Basic Concepts of Fractions, Decimals, and Percentages

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Questions and Answers

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?

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?

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?

The profit margin added to the cost. Signup and view all the answers

Which formula correctly represents the calculation of percentage?

Percentage = Base x Rate Signup and view all the answers

What happens to the selling price when a product is subject to a markdown?

It decreases. Signup and view all the answers

In which type of proportion does the relationship $rac{a1}{b1} = rac{a2}{b2}$ hold true?

Direct Proportion Signup and view all the answers

What does the 'base' in the context of percentages refer to?

The portion being compared. Signup and view all the answers

What is the result of converting 0.75 to a percentage?

75% Signup and view all the answers

How do you express the mixed fraction $2 \frac{1}{4}$ as a decimal?

2.25 Signup and view all the answers

What is the proper way to convert the fraction $\frac{3}{5}$ to a decimal?

0.6 Signup and view all the answers

Which of the following correctly represents a ratio?

3:4 Signup and view all the answers

Which of the following is the correct process to express 80% as a fraction?

$\frac{80}{100}$, which reduces to $\frac{4}{5}$ Signup and view all the answers

What is the decimal equivalent of 30%?

0.3 Signup and view all the answers

In the proportion $\frac{a}{b} = \frac{c}{d}$, which of the following statements is true?

The cross products $ad$ and $bc$ must be equal. Signup and view all the answers

How do you convert the decimal 0.125 to a fraction?

$\frac{1}{8}$ Signup and view all the answers

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.

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.

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.

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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Description

This quiz covers fundamental concepts involving fractions, decimals, and percentages. It will help you understand how to convert between these forms and apply mathematical principles effectively. Perfect for students learning basic arithmetic or preparing for exams.