Name the property, and give the reason for each step in solving an equation

Answer Key - Grade 9 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   To solve 3x = 12, Esme multiplies both sides by 1/3 and writes (1/3) · 3 = 1. Which property of numbers does that step show?

   • Inverse property of multiplication
   • Associative property of multiplication
   • Commutative property of multiplication
   • Identity property of multiplication
2. 2.

   To solve x + 7 = 12, Ari adds −7 to both sides and writes 7 + (−7) = 0. Which property of numbers does that step show?

   • Inverse property of addition
   • Identity property of addition
   • Commutative property of addition
   • Associative property of addition
3. 3.

   Bo rewrites (x · 5) · 4 as x · (5 · 4). Which property of numbers allows this?

   • Inverse property of multiplication
   • Identity property of multiplication
   • Associative property of multiplication
   • Commutative property of multiplication
4. 4.

   Luz rewrites (x + 6) + 4 as x + (6 + 4). Which property of numbers allows this?

   • Commutative property of addition
   • Associative property of addition
   • Inverse property of addition
   • Identity property of addition
5. 5.

   Ren solves 5x − 3 = 2x + 9 and writes 3x − 3 = 9. What is the reason for this step?

   • Subtraction property of equality
   • Division property of equality
   • Addition property of equality
   • Multiplication property of equality
6. 6.

   Tala solves x/4 − 3 = 5 and writes x/4 = 8. What is the reason for this step?

   • Addition property of equality
   • Multiplication property of equality
   • Division property of equality
   • Subtraction property of equality
7. 7.

   Zee solves 3(x + 2) = 18 and writes x + 2 = 6. What is the reason for this step?

   • Distributive property
   • Division property of equality
   • Multiplication property of equality
   • Addition property of equality
8. 8.

   Jun solves x/6 = 2.5 and writes x = 15. What is the reason for this step?

   • Commutative property of multiplication
   • Addition property of equality
   • Division property of equality
   • Multiplication property of equality
9. 9.

   Pia spreads −3(2x − 5) with the distributive property. The first piece is −6x. What is the missing number in −6x + ?

   15
10. 10.

    Kira spreads 4(3x − 7) with the distributive property. The first piece is 12x. What is the missing number in 12x + ?

    -28