Last updated on October 13th, 2020
Crossmultiplication requires you to multiply 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. CrossMultiplication is also useful when you’re trying to solve a ratio. Here is how you can do cross multiplication.
How to Cross Multiply Fractions without Variable
The given fractions are

Multiply the numerator of the lefthand fraction by the denominator of the righthand fraction.
Multiply the numerator of the righthand fraction by the denominator of the lefthand fraction.
Set the two products equal to each other.
How to Cross Multiply Fractions with Single Variable
 Multiply the numerator of the lefthand fraction by the denominator of the righthand fraction.
For Example, The equation is .
Now, multiply 5 * 25 = 125
Multiply the numerator of the righthand fraction by the denominator of the lefthand fraction.
Now, multiply x * 10 = 10x
Set the two products equal to each other.
Just set 125 equal to 10x.
125 = 10x
Solve the variable.
How to Cross Multiply Fractions with Two of the Same Variable
 Multiply the numerator of the lefthand fraction by the denominator of the righthand fraction.
For Example, The equation is
Now, Multiply
Multiply the numerator of the righthand fraction by the denominator of the lefthand fraction.
Now, Multiply
Set the two products equal to each other and combine the like terms.
Solve the equation.
We can check the equation by plugging in 1.
Year 10 Interactive Maths – Second Edition
CrossMultiplication Method
Place the linear factors one above the other as shown below.
Multiply the numbers along the arms of the cross, and then add the products. That is,
xЧ10 + xЧ1 = 10x+ x = 11x. This is not the middle term.
xЧ5 + xЧ2 = 5x+ 2x = 7x. This is the middle term.
 The solution is read across.
 10 = 1 Ч 10 = 2 Ч 5 = –1 Ч –10 = –2 Ч –5
We did not try –1 Ч –10 and –2 Ч –5 because the middle term is positive.  The answer can be checked using the Distributive Law. That is:
Example 9
Solution:
Multiply the numbers along the arms of the cross, and then add the products.
xЧ14 + xЧ1 = 14x+ x = 15x.
We reject this pair as the middle term is 9x.
xЧ7 + xЧ2 = 7x+ 2x = 9x. We accept this pair as the middle term is 9x.
xЧ – 4 + xЧ –3 = – 4x – 3x = –7x. We accept this pair as the middle term is –7x.
We did not try 1 Ч 12, 2 Ч 6 and 3 Ч 4 because the middle term is negative. Also, we did not try
–2 Ч –6 and –1 Ч –12 because we have already obtained the middle term by using –3 Ч – 4.
x Ч –7 + x Ч 1 = –7x + x = –6x. We accept this pair as the middle term is –6x.
We did not try –1 Ч 7 because we have already obtained the middle term by using 1 Ч –7.
We did not try 1 Ч –8, –2 Ч 4 and 2 Ч –4 because we have already obtained the middle term by using –1 Ч 8.
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