Linear Relations Outcomes
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Questions and Answers

What action would be taken to determine the value of an unknown element on a graph by extending it?

  • Interpolate
  • Extrapolate (correct)
  • Match with an equation
  • Analyze the slope

Which of the following best describes the process of finding an approximate value of one variable on a graph when the other variable's value is known?

  • Linear regression
  • Graphing a function
  • Extrapolation
  • Interpolation (correct)

What is expected when matching a given equation of a linear relation with its corresponding graph?

  • Graph a polynomial function
  • Recognize the slope (correct)
  • Illustrate a parabola
  • Identify the intercepts

Which of the following is NOT a performance indicator related to analyzing a linear graph?

<p>Solve using calculus (D)</p> Signup and view all the answers

When analyzing a graph, what would be the primary goal of the performance indicator related to solving problems by graphing?

<p>Use graphs for data interpretation (A)</p> Signup and view all the answers

What does the exponent in a power indicate?

<p>The number of times the base is multiplied by itself (C)</p> Signup and view all the answers

How is the expression $5^3$ correctly read?

<p>Five to the power of three (B)</p> Signup and view all the answers

Which of the following represents $4^3$ in factored form?

<p>$4 imes 4 imes 4$ (B)</p> Signup and view all the answers

What is the standard form of $2^5$?

<p>$32$ (D)</p> Signup and view all the answers

Which expression represents $6^2$ in exponential form?

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

What is $3^4$ in standard form?

<p>$81$ (C)</p> Signup and view all the answers

If a number is expressed as $( rac{1}{3})^2$, what does this represent in factored form?

<p>$ rac{1}{3} imes rac{1}{3}$ (A)</p> Signup and view all the answers

Which of the following representations is NOT a correct form of a power?

<p>Mixed Number Form (D)</p> Signup and view all the answers

What is the product of the integers (-4) and (+6)?

<p>-20 (B)</p> Signup and view all the answers

What is the sign of the product when multiplying three integers: (-4), (+7), and (-8)?

<p>1 (B)</p> Signup and view all the answers

Which two integers from the set (-3, -1, 1, -2, 4) produce the lowest product?

<p>-3 (C)</p> Signup and view all the answers

What is the result of dividing (-36) by (-4)?

<p>9 (B)</p> Signup and view all the answers

When simplifying the expression (-150) ÷ (-5) × 3 × (-2), what is the final sign of the result?

<p>-1 (C)</p> Signup and view all the answers

In the division problem 25 ÷ __ = 5, what is the missing number?

<p>5 (B)</p> Signup and view all the answers

If two integers produce a quotient of -2, which pair could they be?

<p>-8 (C)</p> Signup and view all the answers

How many withdrawals did Karisa make if she withdrew $14 a total of $98?

<p>7 (B)</p> Signup and view all the answers

What is the result of the operation (-4) + (+6)?

<p>2 (D)</p> Signup and view all the answers

If you subtract a negative number (-5) from another positive number (+3), what will the result be?

<p>8 (C)</p> Signup and view all the answers

What is the final temperature in Celsius at 7 pm if the temperature starts at 0°C, rises 9°C, falls by 12°C, and rises again by 5°C?

<p>2°C (C)</p> Signup and view all the answers

How should the expression (+4) - (+2) be rewritten to use the addition method for subtraction?

<p>(+4) + (-2) (B)</p> Signup and view all the answers

If you multiply the integers (-2), 5, (-1), (-4), 3, and (-2), what will the sign of the product be?

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

What is the result of the subtraction (-5) - (+2)?

<p>-7 (A)</p> Signup and view all the answers

In the operation (5)(-4), what is the correct product?

<p>-20 (A)</p> Signup and view all the answers

What is the result of converting the mixed fraction 6 1/2 to an improper fraction?

<p>13/2 (B)</p> Signup and view all the answers

Which of the following is an equivalent fraction to 1/2?

<p>3/6 (A), 5/10 (B)</p> Signup and view all the answers

What method is used to convert an improper fraction 18/5 into a mixed fraction?

<p>Divide and keep the remainder as the numerator (C)</p> Signup and view all the answers

Which process correctly reduces the fraction 54/66?

<p>Divide both by their Greatest Common Factor (D)</p> Signup and view all the answers

How can you find an equivalent fraction for 2/5?

