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To celebrate the release of our new
and free access to our 500+ fraction lessons, today we’re going to show you a handy shortcut for multiplying fractions. This easy trick will help you reduce and simplify the fraction without having to spend much time on it at all. The trick involves cross-dividing before cross-multiplying. The easiest way to show this is by example, so lets get right to it.
4 3
- x – = ?
5 8
If this equation were done normally (by “cross multiplying”), you would cross multiply to get 12/40, a somewhat ugly fraction that you’d then have to simplify:
4 3 12 3
- x – = - = -
5 8 40 10
But, if we use this fraction trick and “cross divide”, we’d save time and skip the last simplification step. We start by finding a numerator and denominator that could be simplified. In this case it’s the 4 and the 8, which will become 1 and 2:
4 3 1 3 3
- x – = – x – = –
5 8 5 2 10
Now the equation gives us the most simplified answer, with less work. This trick is even more effective with larger numbers. Let’s try it with a harder example:
128 72
- x – = ?
300 64
This is more like it. Multiplying these fractions the traditional way will give us a huge numbers in the nominator and denominator, (9216 / 19200 to be exact). But if we try our trick first, the numbers become simple enough to where this multiplication can be done more easily in your head. We first divide the 128 and 64 by 64, leaving only 2 and 1. Then both 300 and 72 are divided by 3, leaving 100 and 24. Then divide them both by two twice, simplifying them to 25 and 6:
128 72 2 72 2 24 2 12 2 6 12
- x - = - x - = - x - = - x - = - x – = -
300 64 300 1 100 1 50 1 25 1 25
Now instead of having a fraction in the thousands, we have the much more manageable 12/25. This trick works on all multiplying fractions, as long as there is something to simplify.
Lesson: Don’t just rush in and multiply. Look for simplification tricks first and you’ll be faster and more able to do math in your head.
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