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### Numerical Expressions

• Mathematicians have agreed upon a convention for performing arithmetic operations, called the order of operations, so that any mathematical expression will always have the same value.
• Order of Operations
1. Parentheses (work inside grouping symbols)
2. Exponents
3. Multiply and Divide in order from left to right
4. Add and Subtract in order from left to right

### Numerical Expressions

18 ×3 − 49 ÷7 ×3 =
• 54 − 49 ÷7 ×3 =
• 54 − 7 ×3 =
• 54 − 21 =
33
44 ÷(16 − 12) + 7 ×5 =
• 44 ÷4 + 7 ×5 =
• 11 + 35 =
46
(14 − 7) + 72 ÷9 − (8 + 3) =
• 7 + 72 ÷9 − (8 + 3) =
• 7 + 8 − (8 + 3) =
• 7 + 8 − 11 =
• 15 − 11 =
4
7.4 + ((57.7 − 41.5) − 9.1) =
• 7.4 + (16.2 − 9.1) =
• 7.4 + 7.1 =
14.5
2(5 + (27.4 − 6 − (15.4 − 2.5))) =
• 2(5 + (27.4 − 6 − 12.9)) =
• 2(5 + (21.4 − 12.9)) =
• 2(5 + 8.5) =
• 2(13.5) =
27
((11 ×2 + 3) ÷5 ×2 + 10) ÷4 =
• ((22 + 3) ÷5 ×2 + 10) ÷4
• (25 ÷5 ×2 + 10) ÷4 =
• (5 ×2 + 10) ÷4 =
• (10 + 10) ÷4 =
• 20 ÷4 =
5
((17 + 5 ×2) ÷3 − 1) ÷4 =
• ((17 + 10) ÷3 − 1) ÷4 =
• (27 ÷3 − 1) ÷4 =
• (9 − 1) ÷4 =
• 8 ÷4 =
2
While shopping for school, you buy two notebooks for \$ 4.25 each, three pens for \$ 1.50 each, and 5 pencils for \$ 0.75 each. How much money did you spend total?
• 2(\$ 4.25) + 3(\$ 1.50) + 5(\$ 0.75) =
• \$ 8.50 + \$ 4.50 + \$ 3.75 =
• \$ 13.00 + \$ 3.75 =
\$ 16.75
A family with 3 children, 2 adults, and 1 senior citizen purchase tickets for a movie. A child ticket costs \$ 7, an adult ticket costs \$ 10.50, and a senior ticket costs \$ 8. What is the total cost of their tickets?
• 3(\$ 7) + 2(\$ 10.50) + \$ 8 =
• \$ 21 + \$ 21 + \$ 8 =
• \$ 42 + \$ 8 =
\$ 50
Michelle is shopping for groceries. She buys 2 apples for \$ 1.50 each, 6 bananas for \$ 0.75 each, 10 strawberries for \$ 0.25 each, and 1 pineapple for \$ 5. How much did Michelle spend on groceries?
• 2(\$ 1.50) + 6(\$ 0.75) + 10(\$ 0.25) + \$ 5 =
• \$ 3 + \$ 4.50 + \$ 2.50 + \$ 5 =
• \$ 7.50 + \$ 2.50 + \$ 5 =
• \$ 10 + \$ 5 =
\$ 15

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

### Numerical Expressions

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• What You'll Learn and Why 0:08
• Topics Overview
• Vocabulary 0:22
• Order of Operations
• Numerical Expression
• Simplify
• Simplifying an Expression 1:44
• Example 1: Simplify the Expression
• Simplifying an Expression 3:26
• Example 2: Simplify the Expression
• Using an Expression to Solve a Problem 4:29
• Example 3: Babysitting
• Using an Expression to Solve a Problem 6:14
• Example 4: Shopping
• Extra Example 1: Simplify the Expression 7:35
• Extra Example 2: Simplify the Expression 8:55
• Extra Example 3: Finding Total Cost 10:02
• Extra Example 4: Finding Total Cost 11:44