<p>Multiply both numerator and denominator by 3 (B)</p> Signup and view all the answers

When reducing the fraction 72/96, what is the simplest form?

<p>3/4 (D)</p> Signup and view all the answers

If you have 7/8 and are converting it to have a denominator of 56, what will the equivalent numerator be?

<p>42 (C)</p> Signup and view all the answers

To find the missing value in the equation 3/4 = __ /18, what value should you find?

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

Which of the following is the additive inverse of -12?

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

What is the correct descending order of the integers: -9, -8, 4, -12, 0, 11, -3?

<p>11, 4, 0, -3, -8, -9, -12 (D)</p> Signup and view all the answers

Which statement is true regarding the comparison of integers 3 and 14?

<p>3 &lt; 14 (C)</p> Signup and view all the answers

What value represents an integer that is 5 less than 0?

<p>-5 (B)</p> Signup and view all the answers

Which of the following statements is correct for the integers -7 and -8?

<p>-7 &gt; -8 (D)</p> Signup and view all the answers

Which of the following pairs represents opposites among integers?

<p>-5 and 5 (C), -3 and 3 (D)</p> Signup and view all the answers

Which set notation correctly represents the set of integers?

<p>I = {..., -3, -2, -1, 0, 1, 2, 3, ...} (C)</p> Signup and view all the answers

If an integer is 2 less than -4, what is the value of that integer?

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

What is the sum of $2/5 + 1/2$ in simplest form?

<p>$9/10$ (D)</p> Signup and view all the answers

What is the result of $3/8 - 1/4$ in simplest form?

<p>$1/8$ (D)</p> Signup and view all the answers

What is the product of $2/4 x 18/22$ in simplest form?

<p>$4/11$ (A)</p> Signup and view all the answers

What is the quotient of $3/4 ÷ 6/5$ in simplest form?

<p>$5/8$ (B)</p> Signup and view all the answers

What is the result of $3 2/5 + 2 1/10$ in simplest form?

<p>$5 3/10$ (D)</p> Signup and view all the answers

What is the product of $4 3/4 × 2 1/5 × 1 1/2$ in simplest form?

<p>$10 1/8$ (C)</p> Signup and view all the answers

Convert $1/3$ to its decimal equivalent.

<p>0.33$̅$ (A)</p> Signup and view all the answers

What is the fraction equivalent of the decimal $0.4$ using a denominator of 10?

<p>$4/10$ (C)</p> Signup and view all the answers

Which of the following fractions is the greatest?

<p>7/8 (C)</p> Signup and view all the answers

Compare the following fractions and choose the correct symbol: 1/2 __ 3/5.

<p>&lt; (C)</p> Signup and view all the answers

Among the following, which fractions are equivalent?

<p>1/2 and 2/4 (B)</p> Signup and view all the answers

Which expression represents the value of 5/3 + (-2.5 + 5) - (1/2 ÷ 1/5) × 1.25?

<p>4/3 (D)</p> Signup and view all the answers

What is the result of comparing 0.875 and 4/5?

<p>0.875 = 4/5 (D)</p> Signup and view all the answers

Which decimal is equivalent to 3/4?

<p>0.75 (B)</p> Signup and view all the answers

Arrange the following numbers in ascending order: 1.9, 1/4, -1 2/3.

<p>-1 2/3, 1/4, 1.9 (C)</p> Signup and view all the answers

Determine the remaining amount after Leon spends 2/3 of $45 on a jacket.

<p>$20 (B)</p> Signup and view all the answers

Which decimal is equivalent to the fraction 7/10?

<p>0.7 (C)</p> Signup and view all the answers

What is the result of the operation 5/10 - 2/12 in simplest form?

<p>1/6 (D)</p> Signup and view all the answers

Which comparison is true for the numbers 4/9 and 0.45?

<p>4/9 &lt; 0.45 (C)</p> Signup and view all the answers

How many days are left when the river fishing season of 210 days is 3/5 over?

<p>126 (A)</p> Signup and view all the answers

Which of the following is a true statement about the fractions 12/10 and 1?

<p>12/10 &gt; 1 (C)</p> Signup and view all the answers

What is the correct comparison for -5/6 and -7/8?

<p>-5/6 &gt; -7/8 (C)</p> Signup and view all the answers

Which expression has the highest value?

