Can someone please help me with solving proportions?

Question

I need to learn to solve proportions using the reciprocal property and the cross probuct property. oh and if you can out it into terms a 14 year old can understand that would be great

Answer 1

Proportion, what is it?

The first thing you need is a definition.

A ratio is one thing compared to or related to another thing; it is just a statement. A proportion is two ratios that are equal to each other; a proportion is an equation that can be solved.

Sample:

(25/x) = (100/40)

Solve for x by cross-multiplication (also known as the cross product rule).

x times 100 = 25 times 40

100x = 1000

Divide each side by 100 to find x.

x = 1000 divided by 100

x = 10

Did you follow?

I used the cross product rule, which is also known as the cross-multiplication rule.

The word property means rule or law.

To use the reciprocal rule, we simply "flip" each fraction and then cross-multiply.

We will get the same answer.

So, 25/x becomes x/25

and 100/40 becomes 40/100

(x/25) = (40/100)

25 times 40 = x times 100

1000 = 100x

Same as above:

1000 divided by 100 = x

10 = x

Guido

Answer 2

I will assume you know how to SET UP a proportion and what it it. Ok?

In math, you learn a "bag of tricks" to push numbers around as easily as you can while obeying "THE RULES" Ok?

Reciprocal property is one of the things in the bag of tricks. It goes back to that Monday when you were zonked out after the big party and the teacher was talking about multiplication and division. He said something like if you have two non-zero numbers A and B, AxB = BxA and this had a cool name. He also said something like, if you have two non-zero numbers C and D, C/D # D/C, and that had another cool name. Right?

Well, division is a pretty dorky thing. But in the heart of every division is a multiplication yearning to be free. To free it, we use the concept of reciprocals. C/D is equal to C x (1/D). Since we can dredge up a number E = (1/D), C/D = CE. Well that's neat. Also, 1/(C/D) is equal to D/C, which is (1/CE), Wow, that's cool and a half. If that isn't enough, D x (1/D) = 1. coolness to the max.

With proportions, we have two pairs of numbers, C and D and R and S. If C = mD, where m is non-zero, and R= mS, THE RULES say that things equal to a third THING are equal to each other. Wousers!!. We can take the reciprocal of D and S, and form C/D = m = R/S. Voila!, a proportion.

Algebra teachers don't like denominators very much. In fact, division is a second-class operation in math. So we want to get rid of denominators. One way to do this is CROSS-MULTIPLY. Multiplication is cool, denominators are dreck, so everyone does it. But, beneath this lurks the reciprocal. That is, when we cross multiply C/D = R/S to get CS = DR, what we ACTUALLY do is a reciprocal thing. So
C (1/D) = R (1/S) . Then, we multiply both sides by DS. Oooooooh, that's sneaky. If you remember,
D x (1/D) = 1, and S x (1/S) = 1.
Then, we get CS = DR. IN OTHER WORDS, cross-multiplying is a sneaky way of doing a reciprocal operation without letting you know it is a reciprocal operation. And why? Because division is a second-rate operation. Is that really FAIR!! What did division ever do to you?

Answer 3

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