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Cross Multiplication: Definition and Examples | EDU.COM

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Cross Multiplication: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Cross MultiplicationCross Multiplication: Definition and ExamplesTable of ContentsCross Multiplication Definition of Cross Multiplication

Cross multiplication is a method used to find unknown values in algebraic equations. For any equation in the form of ab=cd\frac{a}{b}=\frac{c}{d}ba​=dc​, the cross multiplication formula is a×d=b×ca \times d = b \times ca×d=b×c. This involves multiplying the numerator of the first fraction with the denominator of the second fraction, and the numerator of the second fraction with the denominator of the first fraction.

Cross multiplication has several applications in mathematics. It can be used to compare fractions with different denominators, to add or subtract unlike fractions, to find unknown values in expressions, and to compare ratios. When comparing ratios, if ab=cd\frac{a}{b} = \frac{c}{d}ba​=dc​, then the products after cross multiplication will be equal (a×d=b×ca \times d = b \times ca×d=b×c).

Examples of Cross Multiplication Example 1: Comparing Unlike Fractions Problem:

Compare 37\frac{3}{7}73​ and 58\frac{5}{8}85​ using cross-multiplication.

Step-by-step solution:

Step 1, When comparing two fractions with different denominators, we need to make their denominators the same. We can do this by changing the denominators to the product of both denominators: 7×8=567 \times 8 = 567×8=56.

Step 2, To find the new numerator for the first fraction, we multiply the numerator of the first fraction with the denominator of the second fraction: 3×8=243 \times 8 = 243×8=24. So the first fraction becomes: 2456\frac{24}{56}5624​.

Step 3, Next, we multiply the second fraction's numerator by the first fraction's denominator: 5×7=355 \times 7 = 355×7=35. So the second fraction becomes: 3556\frac{35}{56}5635​.

Step 4, Now we can compare the new fractions. Since 24563556\frac{24}{56} 5624​5635​, we can say that 3758\frac{3}{7} 73​85​.

Example 2: Finding an Unknown Value Problem:

If 888 candle-stands cost $40\$40$40, how much will 121212 such candle-stands cost?

Step-by-step solution:

Step 1, Let's find the cost of 111 candle-stand based on the given information. Cost of 888 candle-stands = $40\$40$40, so cost of 111 candle-stand = 408\frac{40}{8}840​.

Step 2, Let's call the cost of 121212 candle-stands "xxx". The cost of 111 candle-stand would then be x12\frac{x}{12}12x​.

Step 3, Since the cost of 111 candle-stand remains the same in both cases, we can write: 408=x12\frac{40}{8} = \frac{x}{12}840​=12x​

Step 4, Now we can cross multiply to solve for x:

40×12=8×x40 \times 12 = 8 \times x40×12=8×x 480=8x480 = 8x480=8x x=4808=60x = \frac{480}{8} = 60x=8480​=60

Step 5, So, 121212 candle-stands will cost $60\$60$60.

Example 3: Solving an Equation with One Variable Problem:

Find the value of xxx in the equation 1215=x10\frac{12}{15} = \frac{x}{10}1512​=10x​

Step-by-step solution:

Step 1, We start with the given equation: 1215=x10\frac{12}{15} = \frac{x}{10}1512​=10x​

Step 2, Apply cross multiplication by multiplying the numerator of each fraction by the denominator of the other:

12×10=15×x12 \times 10 = 15 \times x12×10=15×x

Step 3, Solve for xxx:

120=15x120 = 15x120=15x 12015=x\frac{120}{15} = x15120​=x x=8x = 8x=8

Step 4, Check our answer by substituting back into the original equation:

1215=810\frac{12}{15} = \frac{8}{10}1512​=108​ 1215=45\frac{12}{15} = \frac{4}{5}1512​=54​

Both sides simplify to the same value, so x=8x = 8x=8 is correct.

Comments(1)MCMs. CarterSeptember 17, 2025This explanation of cross multiplication was a lifesaver while helping my daughter with her homework! The step-by-step examples made it so easy to explain. Thanks for breaking it down so clearly!

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