<p>49/16 (B)</p> Signup and view all the answers

What is the product of (-3) and (-6)?

<p>18 (B)</p> Signup and view all the answers

If there are three negative signs in a multiplication involving positive integers, what will be the sign of the product?

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

Using the integers 0, -3, -1, 1, -2, and 4, which pair gives the greatest product?

<p>(-3, -2) (A)</p> Signup and view all the answers

What is the product when multiplying 5 and (-4)?

<p>-20 (D)</p> Signup and view all the answers

When performing the operation 24 ÷ (-6), what is the quotient?

<p>-4 (B)</p> Signup and view all the answers

Calculate the quotient of (-18) ÷ (-9). What is the result?

<p>2 (D)</p> Signup and view all the answers

If a hot air balloon rises at 5 meters per second for 10 seconds and then descends at 2 meters per second for 6 seconds, how high is it off the ground?

<p>38 (C)</p> Signup and view all the answers

What will be the sign of the product when multiplying -2 x 5 x -1 x -4 x 3 x -2?

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

What is the sign of the quotient when dividing three integers, if there are four negative signs in the calculation?

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

If a division involves three integers where two are negative and one is positive, what will be the sign of the quotient?

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

Which of the following pairs yields a quotient of -2?

<p>4 ÷ -2 (D)</p> Signup and view all the answers

What is the greatest quotient that can be obtained using the integers -2, 3, 12, -1, and 4?

<p>4 (C)</p> Signup and view all the answers

Which of the following fractions is an equivalent fraction for 2/5?

<p>4/10 (B)</p> Signup and view all the answers

What is 3 units to the left of -4?

<p>-7 (C)</p> Signup and view all the answers

What is the result of adding (+2) and (-7)?

<p>-5 (B)</p> Signup and view all the answers

What is the reduced form of the fraction 54/66?

<p>9/11 (B)</p> Signup and view all the answers

Which of the following integers is less than -6 but greater than -10?

<p>-9 (B), -7 (D)</p> Signup and view all the answers

Which of the following describes the operation to find equivalent fractions?

<p>Multiply the numerator and denominator by the same number (D)</p> Signup and view all the answers

What is the final temperature at 7 PM if the temperature after each adjustment is 0 + 9 + (-12) + 5?

<p>2 (D)</p> Signup and view all the answers

Which of these statements about multiplying integers is correct?

<p>The product of two positive integers is positive. (B)</p> Signup and view all the answers

What is the result of the expression (+3) - (-5)?

<p>8 (C)</p> Signup and view all the answers

What is the value of the expression $3/4 \div 5/6$ in simplest form?

<p>$9/10$ (D)</p> Signup and view all the answers

What is the simplified result of the product $(2/20) \times (6/11)$?

<p>$3/110$ (A)</p> Signup and view all the answers

What is the simplified result of the expression $(5/2 - 3/2) \times (3/4)$?

<p>$3/8$ (A)</p> Signup and view all the answers

What is the product of the fractions $3/12$ and $5/(1 + 1/10)$?

<p>$1/2$ (A)</p> Signup and view all the answers

Which of the following represents the correct steps to divide the fraction $3/4$ by $1/10$?

<p>Change to multiplication and flip $1/10$ to $10/1$ (C)</p> Signup and view all the answers

What is the result of the operation $(1/4) + (2/3)$ in simplest form?

<p>$11/12$ (D)</p> Signup and view all the answers

Which method is used to convert a mixed fraction like 6 1/2 into an improper fraction?

<p>Multiply the denominator by the whole number (A), Add the numerator to the product of the whole number and the denominator (B)</p> Signup and view all the answers

What is the first step in multiplying fractions?

<p>Reduce both fractions if possible (B)</p> Signup and view all the answers

When adding the fractions 5/6 and 5/8, what is the next step after finding a common denominator?

<p>Add both numerators together (D)</p> Signup and view all the answers

What is the improper fraction equivalent of the mixed fraction 4 3/4?

<p>19/4 (A)</p> Signup and view all the answers

How would you find the GCF of the numbers 30 and 75?

<p>Check for common factors (D)</p> Signup and view all the answers

What is the result of subtracting 3/8 from 1/4?

<p>-1/8 (D)</p> Signup and view all the answers

When reducing the improper fraction 53/9 to a mixed fraction, what is the whole number part?

