Simplify the following fractions to lowest terms. − 42 m n 60 n -\frac{42mn}{60n}

This problem asks us to simplify the following fraction into lowest terms. So, here I can see that we have -42 MN over 60N. Now, to solve this problem, what I'm going to do is recognize something. This is a negative fraction. So, the result that we're going to get is going to be negative. Now, I'm going to fully factor the numerator and then the denominator, and we're going to see what we end up getting. Now, it turns out this is actually not something I necessarily have to break down into prime factors, because there's actually a common thing that I'm noticing here. 42 is the same thing as 6 times 7, and then we can't forget we also have the M and the N being multiplied. Now, 6 is the same thing as 2 times 3. And this is actually completely broken down into prime factors on top, but watch what I'm going to do with the denominator here on bottom. 60 is the same thing as 6 times 10. And what I know is that 6 is also 2 x 3. So, we have 2 times 3 times 10, and then we have times N in the denominator. Now, notice how the 2s and the 3s are going to cancel, but it turns out that there's nothing that's going to reduce for the 7 and the 10 here. So, even though 10 can break down farther, I actually can already recognize that that's as simple as it's going to get. Now, one more thing you need to pay attention to here is notice the variables we have in common, the ends. We can cancel the ends as well. So all we're going to end up with in the numerator, don't forget this negative sign, is going to have 7 m in the numerator, and then in the denominator, we're going to just have 10. Now, if you were skeptical about this or found yourself concerned that you didn't reduce it fully, you could break down 10 into 2 times 5, but again, 7 is already a prime number and none of these numbers are 7, so leaving it as 10 is perfectly fine. So, this is just something that I'll mention here. When solving these types of problems, oftentimes you'll start to just recognize these common factors and be able to solve them faster. But if you're ever skeptical, you can always break everything down into prime factors and then just cancel the common ones and then get your final result. So, however you want to go about it, that's how you can solve this problem. Hope you found this helpful.

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1. Whole Numbers1h 55m

Multiplying Whole Numbers
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Long Division
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Introduction to Integers
16m

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24m

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10m

Dividing Integers
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Intro To Fractions and Mixed Numbers
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Simplifying Fractions
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4. Fractions

Simplifying Fractions

Prealgebra, Beginning Algebra, & Intermediate Algebra

4. Fractions

Simplifying Fractions

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Multiple Choice

Simplify the following fractions to lowest terms.
$- \frac{42 m n}{60 n}$

$- \frac{7 n}{12}$

$-$\frac{7m}{10}$$

$-$\frac{7m}{12}$$

$-$\frac{6m}{10}$$

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Simplify the following fractions to lowest terms.−42mn60n-\(\frac{42mn}{60n}\)

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Simplify the following fractions to lowest terms.
$- \frac{42 m n}{60 n}$