Question

sally and anne went to the movies. they each purchased a drink. they also bought one popcorn and one veggie cup to share. each womans total is modeled with this expression:

\\9 + 1.34 + \frac{1}{2}(3.50 + 1.74)\\

how would you simplify the expression? explain your steps.

Explanation:

Evaluate inside the parentheses

Using the Decimal Arithmetic and Order of Operations knowledge points

$$ 3.50 + 1.74 = 5.24 $$

Multiply by the fraction

Using the Decimal Arithmetic and Order of Operations knowledge points

$$ \frac{1}{2}(5.24) = 2.62 $$

Perform addition from left to right

Using the Decimal Arithmetic and Order of Operations knowledge points

$$ 9 + 1.34 + 2.62 = 10.34 + 2.62 = 12.96 $$

Answer:

To simplify the expression \(9 + 1.34 + \frac{1}{2}(3.50 + 1.74)\), follow the order of operations:

1. Parentheses: Add the values inside the parentheses first:

$$ 3.50 + 1.74 = 5.24 $$

This leaves the expression as \(9 + 1.34 + \frac{1}{2}(5.24)\).

1. Multiplication: Multiply \(\frac{1}{2}\) by \(5.24\) (which is the same as dividing \(5.24\) by \(2\)):

$$ \frac{1}{2} \times 5.24 = 2.62 $$

This leaves the expression as \(9 + 1.34 + 2.62\).

1. Addition: Add the remaining numbers from left to right:

$$ 9 + 1.34 = 10.34 $$

$$ 10.34 + 2.62 = 12.96 $$

The simplified value of the expression is \(12.96\).