Fractions, Ratios, Proportions, Discounts & Markups

Vocabulary flashcards summarizing key terms from the lecture on fractions, ratios, proportions, trade discounts, profit, loss, markup, and related problem-solving concepts.

Fraction

A number written a/b, where a and b are whole numbers and b ≠ 0, representing parts of a whole.

Proper Fraction

A fraction whose value is less than 1 (numerator < denominator), e.g., 1/4.

Improper Fraction

A fraction whose value is equal to or greater than 1 (numerator ≥ denominator), e.g., 9/5.

Mixed Number

A number consisting of a whole part and a fractional part, e.g., 3 1/2.

Decimal (Decimal Number)

A number expressed in the base-10 system containing a whole part and a fractional part separated by a decimal point.

Ratio

A comparison or relation between two or more numbers, often written a to b, a:b, or a/b.

Equal Ratios

Ratios that represent the same relationship, analogous to equivalent fractions.

Proportion

An equation stating that two ratios are equal.

Direct Proportion

A relationship where one value increases as another increases; if a:b = c:d, then ad = bc.

Indirect (Inverse) Proportion

A relationship where one value increases as another decreases; if a:b = c:d, then ab = cd.

Partitive Proportion

A proportion used to divide a quantity into two or more parts according to a given ratio.

Three Ways to Write a Ratio

Using words (3 to 5), a colon (3:5), or a fraction (3/5).

Percentage (Component of Percent Problems)

The part of a whole found by multiplying the base by the rate; usually located near the word "is."

Base (Component of Percent Problems)

The whole quantity in a percent problem; it follows the word "of."

Rate (Component of Percent Problems)

The percent value that compares the part to the base.

Problem-Solving Strategy: Draw a Picture

Visualizing information by sketching to better understand and solve a problem.

Problem-Solving Strategy: Make an Organized List

Listing possibilities systematically to identify patterns or solutions.

Problem-Solving Strategy: Find a Pattern

Observing regularities in data to predict or solve.

Problem-Solving Strategy: Guess and Check

Proposing a solution, testing it, and revising until correct.

Problem-Solving Strategy: Use Logical Reasoning

Applying deductive thinking to eliminate impossibilities and reach conclusions.

Problem-Solving Strategy: Work Backward

Starting from the desired result and reversing steps to reach the given information.

Problem-Solving Strategy: Make an Equation

Translating a word problem into algebraic form to solve.

Profit

The amount by which net sales (revenue) exceed the cost of goods: Profit = Net Sales − Cost.

Loss

The amount by which cost of goods exceeds net sales: Loss = Cost − Net Sales.

Net Sales (Revenue)

Money received from selling goods after returns or allowances.

Cost (Cost of Goods)

The amount paid to acquire or produce goods for sale.

Break-Even

The point at which net sales equal the cost of goods, producing neither profit nor loss.

Trade Discount

A reduction from the list price granted to buyers, such as volume or dealer discounts.

Single Discount

A price reduction calculated using the basic formula P = B × R.

Series of Discounts

Successive reductions applied to the list price beyond the ordinary discount.

Discount Method

Computing the net price by directly applying each discount rate to the current price.

Complement Method

Finding net price by multiplying the list price by the complement of each discount rate (100% − rate).

Single Equivalent Discount

A single rate that produces the same net price as a given series of discounts.

Markup

The amount added to cost to obtain the selling price.

Initial Markup (Mark-On)

The amount added to cost to arrive at the original selling price; also called margin.

Additional Markup

An increase added to the original selling price to create a new selling price.

Markup Cancellation

A reduction in the new selling price that does not fall below the original selling price.

Margin (Gross Margin)

Sales minus cost of goods sold; expresses profit relative to selling price.

Markup vs. Margin

Markup expresses profit relative to cost; margin expresses profit relative to selling price.

Cost of Goods Sold (COGS)

Beginning Inventory + Purchases − Ending Inventory; the cost of merchandise sold during a period.