How Does Cross Canceling Work

Fractions can seem to be a complicated idea in math. But multiplying fractions turns out to be ane of the easier things you can exercise when y'all are working with fractions! One reason is that when multiplying fractions, you do not have to worry about mutual denominators. Instead, you always utilise the aforementioned rule: multiply straight beyond. You can see this in the examples below or you tin scroll downwards for a video example.

Some examples of multiplying fractions

Permit's await at our offset example. Hither, we are finding the product: $\dfrac{3}{4} \times \dfrac{1}{2}$

$example of multiplying two fractions where no simplification is needed$

Notice that the answer was already simplified and that even though the denominators were not the same, you lot could still just multiply across. In the side by side example, we will as well employ that rule, but the answer has to be simplified.

$example of multiplying two fractions where you have to simplify$

There is a shortcut that we can utilize when this happens called cross-cancelling.

Cross-cancelling: simplifying before multiplying fractions

Let's use the same example every bit before. Notice that the iii and the 9 both share a factor of three since $three = three \times i$ and $nine = 3 \times iii$. Because of this, nosotros can cross cancel before we multiply.

$multiplying two fractions when you can cross-cancel$

This is much easier! It even works when the fractions are a scrap more complicated, as in the example beneath where nosotros are finding:

$\dfrac{11}{12} \times \dfrac{26}{55}$

Hither, xi and 55 both share a factor of eleven since $eleven \times 1 x 11$ and $55 = 5 \times xi$. Also, 26 and 12 both share a cistron of 2 since $26 = 2 \times 13$ and $12 = 2 \times 6$.

$multiplying fractions and simplifying with cross cancelling: 11/12 times 26/55$

Video – how to multiply two fractions

The video beneath goes into a little bit of the ideas behind multiplying two fractions and then shows some examples, including examples where you can cross-abolish.

Summary

When adding or subtracting fractions, the process is different depending on whether the denominators are the same or different. However, when multiplying or even dividing fractions, this is no longer a concern. Instead, you multiply the two numbers in the numerators and multiply the ii numbers in the denominators. To save work after, always remember to check if you can cross-cancel.

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