Reducing fractions is the final step when solving a fraction multiplication problem. Your answer won’t be considered correct if it is not reduced to its lowest or simplest form. This may involve making an improper fraction into a proper fraction, or just finding a common divisor for the numerator and denominator.
Reducing fractions isn’t hard, but it’s a skill that takes some practice. Here are some tips for getting the products of those fraction multiplication problems into lowest form!
Look for Easy Divisors
Even if your answer is clearly improper, there are often very obvious ways to divide both the numerator and the denominator into smaller numbers so that the rest of your reducing work is easier.
An obvious example is when the numerator and denominator both end in zero. This means both values are divisible by ten. You can simply cancelling one or more zeroes from the fraction’s numerator and denominator, and the actual quantity represented by the fraction is unchanged. As long as you can cancel a zero from both the numerator and the denominator at the same time, just keep cancelling away until that fraction looks a little friendlier!
If the numerator and denominator are both even, this is often a good time to divide both by two if the number is easy to work with. If you’re good at dividing multi-digit numbers by two in your head, this may be a great way to simplify a problem quickly.
Other good candidates for reducing early might be looking for simple divisibility tricks like numbers that can be divided by five.
Don’t obsess over early reducing too early. Take the easy wins where you find and do any quick mental divisions you can in this first step
Reduce to Mixed Fractions
Once you’ve done any super obvious reducing steps, it’s time to make sure your fraction isn’t improper, and if it is, turn it into a mixed number.
Any time a fraction has a numerator greater than its denominator, it represent a value that is more than a whole amount. We often want this form of a fraction when we are performing certain arithmetic steps to solve a problem, including fraction multiplication, but when you’re presenting your final answer this it’s usually considered bad form.
To turn an improper fraction into a mixed number, you’ll use your long division skills. Divide the numerator by the denominator and whatever whole number you get in the quotient, that’s the number of wholes in the mixed number. The remainder is the new numerator for the fraction component. The denominator remains the same.
If you’re lucky enough that the numerator is divided evenly by the denominator (that is, you didn’t get a remainder in your long division step), then there isn’t a fractional part at all. You shouldn’t ever have a mixed number where there’s a zero numerator in the fractional part, and you should just report your answer as a simple whole number.
Can You Keep Reducing?
If you’ve turned your fraction into a mixed number, or if it wasn’t improper to begin with, you should take a close look at the number that remains to see if it can be reduced further.
If you didn’t need to divide to turn an improper fraction into a mixed number, this may be a good opportunity to try doing a division step to see if a decimal results looks familiar.
Otherwise, use basic rules of division to see if you can find a common denominator. For example, if the sum of the digits in the numerator is a number divisible by three, and the sum of the digits in the denominator is also divisible by three, you know that three is common factor of both, and that you can reduce by dividing both numbers by three.
Reducing is often art as much as skill, and the more practice you get reducing fractions the better you’ll become at it. Keep practicing!
