cross-multiply: meaning, definition, pronunciation and examples
LowTechnical/Educational
Quick answer
What does “cross-multiply” mean?
In mathematics, to multiply the numerator of one fraction by the denominator of another fraction, and vice versa, typically as a step in solving equations or comparing ratios.
Audio
Pronunciation
Definition
Meaning and Definition
In mathematics, to multiply the numerator of one fraction by the denominator of another fraction, and vice versa, typically as a step in solving equations or comparing ratios.
Metaphorically, it can be used to describe any process of applying a consistent rule or method across different domains to compare, equate, or solve a problem.
Dialectal Variation
British vs American Usage
Differences
No significant lexical or grammatical differences. Usage is identical in mathematical contexts.
Connotations
Purely technical; carries no regional connotation.
Frequency
Equally low-frequency in both dialects, confined to maths education and textbooks.
Grammar
How to Use “cross-multiply” in a Sentence
[Subject] cross-multiplies [fractions/ratios].[Subject] cross-multiplies [Object] to find [Result].[Fractions/Ratios] are cross-multiplied.Vocabulary
Collocations
Examples
Examples of “cross-multiply” in a Sentence
verb
British English
- To solve for x, you first cross-multiply the two fractions.
- The pupils were asked to cross-multiply the ratios in their maths books.
American English
- Just cross-multiply to clear the fractions in the proportion.
- I always cross-multiply to check if two fractions are equivalent.
Usage
Meaning in Context
Business
Virtually never used, except perhaps in analytical or data comparison training.
Academic
Used in mathematics, physics, and engineering education when dealing with proportions and equations.
Everyday
Extremely rare; limited to helping children with maths homework.
Technical
Core term in foundational algebra and arithmetic for solving proportions and rational equations.
Vocabulary
Synonyms of “cross-multiply”
Strong
Neutral
Weak
Vocabulary
Antonyms of “cross-multiply”
Watch out
Common Mistakes When Using “cross-multiply”
- Writing as one word ('crossmultiply') or two unhyphenated words ('cross multiply'). The hyphen is standard.
- Using it to mean simple multiplication of two numbers (e.g., 'cross-multiply 3 and 4').
- Confusing the order of multiplication (must multiply numerator of first by denominator of second, and vice versa).
FAQ
Frequently Asked Questions
Primarily yes, it is used with two equal fractions or ratios (a/b = c/d). It can be extended to equations with more terms but the core idea is comparing two ratios.
They are often used synonymously in casual instruction. However, 'cross-multiply' specifically implies the two multiplications in a proportion (a*d and b*c), while 'multiply across' could be misconstrued as just one multiplication.
Yes, but with a crucial caveat: you can only cross-multiply inequalities if you know the denominators are both positive or both negative. If their signs differ, the inequality symbol must be reversed.
The hyphen creates a single compound verb from 'cross' and 'multiply'. It indicates this is a specific, named mathematical operation, not just any multiplication that happens to be 'cross' in some vague sense.
In mathematics, to multiply the numerator of one fraction by the denominator of another fraction, and vice versa, typically as a step in solving equations or comparing ratios.
Cross-multiply is usually technical/educational in register.
Cross-multiply: in British English it is pronounced /ˌkrɒs ˈmʌl.tɪ.plaɪ/, and in American English it is pronounced /ˌkrɔːs ˈmʌl.tə.plaɪ/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “Cross-multiply your way out of it (rare, metaphorical).”
Learning
Memory Aids
Mnemonic
Imagine a large 'X' drawn between two fractions. You multiply along the arms of the X: top-left with bottom-right, and top-right with bottom-left.
Conceptual Metaphor
SOLVING A PROBLEM IS UNTANGLING A KNOT (cross-multiplication simplifies a tangled ratio into a solvable equation).
Practice
Quiz
In which scenario is it correct to use cross-multiplication?