Order of Operations and Estimation (vocabulary)

Learn important vocabulary for order of operations and estimation for integers

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QUESTION OF
Views #: 71
Questions #: 15
Time: 15 minutes
Pass Score: 80.0%
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Vocabulary – Order of Operations Rule

1 pts

Complete the definition:

To evaluate expressions that contain more than one operation, we use the (1) of (2) rule.

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order
operations
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Correct Answer

Explanation

Vocabulary – Grouping Symbols

1 pts

Complete the definition:

Absolute value symbols, parentheses, and brackets are types of (1) symbols.

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Vocabulary – Innermost and Outermost Grouping Symbols

1 pts

Complete the definition using the expression \(-9 + 2[-5 - 6(-3 - 1)]\):

The parentheses are the (1) grouping symbols and the brackets are the (2) grouping symbols.

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innermost
outermost
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Explanation

Vocabulary – Estimation

1 pts

Complete the definition:

In situations where an exact answer is not needed, an (1) is a quick way of obtaining a rough idea of the size of the actual answer.

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Explanation

Match Each Grouping Symbol to Its Name

2 pts

Match each grouping symbol on the left to its correct name on the right.

To complete the line match

  1. Click on an item in the first group
  2. Click on the match in the second group

To delete a match, double click on a line

Symbol

( )
[ ]
| |

Name

Brackets
Absolute value symbols
Fraction bar
Parentheses
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Explanation

Notation – Number Next to Absolute Value Bars

1 pts
volume_mute

The book states: a number immediately outside and next to an absolute value symbol indicates which operation?

\[-2 + 9|8 - (-2 + 4)|\]

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Explanation

Sort the Four Steps of the Order of Operations

2 pts
Please drag and drop the options to sort them

Drag the four steps of the Order of Operations rule into the correct order (Step 1 first, Step 4 last).

Perform all additions and subtractions as they occur from left to right.
Evaluate all exponential expressions.
Perform all calculations within grouping symbols.
Perform all multiplications and divisions as they occur from left to right.
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Explanation

Vocabulary – Fraction Bar as a Grouping Symbol

2 pts
volume_mute

Consider the expression: \(\dfrac{5 + 5(7)}{2 + (4 - 8)}\)

In the numerator, what operation should be performed first? In the denominator, what operation should be performed first?

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Explanation

Classify by Type of Grouping Symbol

2 pts

Drag each expression into the correct category based on the type of grouping symbol it contains.

drag and drop the selected option to the right place

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Explanation

Fraction Bar – What Must Be Done Before Dividing?

2 pts
volume_mute

When evaluating \(\dfrac{-20 + 3(-5)}{21 - (-4)^2}\), select all steps that must be completed before performing the division indicated by the fraction bar.

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Explanation

Common Mistake – Multiply Before Divide

2 pts
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The book warns of a common mistake when evaluating \(40 \div (-4) \cdot 5\).

Which student made the correct calculation?

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Explanation

Identify the Operation-Order Words in the Rule

1 pts
Click or touch the word(s) you want to choose
volume_mute

Read the Order of Operations rule and click on the two words that describe the direction in which multiplications/divisions and additions/subtractions must be performed. Perform all calculations within parentheses and other grouping symbols first. Evaluate all exponential expressions. Perform all multiplications and divisions as they occur from left to right. Perform all additions and subtractions as they occur from left to right.

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Correct Answer

Explanation

Catch the Vocabulary Term!

3 pts

Catch each falling term and drop it into the correct definition box.

Drag and drop each option into the correct category. Click to return an item to the pool.

Options Pool
Types of grouping symbols
Drop here
Estimation vocabulary
Drop here
Order of nesting
Drop here
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Explanation

List the Operations in Order for This Expression

2 pts

For the expression \(5(-2)^2 - 1\), drag the operations into the correct order of evaluation:

First: (1)    Second: (2)    Third: (3)

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Evaluate the exponent: (-2)²
Subtract: result - 1
Multiply: 5 × result
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Explanation

Why Is the Order of Operations Rule Needed?

1 pts
volume_mute

The section opens by explaining why the order of operations rule exists. According to the book, without this rule, an expression such as \(2 + 3 \times 6\) would:

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Keywords
Year 8