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

What is the base in the expression $5^3$?

<p>5 (D)</p> Signup and view all the answers

Which of the following expressions represents the factored form of $6^2$?

<p>$6 imes 6$ (D)</p> Signup and view all the answers

In the expression $y^n$, what does the $n$ stand for?

<p>The number of times to use $y$ as a factor (C)</p> Signup and view all the answers

How is the expression $2^5$ expressed in standard form?

<p>32 (C)</p> Signup and view all the answers

Which of the following correctly represents the exponential notation of the expression $3 imes 3 imes 3$?

<p>$3^3$ (B)</p> Signup and view all the answers

What is the factored form of $( rac{1}{2})^3$?

<p>$ rac{1}{2} imes rac{1}{2} imes rac{1}{2}$ (B)</p> Signup and view all the answers

If $7^4 = 2401$, which statement is true about $7$ and $4$?

<p>7 is the base and 4 is the exponent. (D)</p> Signup and view all the answers

What is the area of a triangle with a base of 6 cm and a height of 4 cm?

<p>12 cm² (C)</p> Signup and view all the answers

Which statement accurately describes the relationship between square roots and perfect squares?

<p>The square root of a perfect square is always an integer. (B)</p> Signup and view all the answers

What is the volume of a cube with a side length of 3 cm?

<p>27 cm³ (D)</p> Signup and view all the answers

If the length of a rectangle is 10 cm and the width is 5 cm, what is its area?

<p>50 cm² (A)</p> Signup and view all the answers

Which of the following represents the area of a square with a side length of 4 cm?

<p>16 cm² (B)</p> Signup and view all the answers

What is the perimeter of a rectangle with a length of 8 cm and a width of 3 cm?

<p>22 cm (D)</p> Signup and view all the answers

Which of the following statements is true about the number √64?

<p>It is equal to 8. (B)</p> Signup and view all the answers

What is the height of a right triangle if the base is 4 cm and the area is 8 cm²?

<p>2 cm (B)</p> Signup and view all the answers

What is the formula for the surface area of a cube?

<p>SA = 6s^2 (D)</p> Signup and view all the answers

For a rectangular prism, which of the following represents its surface area?

<p>SA = 2(lw + lh + wh) (D)</p> Signup and view all the answers

What is the surface area formula for a cylinder?

<p>SA = 2πr^2 + 2πrh (D)</p> Signup and view all the answers

Using Pythagoras, if a triangular prism has a base height of 4 cm and a base width of 4 cm, what is the area of its triangular face?

<p>8 cm^2 (B)</p> Signup and view all the answers

What is the surface area formula for a triangular prism?

<p>SA = 2(½bh) + 3(l x w) (D)</p> Signup and view all the answers

If the radius of a circle is 2 cm, what is its circumference using the formula C = 2πr?

<p>6.28 cm (B)</p> Signup and view all the answers

How do you calculate the surface area of a cylinder with a radius of 1 cm and height of 5 cm?

<p>SA = 2π(1^2) + 2π(1)(5) (D)</p> Signup and view all the answers

What is the surface area of a rectangular prism with a length of 6 cm, width of 4 cm, and height of 3 cm?

<p>108 cm^2 (D)</p> Signup and view all the answers

What is the length of the hypotenuse when the legs of a right triangle are 3 inches and 4 inches?

<p>5 inches (C)</p> Signup and view all the answers

Which of the following numbers is rational?

<p>$\sqrt{16}$ (B)</p> Signup and view all the answers

What is the approximate decimal value of $\sqrt{11}$ using estimation techniques?

<p>3.3 (D)</p> Signup and view all the answers

Which method should be used to round the number 4.6178 to two decimal places?

<p>Round up to 4.62 (C)</p> Signup and view all the answers

If $c^2 = a^2 + b^2$ and $c = 10$ while $b = 6$, what is the value of $a$?

<p>8 (D)</p> Signup and view all the answers

Which statement correctly explains why $\sqrt{5}$ is considered irrational?

<p>No two equal rational numbers multiply out to 5. (B)</p> Signup and view all the answers

What is the square root of 12 rounded to two decimal places?

<p>3.46 (D)</p> Signup and view all the answers

What expression would you use to solve for $b$ if you know $c$ and $a$ in the Pythagorean theorem?

