Podcast
Questions and Answers
What is the absolute value of -7?
What is the absolute value of -7?
Which operation is represented correctly by the Keep-Change-Change rule for the expression 10 - (-4)?
Which operation is represented correctly by the Keep-Change-Change rule for the expression 10 - (-4)?
When multiplying two negative integers, what is the result?
When multiplying two negative integers, what is the result?
What is the first step to perform when adding the fractions 1/4 and 1/6?
What is the first step to perform when adding the fractions 1/4 and 1/6?
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In a proportional relationship, which of the following pairs of ratios are equivalent?
In a proportional relationship, which of the following pairs of ratios are equivalent?
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Which of the following statements correctly defines unit rate?
Which of the following statements correctly defines unit rate?
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What is the unit rate for the ratio of 60 miles in 3 hours?
What is the unit rate for the ratio of 60 miles in 3 hours?
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Which of the following best describes a rational number?
Which of the following best describes a rational number?
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How many cups of water are needed if 1 1/2 cups of corn grits are used?
How many cups of water are needed if 1 1/2 cups of corn grits are used?
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What is the selling price of the shoes after an 85% markup on the original price of $110?
What is the selling price of the shoes after an 85% markup on the original price of $110?
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How many crates of oranges are needed if 2 1/2 crates of apples are used?
How many crates of oranges are needed if 2 1/2 crates of apples are used?
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What percentage of times at bat did Emerson actually hit the ball during Game 1?
What percentage of times at bat did Emerson actually hit the ball during Game 1?
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What is the interest earned after 3 years on a $2,500 loan with a simple interest rate of 4%?
What is the interest earned after 3 years on a $2,500 loan with a simple interest rate of 4%?
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What is 45% of 220?
What is 45% of 220?
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If Maryam rolled 42 strikes out of 70 attempts, what percentage of her attempts were strikes?
If Maryam rolled 42 strikes out of 70 attempts, what percentage of her attempts were strikes?
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What number is Tyson finding when he multiplies 75 by 1.25?
What number is Tyson finding when he multiplies 75 by 1.25?
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What is the formula to calculate the constant of proportionality?
What is the formula to calculate the constant of proportionality?
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Which of the following equations represents a proportional relationship?
Which of the following equations represents a proportional relationship?
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What does the unit rate represent in a proportional relationship?
What does the unit rate represent in a proportional relationship?
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What is the decimal equivalent of 25%?
What is the decimal equivalent of 25%?
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How is percent change calculated?
How is percent change calculated?
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What is the constant of proportionality in the equation $y = 4x$?
What is the constant of proportionality in the equation $y = 4x$?
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If a garden hose fills a 2-gallon bucket in 5 seconds, what equation models the relationship between gallons g and seconds t?
If a garden hose fills a 2-gallon bucket in 5 seconds, what equation models the relationship between gallons g and seconds t?
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Which of the following quantities represents a part in the percent equation?
Which of the following quantities represents a part in the percent equation?
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When calculating simple interest, which term represents the initial amount of money?
When calculating simple interest, which term represents the initial amount of money?
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Which of the following statements is true about the graph of a proportional relationship?
Which of the following statements is true about the graph of a proportional relationship?
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In the expression $-8 - (-6)$, what is the correct result?
In the expression $-8 - (-6)$, what is the correct result?
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If Sarah used 2.5 cups of cheese for 10 people, how much cheese is in one serving?
If Sarah used 2.5 cups of cheese for 10 people, how much cheese is in one serving?
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What is the relationship between decimal and terminating decimals?
What is the relationship between decimal and terminating decimals?
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What does the expression $\frac{5}{2}x - \frac{3}{2}$ simplify to when $x = 2$?
What does the expression $\frac{5}{2}x - \frac{3}{2}$ simplify to when $x = 2$?
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In the situation where a scuba diver is 25 feet below sea level, which number represents the opposite?
In the situation where a scuba diver is 25 feet below sea level, which number represents the opposite?
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Study Notes
Rational Number Operations
- Integers and Absolute Value: Absolute value is the distance from 0. 6 + (-6) = 0.
- Rational Numbers: Rational numbers are fractions or terminating/repeating decimals. Convert between fraction and decimal forms.
- Operations with Integers, Decimals, and Fractions: Practice adding, subtracting, multiplying, and dividing integers, decimals, and fractions. Subtraction is adding the opposite. Multiplication/division of two negative integers results in a positive integer. When adding/subtracting fractions, make denominators equal. Division of fractions uses the "Keep-Change-Flip" rule.
- Word Problems: Solve word problems involving rational numbers, like calculating temperature changes or averages of positive and negative integers.
Analyze and Use Proportional Relationships
- Ratios, Rates, and Unit Rates: Find unit rates; compare unit rates to determine better deals.
- Unit Rates from Fractions: Find unit rates involving unit fractions or other fractions. See examples in Volume 1 book on pages 96 and 97.
- Proportional Relationships and Equivalent Ratios: Use the equivalent ratio test to identify proportional quantities.
- Constant of Proportionality: The constant of proportionality is the unit rate (y/x). The equation for proportional relationships is y = kx where k is the constant.
- Graphing Proportional Relationships: Graphs of proportional relationships pass through (0, 0). The unit rate is the y-value when x = 1.
- Application of Proportional Reasoning: Solve word problems involving ratios (see examples on page 126 in Volume 1).
Analyze and Solve Percent Problems
- Percents and Numbers: Percent means "out of 100". Convert percents into decimal form before calculations.
- Percentages and Proportions: part/whole = percent/100.
- Percent Equation: part = percent × whole; whole = part/percent.
- Percent Change and Error: Calculate percent change: (change/original) × 100.
- Markup and Markdown: Markup = % markup × original value; Final amount = Original + markup. Markdown = % markdown × original value; Final amount = Original - markdown.
- Simple Interest: Interest = Principal × interest rate × time (convert to decimal and years).
Generate Equivalent Expressions
- Algebraic Expressions: Write and evaluate algebraic expressions using variables. Substitute given variable values.
- Equivalent Expressions: Combine like terms to create or identify equivalent expressions. Use the distributive property when necessary. Like terms are either constants or terms with the same variable.
Practice Problems (Selected Examples)
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Absolute Value: |-5| = 5
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Addition of Integers: 5 + (-3) = 2, -32 + 32 = 0, -6 + 12 = 6
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Word Problem Example: Finding the opposite of a value represents a change in direction or position in a similar magnitude.
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Decimal Classification Examples: 3.232323... (repeats), 1.789 (terminates), 0.99 (repeats), 6.25 (terminates).
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Mixed Number to Decimal: 2 1/4 = 2.25
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Proportional Relationships Example: If y = 5.5x, constant of proportionality is 5.5
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Graphing Proportional Relationships Example: Graph passes through (0, 0). Point (3, 16.5) shows a rate of 16.5 when the x variable is 3.
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Unit Rate Example: If 3/10 mile is walked in 1/5 of an hour, speed is 1.5 miles per hour.
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Percent Problem Example: 85% markup on a $110 item: Selling price = $184.50.
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Algebraic Expression Example: 2(x − 6) + 2(8) = 2x + 4.
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Description
This quiz covers essential operations involving rational numbers, including integers, decimals, and fractions. It also explores proportional relationships through ratios and unit rates. Students will practice solving equations, understanding absolute values, and applying these concepts in word problems.
