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Questions and Answers
What is the relationship in a direct proportion as one value decreases?
What is the relationship in a direct proportion as one value decreases?
- There is no predictable relationship.
- The other value increases.
- The other value remains the same.
- The other value also decreases. (correct)
Which of the following best describes inverse proportion?
Which of the following best describes inverse proportion?
- An increase in one quantity leads to a decrease in another. (correct)
- Both quantities decrease together.
- Both quantities increase together.
- Both quantities remain constant.
In a partitive proportion with ratios $a:b:c$, what does the equation $ax + bx + cx = k$ represent?
In a partitive proportion with ratios $a:b:c$, what does the equation $ax + bx + cx = k$ represent?
- The sum of the ratios.
- The fixed quantity of one variable.
- The total partitioned value. (correct)
- The proportion of individual quantities.
What does the term 'mark-up' refer to in business?
What does the term 'mark-up' refer to in business?
Which formula correctly represents the calculation of percentage?
Which formula correctly represents the calculation of percentage?
What happens to the selling price when a product is subject to a markdown?
What happens to the selling price when a product is subject to a markdown?
In which type of proportion does the relationship $ rac{a1}{b1} = rac{a2}{b2}$ hold true?
In which type of proportion does the relationship $ rac{a1}{b1} = rac{a2}{b2}$ hold true?
What does the 'base' in the context of percentages refer to?
What does the 'base' in the context of percentages refer to?
What is the result of converting 0.75 to a percentage?
What is the result of converting 0.75 to a percentage?
How do you express the mixed fraction $2 \frac{1}{4}$ as a decimal?
How do you express the mixed fraction $2 \frac{1}{4}$ as a decimal?
What is the proper way to convert the fraction $\frac{3}{5}$ to a decimal?
What is the proper way to convert the fraction $\frac{3}{5}$ to a decimal?
Which of the following correctly represents a ratio?
Which of the following correctly represents a ratio?
Which of the following is the correct process to express 80% as a fraction?
Which of the following is the correct process to express 80% as a fraction?
What is the decimal equivalent of 30%?
What is the decimal equivalent of 30%?
In the proportion $\frac{a}{b} = \frac{c}{d}$, which of the following statements is true?
In the proportion $\frac{a}{b} = \frac{c}{d}$, which of the following statements is true?
How do you convert the decimal 0.125 to a fraction?
How do you convert the decimal 0.125 to a fraction?
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Study Notes
Basic Concepts
- Fraction: Represents a part of a whole.
- Decimal: A number system based on powers of ten.
- Percentage: A number's ratio to 100, expressed as a form of numbers per hundred.
Conversion
- Fractions to Decimal: Convert to equivalent fraction with a power of ten denominator, or use long division.
- Mixed Fractions to Decimal: Divide the numerator by the denominator and combine with the whole number.
- Decimal to Fractions: Utilize place value for conversion and reduce to lowest terms.
- Decimal to Percent: Move the decimal point two places right and add a percent sign (%).
- Fractions to Percent: Convert fraction to decimal, then move the decimal point two places right and add a percent sign (%).
- Percent to Decimal: Move the decimal point two places left (dividing by 100) and remove the percent sign (%).
- Percent to Fraction: Convert percent to decimal, then to fraction and reduce to lowest terms.
Ratios
- A ratio compares two quantities with the same unit.
- Odds Notation: Expressed as a:b, read as "is to."
- Fractional Notation: Expressed as a/b where b≠0.
- Rate: A ratio comparing different units.
- Unit Rate: A rate expressed per one unit of a given quantity.
Proportion
- A proportion represents the equality of two ratios.
- Direct Proportion: Both values increase or decrease equally, represented as a1/b1 = a2/b2.
- Inverse Proportion: One value increases while the other decreases, represented as a1/a2 = b2/b1.
- Partitive Proportion: A whole divided into parts in equal or unequal ratios, represented in the form ax + bx + cx = k.
Terms related to Proportion
- Base (B): The reference number for percentage calculations; follows "of," "as much as," etc.
- Rate (R): The number of hundredths taken; expressed in percent, decimal, or fraction.
- Percentage (P): Represents the part in relation to the whole; calculated using the formula: Percentage = Base × Rate.
Terms related to Prices
- Mark-up: The additional charge over cost for profit.
- Mark-on: An increase in product price after a previous increase.
- Markdown: A decrease in selling price due to market conditions.
Terms related to Business
- Selling Price: The price set by the seller for a product or service.
- Cost: The price paid to acquire an item.
- Expenses: Costs incurred during business operations.
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