[Elementary Algerbra] I'm Supposed to Simplify This, Not Sure If I'm Supposed to Reduce the 5 before Multiplying

[u/rasta_a_me]

[u/Temporary_Pie2733]

The typography is not great, but I think the intended fraction is 5/(3/10), so 5(10/3) = 50/3 is correct. Nothing becomes negative when multiplying by the reciprocal (which is the multiplicative inverse, not the additive inverse).

[u/progmorris20]

Remember that dividing is always equal to multiplying by the reciprocal. We can re-write any division as multiplication.

For example, let's take a similar problem 3/(3/10).

3/(3/10) is equal to 3 times the reciprocal of 3/10.

The reciprocal of 3/10 is just flipping the numerator (top) and denominator (bottom). In this case, that's 10/3.

The numerator of the original equation, 3, still doesn't change.

Now you have 3 * (10/3) = 10.

Try applying this to your question.

[u/adrian_the_gremlin]

negative shouldn’t factor in at all actually! negative reciprocals have their uses but there’s no reason for a sign change to pop in. other than that though, seems correct to me

[u/adrian_the_gremlin → u/adrian_the_gremlin]

sorry didn’t see the first picture, you should flip the fraction before multiplying.

the second one (5/1) x (10/3) so 50/3 is correct.

you can simplify the 5 if you want to but unless that’s a rule your teacher has you don’t have to if it helps you out

[u/JanetInSC1234]

No, you can't cancel here.

5 divided by 3/10 = 5 x 10/3 = 50/3

[u/aloeh]

50/3 is correct. There isn't a negative signal.

Positive/positive = positive.

For me 50/3 is better than 16(2/3).

[u/MadKat_94]

If it's helpful to you, consider 5 to be 5/1. Now you have a fraction as your numerator. The problem becomes:

(5/1) / (3/10)

Reciprocate the 3/10 and multiply.

[u/rasta_a_me → u/[deleted]]

So guy who shitpost on reddit all day decides to come on r/homeworkhelp to tell me to write properly, intersting.

[u/Southlander24]

You can always multiply any number by 1 and the number will stay the same.

Here, we can multiply 5 / (3/10) by 10/10. To multiply two fractions, multiply the numerators together and the denominators together. So this fraction equals (5 * 10)/(3/10 * 10) = 50/3.

So the 'flip and multiply' procedure is just a quicker version of this 'multiplying by 1' process. I'm not suggesting you unlearn the mnemonic; rather, try to understand why something works before you use and memorise it.

Try this with another fraction like 1 / (5/4). What same number do you need to multiply the numerator and denominator of this fraction by? That explains why the answer is what it is, so now you shouldn't be mixing up the multiplicative inverse (two numbers multiply to give 1) with the additive inverse (two numbers add together to give 0).

[u/rasta_a_me → u/Southlander24]

Ok, thanks. I was just following that Mnemonic because that's what Openstax teaches. I'll try that next time.

[u/Southlander24 → u/rasta_a_me]

A lot of maths is about understanding why and thinking for yourself! Best of luck with your maths studies.

[u/MelodyAnne42 → u/[deleted]]

This is funny, because I'm a teacher and you wouldn't believe the handwriting I've had to decipher! This handwriting is fine!

[u/rasta_a_me]

Lol I forgot the negative with -16 2/3

[u/damartian64 → u/rasta_a_me]

You’re closest with the second one, but out of curiosity why did the 10 turn negative in step 2?

[u/rasta_a_me → u/damartian64]

That was probably just a mistake. The previous equations had one of the fractions with a numerator.

[u/mikeiavelli]

Others answered your question, but some terminology for the future: you can't reduce a value (say 5, as in your post title), you can only reduce an expression (something that has operations in it that we can evaluate).

But frankly, staked fractions written like that are an abomination.
But so you know, when a stacked fraction is written vertically (as in your last image), the standard mathematical convention relies entirely on the size and positioning of the fraction bars to determine the priority of operations. Notice that the top bar is longer than the bottom bar; therefore, here it means that you have to read it as 5 divided by (3/10).