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%

Style

Step

List

Mode

Exam

Practice

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.

Please drag and drop the selected option in the right place or type it instead

order

operations

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Explanation

Vocabulary – Grouping Symbols

1 pts

Complete the definition:

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

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Explanation

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

Click on an item in the first group
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?

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

Addition

Subtraction

Multiplication

Division

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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?

Numerator: addition first. Denominator: subtraction first.

Numerator: multiplication first. Denominator: subtraction inside parentheses first.

Numerator: division first. Denominator: addition first.

Both: work left to right without any grouping.

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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.

Evaluate the numerator: \(-20 + 3(-5)\)

Evaluate the denominator: \(21 - (-4)^2\)

Add numerator and denominator together

Find the absolute value of the numerator

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Explanation

Common Mistake – Multiply Before Divide

2 pts

volume_mute

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

Which student made the correct calculation?

Student A: \(40 \div (-4) = -10\), then \(-10 \cdot 5 = -50\)

Student B: \((-4) \cdot 5 = -20\), then \(40 \div (-20) = -2\)

Both students are correct.

Neither student is correct.

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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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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:

Always equal 20.

Always equal 36.

Have more than one value, depending on the order operations are performed.

Be undefined, because addition and multiplication cannot mix.

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Explanation

Year 8

Vocabulary – Order of Operations Rule

Correct Answer

Explanation

Vocabulary – Grouping Symbols

Correct Answer

Explanation

Vocabulary – Innermost and Outermost Grouping Symbols

Correct Answer

Explanation

Vocabulary – Estimation

Correct Answer

Explanation

Match Each Grouping Symbol to Its Name

Symbol

Name

Correct Answer

Explanation

Notation – Number Next to Absolute Value Bars

Correct Answer

Explanation

Sort the Four Steps of the Order of Operations

Correct Answer

Explanation

Vocabulary – Fraction Bar as a Grouping Symbol

Correct Answer

Explanation

Classify by Type of Grouping Symbol

drag and drop the selected option to the right place

Correct Answer

Explanation

Fraction Bar – What Must Be Done Before Dividing?

Correct Answer

Explanation

Common Mistake – Multiply Before Divide

Correct Answer

Explanation

Identify the Operation-Order Words in the Rule

Correct Answer

Explanation

Catch the Vocabulary Term!

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

Correct Answer

Explanation

List the Operations in Order for This Expression

Correct Answer

Explanation

Why Is the Order of Operations Rule Needed?

Correct Answer

Explanation

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