Properties & Patterns
Which property is shown? 12 + 7 = 7 + 12
Answer: Commutative property of addition
Step-by-step solution
The numbers switch places, but the sum stays the same: 12 + 7 = 19 and 7 + 12 = 19.
Solve: x + 8 = 19
Answer: x = 11
Step-by-step solution
Subtract 8 from both sides: x = 19 − 8 = 11.
Find the next number: 6, 10, 14, 18, __
Answer: 22
Step-by-step solution
The pattern adds 4 each time. So 18 + 4 = 22.
Is 5x + 9 an expression or an equation?
Answer: Expression
Step-by-step solution
There is no equals sign. It represents a mathematical quantity.
Does x = 6 make x + 5 = 11 true?
Answer: Yes
Step-by-step solution
Substitute 6 for x: 6 + 5 = 11. Both sides equal 11.
Simplify: 6 + (4 + 3)
Answer: 13
Step-by-step solution
First add inside the parentheses: 4 + 3 = 7. Then add 6 + 7 = 13.
Solve: y − 6 = 15
Answer: y = 21
Step-by-step solution
Add 6 to both sides: y = 15 + 6 = 21.
Find the next number: 3, 6, 12, 24, __
Answer: 48
Step-by-step solution
The pattern multiplies by 2 each time. So 24 × 2 = 48.
Write an expression: 7 less than a number n
Answer: n − 7
Step-by-step solution
Start with n. '7 less than' means subtract 7 from n.
Does y = 4 make 3y = 15 true?
Answer: No
Step-by-step solution
Substitute 4: 3 × 4 = 12, not 15.
Which property is shown? 5 × (2 × 4) = (5 × 2) × 4
Answer: Associative property of multiplication
Step-by-step solution
The grouping changes, but the order of the factors stays the same.
Solve: 5n = 35
Answer: n = 7
Step-by-step solution
Divide both sides by 5: n = 35 ÷ 5 = 7.
A notebook costs $3. Complete the rule for n notebooks: total cost = ?
Answer: 3n
Step-by-step solution
Multiply the number of notebooks by $3. For n notebooks, the cost is 3n dollars.
Write an equation: Three times a number y is 21
Answer: 3y = 21
Step-by-step solution
'Three times' means 3y. 'Is' means equals 21.
Does x = 5 make 2x + 3 = 13 true?
Answer: Yes
Step-by-step solution
Substitute 5: 2 × 5 + 3 = 10 + 3 = 13.
Use the distributive property: 4( x + 6)
Answer: 4x + 24
Step-by-step solution
Multiply 4 by both terms: 4 × x = 4x and 4 × 6 = 24.
Solve: x ÷ 4 = 6
Answer: x = 24
Step-by-step solution
Multiply both sides by 4: x = 6 × 4 = 24.
A table shows 2 tickets cost $8 and 4 tickets cost $16. What is the cost per ticket?
Answer: $4
Step-by-step solution
Divide total cost by the number of tickets: $8 ÷ 2 = $4. Check: $16 ÷ 4 = $4.
Are 3(x + 4) and 3x + 12 equivalent?
Answer: Yes
Step-by-step solution
Distribute 3: 3 × x = 3x and 3 × 4 = 12. Both expressions equal 3x + 12.
Is 14 greater than or equal to 14?
Answer: Yes
Step-by-step solution
The symbol ≥ means greater than or equal to. Since the two numbers are equal, the statement is true.
Simplify using a property: 8 × 17 × 0
Answer: 0
Step-by-step solution
The zero property of multiplication says any number multiplied by 0 equals 0.
Solve: 3x + 4 = 19
Answer: x = 5
Step-by-step solution
Step 1: Subtract 4: 3x = 15. Step 2: Divide by 3: x = 5.
A rectangle has 4 rows of tiles. Each row has x red tiles and 3 blue tiles. Write two equivalent expressions for the total number of tiles.
Answer: 4(x + 3) and 4x + 12
Step-by-step solution
There are 4 groups of (x + 3), so the first expression is 4(x + 3). Distribute 4: 4 × x + 4 × 3 = 4x + 12.
Are 2(x + 5) and 2x + 5 equivalent? Explain.
Answer: No
Step-by-step solution
Distribute 2 to both terms: 2(x + 5) = 2x + 10, not 2x + 5.
Does x = 3 make 4x − 2 > 10 true?
Answer: No
Step-by-step solution
Substitute 3: 4 × 3 − 2 = 12 − 2 = 10. The statement becomes 10 > 10, which is false because 10 is not greater than 10.