Fractions: Multiplication and Division
In my previous post we talked about adding and subtracting fractions, and today we tackle multiplication and division of fractions in a clear and practical way.
Multiplication of fractions
To multiply fractions, follow these steps: multiply numerator by numerator; multiply denominator by denominator; simplify the result by looking for common factors until you get the irreducible fraction.
Practical tip: before multiplying, you can perform cross-cancellation between numerators and denominators to work with smaller numbers and avoid unnecessary calculations.
Multiplication example: 2/3 times 4/5 = 8/15. If there were a common factor, it would be simplified to leave the irreducible fraction.
Division of fractions
To divide fractions: keep the first fraction, invert the second fraction, and change the operation to multiplication; then apply the multiplication steps, including prior or subsequent simplifications.
Division example: 3/4 divided by 2/5 becomes 3/4 times 5/2 = 15/8. If possible to simplify, perform cancellations before multiplying.
Key concept
An irreducible fraction is one whose numerator and denominator share no divisor greater than 1. It is always advisable to simplify to express results in their simplest form.
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