2/7x + x/2 = ? This Algebra Problem HAS a GREAT SHORT CUT!

[@Hi-rw8vr]

Common denominator: 4/14x + x²/14x Add the top: (x²+4)/14x

[@stevendebettencourt7651]

Okay, let’s jump right in with the standard process. 2/(7x) + x/2 First, we need to get the LCM (Least Common Multiple) in the two denominators. Let’s break down those two to find it: 7x = 7 * x 2 = 2 Since there are no factors in common between these two, the LCM is the product of the two: 7x * 2 = 14x Before we plug 14x into our denominator, though, we have to multiply the top and bottom of each term in our equation. Since 14x/7x=2, the left term is multiplied by 2/2. By a similar process, 14x/2=7x, the right term is multiplied 7x/7x. Both of these are equal to 1, and multiplication by 1 does not change a number. = (2/(7x)) * (2/2) + (x/2) * (7x/7x) = 4/(14x) + (7x^2)/(14x) Because we have a common denominator, we can combine two terms into one: = (4 + 7x^2)/(14x) And that is our answer. Addendum: The Bow-Tie Hack works in any situation where the denominators are relatively prime to each other (that is, they share no common factors). It will always work regardless, but keep in mind there could be some simplification you’ll have to do afterward to get full credit.

[@frankinga3120]

Why leave as a fraction,? X top and bottom by 14x = 56x+98x cubed (on one). Anything wrong with this answer?

[@Teronix100]

Yes, how do you even get to that solution? The equation looks like (4+7x^2)/(14x)=y. Use y instead of ? to not get confused. Multiply by 14x gives you 4+7x^2=14xy But you muliplied again so 56x + 98x^3 = 196yx^2

[@Rev03FFL]

Its an expression not an equation. So cannot multiply terms by anything but one.

[@paulfrank8738]

What you are showing is not what you end up with if you multiply the top and bottom by 14x; the actual result is still a fraction, but it's no longer in the simplest form. In this problem, you can't get rid of the fraction. Multiplying both sides of an equation with the denominator in order to get rid of a fraction sometimes helps simplify and solve some equations. But, that process doesn't help with this problem.

[@dazartingstall6680]

If you do that you get (56x+98x³)/196x² not (56x+98x³)/1. But just a simple check by substitution should have told you something was wrong with your reasoning. If we say x = 2 we end up with: 2/14 + 2/2 = 16/14 = 8/7 We don't even need to calculate 56(2) + 98(8) to see that there's a disparity.

[@frankinga3120]

@@dazartingstall6680 Yep, I made a bobo.

[@bradlewis8036]

Great reminder of past taught Mathematics.

[@Stylux-z1p]

This is an expression : 2/7x + x/2 [2(2) + 7x(x)] / [7x(2)] [4 + 7x²] / [14x]

[@playgirl7305]

In Zimbabwe that is grade 4 stuff. With 10/11 years we learned that in in primary school.

[@pi5355]

If 2/7x+x/2=0 2/7x=-x/2 4=-7x^2 x^2=-4/7=-0.571 =0.571(I)^2 x=(4/7)^0.5 i

[@georgecattani7199]

Bow tie = 4 + 7X^2 / 14X

[@daniellerosalie2155]

4+7x^2/14x. Get the LCM.

[@coreygraham860]

Another way is to just multiply the numerators of the entire equation by each denominator and then solve accordingly.

[@harrymatabal8448]

(7x^2+4)/14x

[@davidwilliams1060]

I very rarely assume that former Marines wear bow ties or have pocket protectors. Unless it’s Drew Carey in a sitcom.

[@bazkeen]

Bow Tie method 👍🏻

[@russelllomando8460]

got it LCD is 14X thanks for the fun.

[@roundtwo3321]

Are short cuts really math?

[@paulfrank8738]

Of course they are. Shortcuts are just previously proven formulas or procedures. They just get the name "shortcut" because they tend to be faster or easier than the formulas or procedures that we usually use.

[@dazartingstall6680]

It's not a short cut. It's the exact same method as was explained in the first part of the video. I have no idea why John thinks it's a "hack".

[@coreygraham860]

​@dazartingstall6680 It's a "hack" so to speak because it's a mnemonic. It's an easy pattern to memorize, but by itself, it doesn't give you any understanding of how fraction addition works.

[@coreygraham860]

No Shortcuts = Pure Math Shortcuts = Applied Math

[@pas6295]

ANSWER is √2/7

[@panlomito]

Just bowtie to simplify: 4 + 7x² / 14x

[@chrisdissanayake6979]

Answer: 4 + 7X^2 ----- 14X Thank you for reviewing the bow-tie method, Mr John 🙏🏽

[@simonmengesha9369]

ኢትዮጵያ ውስጥ ርክሽ ነገር ሴትና ድንች በዳቦ ነው