 3

k ÷ 4 = 12 ÷ 4 = 3. Division with variables works like regular division.

Question 19: Which expression means '5 less than a number'?

Answer: 0

'5 less than a number' means n - 5. Order matters in subtraction!

Question 20: If w = 6, what is 2w + 3? ___

Answer: 15

2w + 3 = 2(6) + 3 = 12 + 3 = 15. Multiply first, then add.

Question 21: A baker makes 4 cookies on day 1, 8 on day 2, 12 on day 3. How many on day 5 if the pattern continues?

Answer: 20

Pattern: 4, 8, 12, 16, 20. Rule: add 4 (or day × 4). Day 5: 20 cookies.

Question 22: What number is missing? 7, 14, ___, 28, 35

Answer: 0

The pattern adds 7 each time: 14 + 7 = 21.

Question 23: Solve: y + 12 = 20. y = ___

Answer: 8

Subtract 12 from both sides: y = 20 - 12 = 8. Check: 8 + 12 = 20 ✓

Question 24: The expression 'triple a number' can be written as 3n.

Answer: True

True! 'Triple' means multiply by 3, so 'triple a number' is 3n.

Question 25: Maria has d dollars. She spends half. Write an expression for the money she has left.

Answer: d ÷ 2

'Half' means divide by 2: d ÷ 2 or d/2 dollars left.

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