Meaning & use
cross-multiply
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Meaning
verbtransitive or intransitivemathematics
To multiply the numerator of one fraction by the denominator of the other, especially to solve an equation with two fractions.
Grammar: Can be used with an object ('cross-multiply the two fractions') or without ('cross-multiply to solve for x').
Patterns
- cross-multiply the fractions
- cross-multiply to solve for something
- cross-multiply both sides
To solve the proportion 2/3 = x/9, cross-multiply to get 18 = 3x.
If you cross-multiply the two fractions, you can compare them easily.
The teacher showed us how to cross-multiply both sides of the equation to eliminate the denominators.
Word forms
| third person singular | cross-multiplies |
|---|---|
| past tense | cross-multiplied |
| past participle | cross-multiplied |
| -ing form | cross-multiplying |
Common combinations
- cross-multiply to solve
- Cross-multiply to solve for the unknown value.
- cross-multiply the equation
- You should cross-multiply the equation to get rid of the fractions.
- cross-multiply both sides
- Cross-multiply both sides by the denominators.
Synonyms and how they differ
- multiply
- A general term for finding the product of numbers; cross-multiply is a specific method used with two fractions.
Word family
- cross-multiplication noun
- The process or result of cross-multiplying.
- multiply verb
- To increase a number by a specified factor.
Commonly confused: cross-multiply or cross out?
cross-multiply vs cross out
To cross out means to draw a line through something to cancel it, not to multiply fractions.
Practice
What is the result of cross-multiplying the fractions 3/4 and 5/6?
Choose one answer.
Cross-multiplying means multiplying the numerator of the first fraction by the denominator of the second (3 × 6 = 18) and the denominator of the first by the numerator of the second (4 × 5 = 20), giving 18 and 20. Option 0 gives 18 and 20, but the question asks for the result of cross-multiplying, which is 15 and 24 if you multiply straight across, so option 1 is correct. Wait, let me re-evaluate: The correct cross-multiplication of 3/4 and 5/6 is 3×6 = 18 and 4×5 = 20. So the correct answer should be 18 and 20. However, the options list 18 and 20 as option 0. I mistakenly marked option 1 as correct. The correct answer is option 0. Let me correct that.
Make it your own
Write a sentence using “cross-multiply”, then check it and compare it with the examples above.