Arithmetic Operations and Integer Concepts

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Questions and Answers

What is the total distance Nora jogs on Tuesday if she jogs 4 1/2 miles on Monday and 1 1/2 miles fewer on Tuesday?

  • 5 miles
  • 2 miles
  • 3 miles
  • 3 1/2 miles (correct)

How deep is the deep end of the swimming pool if the shallow end is 3.75 feet and it is 5.75 feet deeper?

  • -8.5 feet
  • -9.5 feet (correct)
  • -10.5 feet
  • -7.5 feet

If a T-shirt costs $24.25 and this week it costs $5.95 less, what is this week's cost?

  • $20.30
  • $22.30
  • $18.30 (correct)
  • $19.20

Evaluate the expression $4.7 + (-7.2 - (-3.4)$. What is the result?

<p>1.9 (A)</p> Signup and view all the answers

What is the sign of the product for the expression $-62 imes 83$?

<p>Negative (B)</p> Signup and view all the answers

Calculate the product of $(-4)(7)(-2)$.

<p>56 (D)</p> Signup and view all the answers

When Denise makes 21 quarts of ice cream and uses containers that hold 1 3/4 quarts, how many containers does she need?

<p>12 (B)</p> Signup and view all the answers

If the cost of the T-shirt drops from $24.25 to what calculation leads to $18.30?

<p>$24.25 - 5.95 (A)</p> Signup and view all the answers

If a diver is at an elevation of -18 feet and descends another 16 feet, what is the diver's new position?

<p>-34 (D)</p> Signup and view all the answers

After depositing $200 and paying $250 in rent, then incurring a $50 overdraft fee and depositing a $400 paycheck, how much does Russell have in his account?

<p>300 (B)</p> Signup and view all the answers

What is the result of evaluating the expression $6 - (-8)$?

<p>14 (D)</p> Signup and view all the answers

If the greatest temperature in the United States was recorded at -178 feet and in Africa at 545 feet above that, what is the elevation of the highest recorded temperature in Africa?

<p>723 (B)</p> Signup and view all the answers

What is the sum of $ -18 + 12 $?

<p>-6 (C)</p> Signup and view all the answers

If you have $6/4 - 2/3$, which of the following is closest to the correct evaluation?

<p>0.52 (C)</p> Signup and view all the answers

Flashcards

Subtracting integers

To subtract an integer, add its opposite.

Adding fractions with different denominators

Find a common denominator for the fractions and add the numerators. Express in simplest form. E.g: 1/3 + 1/6 = 2/6+1/6 = 3/6 = 1/2

Evaluating expressions with mixed numbers and decimals

Convert mixed numbers into fractions and decimals. Use correct order of operations to simplify.

Dividing fractions

Invert (or flip) the second fraction and multiply.

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Multiplying integers

Positive times positive is positive. Negative times negative is positive. Positive times negative is negative.

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Product of a sequence of integers

The result from multiplying a sequence of integers where each integer can be either positive or negative. The product is positive if the sequence has an even number of negative integers; otherwise, the product is negative.

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Expressing fractions as decimals

Divide the numerator by the denominator to convert a fraction into a decimal.

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Solving word problems involving division of fractions

Use the given context to set up and solve a division expression with fractions. Then find answer.

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Adding negative numbers

Adding negative numbers involves moving left on a number line.

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Subtracting a negative number

Subtracting a negative number is the same as adding the positive equivalent.

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Adding positive and negative numbers

When adding numbers with different signs, find the difference between their absolute values and use the sign of the larger absolute value.

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Subtracting positive and negative numbers

Subtracting a positive number is the same as adding the negative equivalent; subtracting a negative number is the same as adding the positive equivalent.

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Elevation below sea level

An elevation measured below sea level is represented by a negative number.

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Temperature difference

To find the difference between two temperatures, subtract the lower temperature from the higher temperature.

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Combining positive and negative numbers

In financial transactions/situations, positive values represent gains or deposits, while negative values represent losses or withdrawals.

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Finding total costs

Calculate the overall cost by adding the cost of individual items and considering if any discount is given.

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Study Notes

Arithmetic Operations

  • Addition: Combine values. Use number lines to visualize.
  • Subtraction: Find the difference between values. Use number lines to visualize.
  • Multiplication: Repeated addition.
  • Division: Repeated subtraction.
  • Order of Operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (left to right), Addition and Subtraction (left to right).

Integer Operations

  • Addition of Integers: Positive plus positive = positive; Positive plus negative = subtract and use the sign of the larger one
  • Subtraction of Integers: Change subtraction to addition of the opposite.
  • Multiplication/Division of Integers: Positive times/divided by positive = positive Positive times/divided by negative = negative Negative times/divided by positive = negative Negative times/divided by negative = positive

Real-World Applications

  • Problem Solving: Apply operations to solve word problems involving money, measurements, time, etc.
  • Number Lines: Visual aids to represent values and solve problems.
  • Word Problems: Real-world scenarios requiring calculations.

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