Multiplying Fractions with Variables

Now, consider the fraction is multiplied with a variable, then the results or outcome will be as per the below example.

Example 7: Multiply 5x/2y × 2x/3z

Solution: Given, 5x/2y × 2x/3z

Therefore, we can solve the above-given expression as;5⁢�×2⁢�2⁢�×3⁢�=10⁢�26⁢�⁢�

Properties of Fractional Multiplication

The following are the properties of multiplication of fractions:

• If the two given fractional numbers are multiplied in either order, the product of the fraction remains the same. 

           For example, (⅔) × (4/6) = 8/18 = 4/9

           Similarly, (4/6)×(⅔) = 8/18 = 4/9

• If the given fractional number is multiplied by (1/1), the product remains the same fractional number.

           For example, (⅘)× (1/1) = (⅘)

• If a given fractional number is multiplied by 0, the product remains zero.

           For example, (½)× 0 = 0

Multiplying Mixed Fractions

Multiplication of simple fractions is easy, we just need to multiply numerators and denominators respectively. But to multiply mixed numbers or fractions we need to add one more step. 

• First, convert the given mixed fraction into improper fractions
• Now multiply the fractions
• Simplify the answer
• Again convert into mixed numbers

Multiplying Fractions Tricks:

• Usually, we will simplify the fraction after the fractions are multiplied. However, to make the calculations easier, we can simplify the fractions into their lowest terms before multiplication if possible.  For example, (6/2)×(8/10) can be simplified as (3/1)×(4/5). Now, we can multiply the fractions (3/1)×(4/5)= 12/5.
• Simplification can be performed across two fractions also. For example, (10/7)×(21/5) can be simplified into (2/1)×(3/1) and we can multiply fractions, which will result in 6/1.