Let’s Solve The PROPORTION! One step at a time…

How to solve a proportion using the cross product.

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TC Math Notes

[mr.mxyzptlks]

My basic rule for this type of question: memorize the language. ‘Is to’ means divide. ‘As’ means equate ‘=‘. Don’t overthink it and apply the rules from there. I personally prefer abstract math, but in applied mathematics this kind of input is pretty common. Wanted to, expand on way more l but keeping at this, for now 😊

[russellbonesteel]

Sine Cosine and Tangent are Really nothing more than Ratio Proportions! The Constant side is supplied by a "Trig Table" The variable is one of 3 sides of a Right Triangle determined by one of two complimentary Angles called Theta. The sides Opposite and Adjacent are defined in relation to an acute Complimentary angle called theta.The remaining Long side which which is Always opposite the Right 90 degree angle is the Side Hypotenuse.

Moral of the rant Ratio Proportions are very powerful and the time You invest with them shall be handsomely rewarded! (It only took Me 6 Months to figure this out as I was muddling my way through basic trig)!

[d_Howard]

Mental Math! Set it up so you don't need a calculator if you can. I want to visualize the 15 and 45 on the same side of the ratio. So the sentence "x is to 15" needs to be converted to mathematical language. Let "is to" mean " = ".

It will look like this:

_x_ = _15_
8 45

or

_8_ = _45_
x 15


I can see that 45 is 3 times the number above or below it ( 15 ), so x must be three times what's above or below it ( 8 ).

What number is 3 times 8?

Answer: 24

Done.

Doesn't work all the time. If the answer will be a fraction or a decimal, use the calculator.

[timhansn]

I have always done things backwards. 45 divided by 15 times 8 equals 24

[imagseer]

Saw it in my head instantly as the denominator is 3 times 15, so to stay in proportion x has to be 3 times 8 = 24

[devonwilson]

Greetings. The solution is obtained by saying 8/15=X/45 from which it is determined that X = 360/15=24, answer arrived at after cross multiplying.

[elberthiggins]

The answer is 24. Culturally we stopped talking like "x is to" about 200 years ago. It's just a confusing way to state a simple problem. It's a language problem more than a math problem.

[rogerdudra]

Greetings from the BIG SKY. It's good to rattle the chains occasionally. Class of 1968 C.M.Russell High School.

[Geoff_G]

24
Because 15 is 1/3 of 45 so the answer is 8×3=24

[carolemckee]

I just looked at the original phrase and cam4e up with the answer.

[The_Vaporizer]

It's easy when they're numbers... but what about when they're shapes?

[diamondsandgems]

Sir why to make it so hard? I had the answer in 2 seconds just by looking at the question and you took 10 min to resolve by confusing the audience.
It is simple 8 is to 15
As. X is to 45

So simple multiply 15 x 3 to make it 45
And 8 x 3 to get the answer 24.
I hope you like the answer.

[maxxheadroom]

A very laboured and disproportionate perspective if I might say so, when this could be made much more interesting and intuitive. This maths tutor must be a nightmare in real life class situation or worse still on a 1-2-1 basis! Very boring for a very interesting topic!