15.5 Multiplication Phrase Translation

Multiplication Phrase Translation catalogs the verbal phrasings that signal a multiplication operation, from a plain "product of" two quantities to specific multiples, fractions, and percentages of a quantity, all converting into the same underlying symbolic multiplication.

Basic Product Phrasing

Product of Two Quantities

The phrase "the product of" two named quantities translates directly into those two quantities multiplied together, with the order of the phrase matching the order they are written in the symbolic product, though order does not affect the value since multiplication is commutative.

Number Times a Quantity

The phrase "a number times a quantity" translates into that number multiplied by the quantity, written conventionally as a coefficient directly in front of the variable rather than with an explicit multiplication symbol.

Naming Specific Multiples

Multiple of a Quantity

The general phrase "a multiple of" a quantity indicates that the quantity is being multiplied by some whole number, and this whole number is written as the coefficient of the variable representing that quantity.

Twice a Quantity

The phrase "twice a quantity" translates into that quantity multiplied by two, using the specific word "twice" as shorthand for the multiplier two.

Three Times a Quantity

The phrase "three times a quantity" translates into that quantity multiplied by three, following the same pattern as any other stated multiple, with the number written as the coefficient.

General Integer Multiple

Any stated whole-number multiple, whether given as a word like "twice" or as a written numeral, translates the same way: the stated whole number becomes the coefficient multiplying the quantity described.

Fractional and Percentage Multipliers

Fraction of a Quantity

The phrase "a fraction of a quantity," such as "one third of a number," translates into that fraction multiplying the quantity, following the same coefficient pattern used for whole-number multiples.

Percentage Phrase Translation

The phrase describing a percentage of a quantity translates into that quantity multiplied by the percentage converted to its decimal or fractional equivalent, since a percentage always represents a proportion of the quantity it modifies.

Products with More than Two Factors

Product Containing Several Factors

When a verbal statement describes a product of more than two quantities, all of the named quantities are multiplied together in sequence, extending the same product pattern used for two quantities to any number of them.

Notational Conventions

Juxtaposed Product Notation in Verbal Translation

When translating a multiplication involving a number and a variable, or two variables, the multiplication symbol is conventionally omitted, with the two factors written directly adjacent to each other, since this juxtaposition is the standard way multiplication is denoted in algebraic notation.

Multiplier Applied to a Grouped Quantity

When a verbal statement describes a multiplier applied to an entire sum or difference, such as "three times the sum of a number and five," the sum or difference is enclosed in parentheses in the symbolic translation, ensuring the multiplier applies to the whole grouped quantity rather than to only part of it.