Math Properties Quiz
Questions: 16 · 10 minutes
1. Which property is demonstrated by (2 × 5) × 8 = 2 × (5 × 8)?
Commutative property of multiplication
Distributive property
Multiplicative inverse property
Associative property of multiplication
2. A student rewrites 9 × 17 + 9 × 3 as 9(17 + 3). Which property justifies the step?
Associative property of multiplication
Distributive property
Multiplicative identity property
Additive inverse property
3. Complete the equivalent expression: 4(x + 6) = 4x + ___.
24
6
10
4x
4. Nora wants to multiply 18 by a number without changing its value. Which choice uses the multiplicative identity property?
Add 1 to 18 to obtain 19.
Multiply 18 by 0 to obtain 0.
Multiply 18 by 1 to obtain 18.
Add 0 to 18 to obtain 18.
5. A game score is 8 points below zero. Which calculation adds the opposite amount and returns the score to zero?
Multiply -8 by 0 to get 0.
Multiply -8 by 1 to keep -8.
Add 0 to -8 to keep -8.
Add 8 to -8 to get 0.
6. A calculation contains the factor 0: 14 × 6 × 0. What does the zero property of multiplication tell you?
The product equals 20.
The product equals 0.
The product equals 84.
The product is undefined.
7. What happens when the nonzero number 7/9 is multiplied by its reciprocal, 9/7?
Their sum becomes 1 because the denominators match.
The original fraction remains unchanged because 9/7 is an identity.
Their product is 1, illustrating the multiplicative inverse property.
Their product is 0 because the factors cancel completely.
8. Jordan wants to calculate 25 × 37 × 4 efficiently. Which rewrite correctly applies multiplication properties and gives the right result?
Change multiplication to addition: 25 × (37 + 4) = 1,025.
Add the outside factors first: (25 + 4) × 37 = 1,073.
Reorder and regroup the factors: (25 × 4) × 37 = 3,700.
Keep the original grouping but report 25 × (37 × 4) as 3,600.
9. A student writes 3(8 + 2) = 24 + 2. What best explains the error?
The factor 3 must be multiplied by both 8 and 2.
The values inside the parentheses should be multiplied instead of added.
The order of 8 and 2 must be reversed before multiplying.
The factor 3 should be added to both terms inside the parentheses.
10. How should the distributive property be applied to 7(10 + 3)?
Multiply 7 by 10, then add the unchanged 3.
Multiply 7 by each addend, giving (7 × 10) + (7 × 3).
Add 7 to 10, then multiply the result by 3.
Combine 10 and 3, then add another factor of 7.
11. A student wants to factor the greatest common numerical factor from 5a + 5b. Which result is correct?
Place both variables in a product: 5(ab).
Double the common factor: 10(a + b).
Place the common factor outside the sum: 5(a + b).
Separate the factor from the variables: 5 + (a + b).
12. Which equation demonstrates the commutative property of addition?
6 + 11 = 11 + 6
6 + 0 = 6
6 + (11 + 4) = (6 + 11) + 4
6(11 + 4) = 66 + 24
13. A store has 23 notebooks and receives no additional notebooks. Which equation models this using the additive identity property?
23 - 23 = 0
23 × 0 = 0
23 × 1 = 23
23 + 0 = 23
14. Maya claims that 12 - 5 and 5 - 12 are equal because she only changed the order of the numbers. Which evaluation is correct?
They are equal by the commutative property.
They are not generally equal because subtraction is not commutative.
They are equal because both expressions contain 12 and 5.
They are equal by the associative property.
15. For nonzero, unequal real numbers a and b, a student proposes four general rules. Which proposed rule is not valid?
Changing the order in division: a ÷ b = b ÷ a
Regrouping three factors: (ab)c = a(bc)
Changing the order in addition: a + b = b + a
Distributing over a sum: a(b + c) = ab + ac
16. Without changing the order of the addends, how can 6 + (4 + 9) be regrouped using the associative property of addition?
Reorder the addends to make 9 + (4 + 6).
Replace addition with multiplication to make 6 × (4 + 9).
Exchange the last two addends to make 6 + (9 + 4).
Move the grouping symbols to make (6 + 4) + 9.