**Cross Multiply**

Cross multiplication is a method used to compare two fractions to determine which is greater or if they are equivalent. This method involves multiplying the numerator of one fraction by the denominator of the other fraction and vice versa. The resulting products are then compared to determine the relationship between the two fractions.

**What Is Cross Multiplication?**

Cross multiplication is a method used to compare two fractions or solve equations that involve fractions. The method involves multiplying the numerator of one fraction by the denominator of the other fraction and vice versa. This results in two products, which can be used to compare the fractions or solve the equation.

If we have two fractions:

**a/b and c/d**

To cross-multiply these fractions,

**Step 1:** Multiply the numerator of the first fraction (a) by the denominator of the second fraction (d).

** Step 2:** In the second step, multiply the numerator of the second fraction (c) by the denominator of the first fraction (b). The resulting products are then compared to determine the relationship between the two fractions.

The **formula for cross-multiplication** is:

If ad is greater than bc, then the fraction a/b is greater than the fraction c/d. If ad is less than bc, then the fraction c/d is greater than the fraction a/b. If ad is equal to bc, then the fractions are equivalent.

**How To Cross Multiply Fractions?**

Cross multiplication can also be used to compare two fractions to determine which is **greater** or if they are **equivalent**. To do this, we multiply the numerator of one fraction by the denominator of the other fraction and vice versa. We can then compare the resulting products to determine the relationship between the two fractions.

Here is given below how to cross-multiply fractions:

**For example,** consider the equation:

2/4 = x/8

To solve for x, we can use the cross-multiplication method. Multiplying the **numerator** of the first fraction (2) by the **denominator** of the second fraction (8) gives us:

2 x 8 = 16

We then multiply the numerator of the second fraction (x) by the denominator of the first fraction (4), which gives us:

4x

We can now put equal to each other:

3 x 8 = 4x

24 = 4x

Simplifying the equation, we get:

x = 6

Therefore, the solution to the equation 3/4 = x/8 is x = 6.

**Cross Multiply Fractions to Compare Unlike Fractions**

Let’s cross-multiply the fractions 3/4 and 5/6 to determine which is greater.

3/4 = 5/6

To cross-multiply these fractions, we need to multiply the numerator of the first fraction (3) by the denominator of the second fraction (6), and then multiply the numerator of the second fraction (5) by the denominator of the first fraction (4).

3 x 6 = 18 5 x 4 = 20

Since 20 is greater than 18, the fraction 5/6 is greater than the fraction 3/4.

### Facts:

- Cross multiplication is a quick and easy method to compare two fractions.
- This method is useful when comparing fractions with unlike denominators.
- Cross-multiplication can also be used to determine if two fractions are equivalent.
- Cross multiplication is also known as the “butterfly method” because of the way the numbers are arranged during the process.

### Frequently Asked Questions on Cross Multiply

Here are some frequently asked questions on cross multiplication:

**What is cross multiplication?**

Cross multiplication is a method used to compare two fractions or solve equations involving fractions. It involves multiplying the numerator of one fraction by the denominator of the other fraction, and vice versa.

**How do I use cross multiplication to compare two fractions?**

To compare two fractions using cross multiplication, you multiply the numerator of one fraction by the denominator of the other fraction, and vice versa. You then compare the resulting products to determine the relationship between the two fractions.

**Can cross multiplication be used to simplify fractions?**

No, cross multiplication is not used to simplify fractions. To simplify a fraction, you need to divide both the numerator and the denominator by their greatest common factor.

**When should I use cross multiplication?**

You should use cross multiplication when you need to compare two fractions or solve equations involving fractions.

**Is cross multiplication the only method for comparing fractions?**

No, there are other methods for comparing fractions, such as finding a common denominator or converting the fractions to decimals.

**Can cross multiplication be used with mixed numbers?**

Yes, cross multiplication can be used with mixed numbers, but it can be more complicated. It is usually easier to convert mixed numbers to improper fractions before using cross multiplication.