<p>$b = \sqrt{c^2 - a^2}$ (C)</p> Signup and view all the answers

Flashcards

Describe a graph's pattern

Identifying and explaining the trend or pattern shown in a graph, considering the slope, intercept, and direction.

Graph a linear relation

Creating a visual representation of a linear equation on a coordinate plane, ensuring accurate positioning of points and maintaining a straight line.

Interpolate a value

Finding the value of one variable (x or y), on a graph, when you know the value of the other variable, but it falls within the plotted range.

Extrapolate a value

Finding the value of one variable (x or y), on a graph, when you know the value of the other variable, but it falls outside of the plotted range, This requires extending the line.

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Solve a problem using a graph

Solving a problem by representing the relationship between variables using a graph and then analyzing the graph for insights and solutions.

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What is a power?

A way to represent repeated multiplication using a base and an exponent.

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What is a base?

The number being multiplied repeatedly in a power.

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What is an exponent?

The number that indicates how many times the base is multiplied by itself.

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What is exponential notation?

Writing a number as a power using a base and an exponent.

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What is factored form?

Writing a power as a multiplication question using the base as a factor the number of times indicated by the exponent.

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What is standard form?

The actual value of a power, obtained by performing the multiplication.

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Exponential Notation

Represents a number written as a power (base and exponent).

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Factored Form

Represents a number as a multiplication question, where the base is multiplied by itself a number of times equal to the exponent.

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What is an integer?

A positive or negative whole number, including zero.

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Describe the integer set.

The set of all natural numbers (counting numbers), their opposites, and zero.

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What are opposite integers?

Two numbers that are the same distance from zero on a number line but in opposite directions. For example, 5 and -5 are opposites.

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What is the additive inverse of a number?

The additive inverse of a number is the number that, when added to the original number, results in zero. Example: The additive inverse of 5 is -5, because 5 + (-5) = 0.

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What does it mean to order integers in descending order?

To arrange numbers from largest to smallest.

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What does it mean to order integers in ascending order?

To arrange numbers from smallest to largest.

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How are negative integers used?

A way to represent a number that is less than zero.

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How are positive integers used?

A way to represent a number that is greater than zero.

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Adding Integers with Different Signs

Adding numbers with different signs means finding the difference between their absolute values and assigning the sign of the larger absolute value.

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Adding Integers with Same Signs

Adding numbers with the same sign means adding their absolute values and keeping the same common sign.

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Subtracting Integers

Subtracting integers involves adding the opposite of the second integer to the first integer.

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Multiplying Integers (Same Signs)

The product of two integers with the same sign is always positive.

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Multiplying Integers (Different Signs)

The product of two integers with different signs is always negative.

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Multiplying More Than Two Integers

When multiplying more than two integers, the product is positive if there are an even number of negative signs and negative if there's an odd number.

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Negative Integer

A number that is below zero on a number line.

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Positive Integer

A number that is above zero on a number line.

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Multiplying integers with the same sign

The product of two integers with the same sign is positive.

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Multiplying integers with different signs

The product of two integers with opposite signs is negative.

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Dividing integers with the same sign

The quotient of two integers with the same sign is positive.

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Dividing integers with different signs

The quotient of two integers with different signs is negative.

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Sign rule for dividing multiple integers (even negative signs)

If there is an even number of negative signs in the division problem, the quotient will be positive.

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Sign rule for dividing multiple integers (odd negative signs)

If there is an odd number of negative signs in the division problem, the quotient will be negative.

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What is a fraction?

A part of a whole represented by a fraction.

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What is the numerator?

The top number in a fraction, representing the number of parts considered.

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Simplest Form

A fraction is in its simplest form when the numerator and denominator have no common factors other than 1.

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Multiplying Fractions

To find the product of two fractions, multiply the numerators and the denominators.

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Dividing Fractions

To divide by a fraction, multiply by its reciprocal.

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Mixed Number

A mixed number is a number that has a whole number part and a fraction part.

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Fraction to Decimal

To convert a fraction to a decimal, divide the numerator by the denominator.

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Equivalent Fractions

Fractions that represent the same value but are written differently.

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Decimal to Fraction

To convert a decimal to a fraction, write the decimal as a fraction with a denominator of 10, 100, 1000, etc., depending on the number of decimal places.

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Reduced Fraction

A fraction expressed in its simplest form; cannot be simplified further.

