0

Simplify -270y^2/189x^3

Not too sure how to go about simplifying this. I googled it, and google showed me the steps but no explanation.

Step 1: Cancel terms that are in both numerator and denominator

     -270y^2/189 * x^3

Reduced: -10y^2/7 * x^3

Step 2: combine multiplied terms into a single fraction

     -10y^2/7 * x^3

 -10y^2 * x^3 / 7

Solution: -10y^2 * x^3 / 7

Why did 7x^3 get separated into 7 and x^3?

Why did the equation get multiplied or looks multiplied by x^3?

Why do we combine x^3 with 10y^2 in the numerator? I.E. 10y^2*x^3 / 7?

Can someone go over simplifying this in a more detailed manner?

TIA

JMoravitz
  • 80,908
Eden Boychyn
  • 11
  • Do you know about Mathjax? its a tool to format your question – Aven Desta Feb 16 '21 at 17:33
  • 1
    To clarify... are you talking about $\dfrac{-270y^2}{189x^3}$ where the $x^3$ is a part of the denominator? Or are you talking about $\dfrac{-270y^2}{189}x^3$ where $x^3$ is not a part of the denominator. Writing this without parentheses and with a slash rather than properly writing as a fraction with a bar is ambiguous. – JMoravitz Feb 16 '21 at 17:35
  • 1
    It sounds like your question boils down to whether a/bc is in reference to (a/b)c which would be $\dfrac{a}{b}\cdot c = \dfrac{ac}{b}$ or if it is in reference to a/(bc) which would be $\dfrac{a}{bc}$. It is common to imagine implied parentheses on the denominator and so this second one is the more common choice... but the ambiguous notation should have been avoided in the first place. – JMoravitz Feb 16 '21 at 17:38
  • 1
    @AvenDesta Your attempt at editing the post with MathJax, while ordinarily helpful, removed the ambiguous expressions and replaced with one of the two interpretations without knowing if that was the intended interpretation... and indeed with the interpretation that does not match the workflow shown. In this case, it seems clear that the work shown was for treating a/bc as (a/b)c and your edit would have made it harder for people to recognize that this is what is actually at issue here. – JMoravitz Feb 16 '21 at 17:41
  • I am talking about how x^3 is part of the denominator with 189. So altogether 189x^3 as the denominator. – Eden Boychyn Feb 16 '21 at 22:32
  • Did you understand the answers you have been given? Putting an expression into a calculator does not always give you the correct answer, because the calculator may interpret your input differently from your intention. In this case, it treated the input as -270×(y^2)÷189×(x^3) evaluated from left to right, giving a wrong answer. – user21820 Feb 25 '21 at 07:23

1 Answers1

0

It is often useful to use parentheses in order to avoid ambiguity. We have $$ (-270y^2) / (189x^3) = \frac{-270y^2}{189x^3} = \frac{-10y^2}{7x^3} $$ since $$ 270 = 2 \times 3^3 \times 5 \qquad \text{and} \qquad 189 = 3^3 \times 7. $$

fanfly
  • 181