Add the Fractions 7/323 + 2/27=? Fastest way is THIS! 

This was quite a straightfoward one for my 65 year old brain, and I am pleased that I was able to do the multiplications without a calculator .. which we were not allowed to use at school.

when they talk about algebra they frequently talk about "apples and oranges." Fractions are same as denominators gotta agree; cannot add apples and oranges. In this case we have some "323's" and some "27's" that we want to combine. The surest way is to multiply 323 × 27.. (I'd guess this is easiest way too??) Next might be finding common multiples between 323 and 27 to attempt to find LCD .. lowest (least) common denominator. Thanks to John, I just recently learned that a number is divisible by 3 if its digits added are divisible by 3. Example; 27 => 2+7 = 9 and 9 ÷ 3 = 3✔️✔️. However... 323 => 3+2+3= 8 and 8/÷ by 3. Since 27 = 3×3×3 so there's no common factors between 323 and 27. So no choice but to multiply 323 by 27 and 27 by 323 i.e ((7/323) +(2/27)) => or ( (27/27)(7/323) + (323/323)(2/27) ) or ( (27×7)/(27×323) + ( (323×2)/(323×27) ) or ( ((27×7)+(323×2))/(323×27) ) or ( (189+646)/(8721) ) or 835/8721 The method John will detail is the "X" method of: (-1-) multiply left numerator by right denominator and add to (-2-) multiply right numerator by left denominator (-3-) divide that sum by both denominators multiplied together. SUMMARY: ((N.L×D.R)+(N.R×D.L))/(D.L×D.R) v e r i f y (7/323) + (2/27) 0.02167 + 0.07407 =0.09574 835/8721 = 0.09574 0 09574 =❤ 0.99574✔️ FINAL ANSWER 835/8721 DISCUSSION: I the world of electronics and electricity the resistor is a basic element.... the very simple law/rule for electricity is called Ohm's Law. Simply voltage across the resistor, current thru the resistor and the resistance of the resistor are related: V = I × R maniplulated R = V ÷ I R// ohms V// volta I// amps if two resistors are in parallel, their combined resistance is: (1) / [ (1/R1) + (1/R2) ] so, if R1 =1000 and R2 = 5000 in parallel they form a circuit of = (1)/[(1/1000)+(1/5000)] = (1)/[(5/5000)+(1/5000)] = (1)/[(6/5000)] = 5000/6 = 833.33 Ohms manipulating fractions becomes a well known method when dealing with Ohm's law. Electronics gets REAL interesting when considering inductors and capacitors. These two devices result in a.c. current becoming 90° offset from their driving a.c. voltage. Recall sine and cosine are offset by 90°. In an inductor the a.c. current lags applied a.c. voltage by 90°. Because there's 90° offsets the use of the imaginary "i" is used but in electronics "j" is used instead. In a capacitor the a.c. current leads the a.c. voltage by 90°. to distinguish leading and lagging current the term used instead of RESISTANCE is REACTANCE. How an inductor reacts to (impedes current) from changing voltage is inductive-reactance. A capacitor is capacitive reactance. XL - inductive reactance XC - capacitive reactance Revise ohms's law V = I R to. V = I × XL (for inductor) V = I × XC (for capacitor) sidebar: a pure inductor is a SHORT for d.c. voltages a pure capacitor is infinite for d.c. voltages specifically XL = 2(pi)FL XL increases with F F = frequency L = inductance XC = (1)/[2(pi)FC] XC decreases with F F = frequency C = capacitance Ohm's Law Still applies: V = I × R V = I × XL V = I × XC OLD AS NOAH is the learning aid: ELI the ICE man. E (voltage) in L inductor leads I I in C capacitor leads E (volts) always by 90°

Great way to do it. Thanks.

You don't need to know the prime factors of 323, once you know it's not divisible by 3, you know it shares no common factors with 27, so the only thing you can do is multiply the 2 denominators.

Thank you!!!

Your method is no easier than the one I learned 75 years ago.

got it cross multiply - thanks for the fun

189/646 after cross multiplying. If you take that fraction is ends up becoming a decimal of .2925 and so on which is 29 percent. Wait cross multiply is only when the plus is a division symbol I think. So i was close i just need to take what i have as my numerator and denominator and add them together and make it the new nominator and then do the last step of bowtie to flget correct dominator.

Much better when it does not say that many will get it wrong

Since we were allowed to use our calculator it was not that impressive IF we know the bow tie method. But I'll take the compliment anyway because I need all the encouragement I can get in my maths adventures. :)

835/8721

No way to simplify these fractions so let's BOWTIE them: Denominator = 323 . 27 = 8721 and numerator = 7 . 27 + 2 . 323 = 189 + 646 = 835 So the answer is 835/8721

The fastest way to do this problem is not waste over 15 minutes on extraneous examples and get right to the point. The quickest explanation is to cross multiply since there is no simple LCD for these two fractions. And then you are done.

Cross multiply, never heard it called bow tie method, you live and learn . Guess that's the difference between math and maths.

Stop saying Ok!

18 minutes about "the fastest way"... 😂

7/323×2/27 189/646