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Repeating Decimal

A repeating decimal is a decimal that has a repeating pattern of digits after the decimal point.

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Terminating Decimal

A terminating decimal is a decimal that stops after a certain number of digits.

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Mixed Fraction vs Improper Fraction

A mixed number is a whole number and a fraction combined, like 2 1/2. An improper fraction is a fraction where the numerator is greater than or equal to the denominator, like 5/2.

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MAD Method

A method to convert a mixed fraction to an improper fraction. Multiply the denominator by the whole number, add the numerator, and keep the same denominator.

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Adding and Subtracting Fractions

To add or subtract fractions, they must have the same denominator. If they don't, you need to find a common denominator.

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Reducing Fractions with GCF

Finding the greatest common factor (GCF) of the numerator and denominator and dividing both by it.

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Equivalent Fractions and Division

A fraction where both the numerator and denominator can be divided by the same value to find an equivalent fraction.

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Fractions are Multiples

Fractions are multiples of each other. One fraction's numerator and denominator are multiplied by the same number to get the other fraction.

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What is a proper fraction?

A fraction whose numerator (top number) is less than the denominator (bottom number). It represents a value less than 1.

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What is an improper fraction?

A fraction where the numerator (top number) is greater than or equal to the denominator (bottom number). Represents a value greater than or equal to 1.

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What is a mixed number?

A mixed number combines a whole number and a proper fraction, representing a value greater than 1.

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How do you convert an improper fraction to a mixed number?

Converting an improper fraction to a mixed number involves dividing the numerator by the denominator. The quotient becomes the whole number, the remainder becomes the new numerator, and the denominator stays the same.

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How do you convert a mixed number to an improper fraction?

Converting a mixed number to an improper fraction requires multiplying the whole number by the denominator, adding the numerator, and keeping the same denominator.

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How do you compare fractions with the same denominator?

Comparing fractions with the same denominator involves comparing the numerators directly. The fraction with the larger numerator is the greater one.

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How do you compare fractions with different denominators?

To compare fractions with different denominators, find a common denominator by finding the least common multiple (LCM) of the denominators. Convert both fractions to equivalent ones with the LCM as the new denominator and then compare the numerators.

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Ordering fractions

Ordering fractions in ascending or descending order requires comparing and arranging them from smallest to largest or largest to smallest, respectively. Use strategies like finding a common denominator to make the comparison easier.

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Multiplying more than two integers (even negatives)

When multiplying more than two integers, if there is an even number of negative signs, the product is positive.

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Multiplying more than two integers (odd negatives)

When multiplying more than two integers, if there is an odd number of negative signs, the product is negative.

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Dividing multiple integers (even negatives)

If there is an even number of negative signs in the division problem, the quotient will be positive.

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Dividing multiple integers (odd negatives)

If there is an odd number of negative signs in the division problem, the quotient will be negative.

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Simplest Form of a Fraction

A fraction in its simplest form has no common factors (other than 1) between its numerator and denominator.

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Sign rule (even negative signs)

If there is an even number of negative signs in the division problem, the quotient will be positive. For example: (-240) ÷ (-2) ÷ (3 ÷ 5) ÷ (-2) = 4 (four negative signs = positive quotient).

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Sign rule (odd negative signs)

If there is an odd number of negative signs in the division problem, the quotient will be negative. For example: (240) ÷ 2 ÷ 3 ÷ (5 ÷ 2) = -4 (three negative signs = negative quotient).

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Fraction

A part of a whole.

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Numerator

The top number in a fraction; tells you how many parts you have.

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Simplifying Fractions

Finding the greatest common factor (GCF) of the numerator and denominator, and then dividing both by the GCF to simplify the fraction.

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Improper Fraction

A fraction where the numerator is larger than or equal to the denominator. It represents a value greater than or equal to 1.

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Mixed to Improper

Convert a mixed number to an improper fraction by multiplying the whole number by the denominator, adding the numerator, and keeping the same denominator.

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Improper to Mixed

Convert an improper fraction to a mixed number by dividing the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator, and the denominator remains the same.

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Comparing Fractions

Finding a common denominator for fractions by finding the least common multiple (LCM) of the denominators. Convert both fractions to equivalent ones with the LCM as the new denominator, then compare the numerators.

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What are integers?

