Mr. Rosenberger asked his students to use the distributive property to rewrite the expression 18 (24) by using friendlier numbers. The table below shows the expressions that four students created.

Question

Expressions Created by Students
Student
Expression
Aaron
10 + 8 times 4 + 20
Brian
10 + 8 (4 + 20)
Cece
18 (4 + 6)
Diana
18 (4 + 20)

Which student’s expression is equivalent to 18(24)?
Aaron
Brian
Cece
Diana

Answer 1

To determine which student's expression is equivalent to \( 18(24) \), we can rewrite \( 18(24) \) using the distributive property:

1. Rewrite 24: We can express 24 as \( 20 + 4 \). Thus, \[ 18(24) = 18(20 + 4). \]
2. Apply the distributive property: \[ 18(20 + 4) = 18 \times 20 + 18 \times 4. \] This becomes: \[ 360 + 72 = 432. \]

Now let's evaluate each student's expression to see if they yield 432:

• Aaron: \( 10 + 8 \times 4 + 20 \)

  • Calculate: \[ 10 + 8(4) + 20 = 10 + 32 + 20 = 62. \]

• Brian: \( 10 + 8(4 + 20) \)

  • Calculate: \[ 10 + 8(24) = 10 + 192 = 202. \]

• Cece: \( 18(4 + 6) \)

  • Calculate: \[ 18(10) = 180. \]

• Diana: \( 18(4 + 20) \)

  • Calculate: \[ 18(24) = 432. \]

Therefore, after evaluating all the expressions, we find that Diana's expression is equivalent to \( 18(24) \).