Cross Multiply

Cross Multiply

Do you know how to solve equations with fractions that too by multiplication?

What is the result of cross multiplying two fractions.

The answer is using cross multiply, an easy and simple method to get the answers in seconds.

In this mini-lesson, we will explore the world of cross multiply by finding the answers to the questions like what is meant by cross multiplication, how to do a cross multiply, and how to do a cross multiply with variables with the help of interactive questions.

Lesson Plan

What Is Meant By Cross Multiplication?

Cross-Multiply Definition

When two fractions \(\dfrac{p}{q}\) and \(\dfrac{r}{t}\) are multiply by each other is termed as cross-multiplication method.

In the cross-multiplication method, the numerator of the first fraction value is multiplied by the denominator of the second fraction.

It can be termed as a cross-multiplication method or a cross multiply.

Cross-Multiply Formula

cross multiplication of two fractions


How To Cross Multiply?

Let us learn how to do cross multiply. Consider the example, \(\dfrac{4}{6}=\dfrac{2}{3}\)

Step 1

Multiply the numerator of the right-hand side fraction value with the denominator of the left-hand side fraction value.

Example of a cross-multiply

Step 2

Multiply the denominator of the right-hand side fraction value with the numerator of the left-hand side fraction value.

Example of a cross-multiply

Step 3

LHS is equal to RHS

Example of a cross-multiply step 3 LHS=RHS

\(12=12\)


How To Cross Multiply With A Variable?

Let us learn how to do cross multiply with a variable. Consider the example, \(\dfrac{x}{6}=\dfrac{6}{x}\)

We will be using the general cross multiply formula,

cross multiplication of two fractions

\(\dfrac{x}{6}=\dfrac{6}{x}\)

Multiply the numerator of the right-hand side fraction value with the denominator of the left-hand side fraction value and vice-vera.

\(x^{2}=6\times6\)

\(x^{2}=36\)

\(x=\pm6\)

 
important notes to remember
Important Notes

a) Cross multiply is not applicable when the value of numerator or denominator is \(0\)
b) Cross multiply formula can be used to solve fractions and ratios value.
c) Cross multiply formula is given as:

\(\begin{align}\dfrac{p}{q} &=\dfrac{r}{t}\\\ p\times t &=q\times r\end{align}\)

Solved Examples

Let us have a look at cross multiply examples, to solve problems on cross multiply easily without using a cross multiply calculator

Example 1

 

 

Help Jamie in finding the value of \(b\) using the cross multiplication method.

\(\dfrac{7}{b}=\dfrac{14}{18}\)

Solution

Using the cross multiplication method.

\(\Rightarrow\dfrac{7}{b}=\dfrac{14}{18}\)

\(\Rightarrow\ 7\times18=14\times b\)

\(\Rightarrow\ 126=14b\)

\(\Rightarrow\ b=\dfrac{126}{14}\)

\(\Rightarrow\ b=9\)

\(\therefore\) \(b=9\)

Example 2

 

 

Help Alexa in finding the value of \(x\) using the cross multiplication method.

\(\dfrac{x+1}{8}=\dfrac{3}{x-1}\)

Solution

\(\Rightarrow\dfrac{x+1}{8}=\dfrac{3}{x-1}\)

\(\Rightarrow\ x^{2}-1=24\)

\(\Rightarrow\ x^{2}=25\)

\(\Rightarrow\ x=\pm5\)

\(\therefore\) \(x=\pm5\)
Example 3

 

 

Help Alexa in finding the value of \(b\) using the cross multiplication method.

\(\dfrac{b}{36}=\dfrac{6}{b^{2}}\)

Solution

\(\Rightarrow\dfrac{b}{36}=\dfrac{6}{b^{2}}\)

\(\Rightarrow b \times b^{2}=6\times36\)

\(\Rightarrow b^{3}=6\times36\)

\(\Rightarrow b=\sqrt[3]{216}\)

\(\Rightarrow b=6\)

\(\therefore\) \(b=\pm6\)

Interactive Questions

Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.

 
 
 
 
 
 
 
Challenge your math skills
Challenging Question
Find the value of the variables in the following equations without using a cross multiply calculator.
a)\(\dfrac{y^{2}}{27}=\dfrac{3}{y^{2}}\)
b)\(\dfrac{x-3}{9}=\dfrac{3}{x+3}\)
c)\(\dfrac{4x-1}{7}=\dfrac{9}{4x+1}\)

Let's Summarize

The mini-lesson targeted the fascinating concept of cross multiply. The math journey around cross multiply starts with what a student already knows, and goes on to creatively crafting a fresh concept in the young minds. Done in a way that not only it is relatable and easy to grasp, but also will stay with them forever. Here lies the magic with Cuemath.

About Cuemath

At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students!

Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.

Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.


Frequently Asked Questions(FAQ's)

1. Do you cross multiply when multiplying fractions?

Yes, we use the cross multiplication method when we multiply fractions.

For Example,

cross multiplication of two fractions

cross multiplication of two fractions

2. What is cross multiplying used for?

We use the cross multiplication method or cross multiplying process to multiply fractions.

3. Can you cross multiply ratios?

Yes, we can cross multiply ratios.

For example,

\(a:27=1:3\)

\(\dfrac{a}{27}=\dfrac{1}{3}\)

\(a\times3=1\times27\)

\(a=\dfrac{1\times27}{3}\)

\(a=9\)

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