How to cross multiply

Last updated on October 13th, 2020

Cross-multiplication 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. Cross-Multiplication 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 left-hand fraction by the denominator of the right-hand fraction.

Multiply the numerator of the right-hand fraction by the denominator of the left-hand fraction.

Set the two products equal to each other.

How to Cross Multiply Fractions with Single Variable

1. Multiply the numerator of the left-hand fraction by the denominator of the right-hand fraction.

For Example, The equation is .

Now, multiply 5 * 25 = 125

Multiply the numerator of the right-hand fraction by the denominator of the left-hand 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

1. Multiply the numerator of the left-hand fraction by the denominator of the right-hand fraction.
   
   For Example, The equation is

Now, Multiply

Multiply the numerator of the right-hand fraction by the denominator of the left-hand 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

Cross-Multiplication 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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