A number that can be written without a fractional part and is used to represent quantities greater than zero, less than zero, or exactly zero. Examples: -5, 0, 12

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Adding integers with the same sign

Adding two integers with the same sign means adding their absolute values and keeping the same sign. For example, (+5) + (+3) = +8 and (-7) + (-2) = -9.

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Multiplying multiple integers

When multiplying more than two integers, the product will be positive if there is an even number of negative signs and negative if there is an odd number of negative signs. For example: (-2) x (-3) x (+4) = +24 (even number of negative signs) and (-1) x (+2) x (-5) x (-3) = -30 (odd number of negative signs)

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What is a number line?

A number line is a visual representation of numbers, with positive numbers to the right of zero and negative numbers to the left. It helps visualize integer operations and relationships.

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What is a fraction in simplest form?

A fraction is reduced to its simplest form when the numerator and denominator share no common factors other than 1. This means you cannot simplify the fraction any further.

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How convert mixed number to improper fraction?

To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and keep the same denominator.

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How to convert improper fraction to mixed number?

To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient becomes the whole number, the remainder becomes the new numerator, and the denominator stays the same.

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What is reducing a fraction with GCF?

Finding the greatest common factor (GCF) of both the numerator and denominator, and then dividing both by that factor.

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Reducing fractions with division.

Dividing both the numerator and denominator by the same number to find an equivalent fraction. This doesn't change the fraction's value, just its representation. Example: 3/4 is equivalent to both 6/8 and 9/12.

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How do you calculate a power?

The base multiplied by itself the number of times indicated by the exponent. Example: 2^3 = 2 * 2 * 2 = 8.

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Diameter

The distance across a circle, passing through the center.

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Radius

The distance from the center of a circle to any point on its edge.

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Surface Area

The total area of all the surfaces of a three-dimensional shape.

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Cube

A three-dimensional shape with six square faces and all edges equal.

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Rectangular Prism

A three-dimensional shape with six rectangular faces, where opposite faces are identical.

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Triangular Prism

A three-dimensional shape with two identical triangular bases and three rectangular sides.

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Cylinder

A three-dimensional shape with two circular bases and a curved side.

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Surface Area of a Pyramid

The total area of all the surfaces of a pyramid.

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Rational Numbers

A set of numbers that can be expressed as a fraction, where the numerator and denominator are integers (whole numbers), and the denominator is not zero.

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Irrational Numbers

A set of numbers that cannot be expressed as a fraction of two integers. These numbers have decimal representations that are non-repeating and non-terminating.

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Perfect Squares

The product of a number multiplied by itself. Example: 4 is a perfect square because 2 x 2 = 4.

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Pythagorean Theorem

A formula used to find the unknown side length of a right-angled triangle. The formula is a² + b² = c² where 'a' and 'b' are the lengths of the shorter sides (legs) and 'c' is the length of the longest side (hypotenuse).

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Hypotenuse

The opposite side of a right triangle, always the longest side and across from the right angle.

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Legs

The two shorter sides of a right triangle that form the right angle.

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Irrational Square Roots

The square root of any number that isn't a perfect square; it cannot be expressed as a simple fraction and continues indefinitely.

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Decimal Approximation

A decimal approximation with a fixed number of digits after the decimal point. Rounding helps simplify a number's representation.

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Study Notes

Linear Relations Outcomes

  • Students will graph linear relations, analyze graphs and interpolate/extrapolate to solve problems.
  • Performance indicators include describing patterns in graphs, graphing linear relations (including horizontal and vertical lines), matching equations to graphs, extending graphs to find unknown values, interpolating approximate values from graphs, solving problems by graphing and analyzing graphs, understanding the coordinate plane (x-axis, y-axis, quadrants, origin, ordered pairs), determining the slope of a line (using the rise over run method), applying these concepts to real-world problem solving, understanding linear relationships as represented in tables, equations in the form y=mx+b, and identifying independent and dependent variables within real-world contexts.

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Related Documents

Unit 5 Notes - PDF
Math 9 Surface Area Part 1 PDF

Description

This quiz focuses on graphing linear relations and analyzing various graphs to solve problems. Students will demonstrate their ability to describe patterns, match equations with graphs, and interpolate or extrapolate values. Mastery of these skills is essential for understanding linear relationships in mathematics.

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