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pokemonfan58

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Usernamepokemonfan58
Score59
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Questions 0
Answers 11

 #1
avatar+59 
+5

The sum of 1/6 and 1/7 would be 13/42, or, if you wanted the answer in decimal form rounded to the nearest hundredth, it would be about 0.31.

To find the sum of 1/6 and 1/7, we cannot simply add the numerators together and maintain the same denominator. This is because 1/6 and 1/7 have different denominators, so we don't know which denominator to maintain!

To fix this we need to find a number that is divisible by both 6 and 7. One easy way to do this is to multiply the two numbers together:

6 x 7 = 42

If we were to change the denominator to 42 for each fraction, we could add the numerators together and maintain a denominator of 42. However, this means we must change the numerator of each fraction along with its denominator.

Let's start with 1/6. We can multiply 6 by 7 to obtain 42, but this means we also have to multiply 1 by 7 to keep the fraction proportionate. If the fraction does not maintain the same proportion, it will be a completely different fraction!

We know that 1 x 7 = 7, so it is safe to say that 1/6 is equal to 7/42.

We can apply the same logic to 1/7. Since 7 x 6 is 42 we need to multiply 1 by 6 along with 7. Note: you cannot multiply each number by 7 this time, because 7 x 7 would be 49, not 42. In multiplying the numerator and denominator by 6 we know that 1/7 = 6/42.

Now we have an equation of:

6/42 + 7/42

Now we can add it as we would normally by adding the numerators and keeping the denominator to get:

6/42 + 7/42 = 13/42

If you needed the answer in decimal form it would be about 0.3095238095, or 0.31 rounded to the nearest hundredth.

I hope this helped.

-pokemonfan58

Jun 29, 2014
 #1
avatar+59 
0

To solve non-linear simultaneous equations, you must find the point at which they overlap. This can be done by finding the "x" and "y" values that apply to both equations.

Let's assume we have the following two simulatenous equations:

y = 3x

y = x + 12

We know that in each of these equations both "3x" (the same as 3 multiplied by x) and "x + 12" are equal to the variable of "y". Since the two equations are simultaneous, or occuring on the same graph, 3x and x + 12 must be equal. Thus, we can safely infer that:

3x = x + 12

Now we can simplify this equation using algebra. We can start by subtracting x from both sides to cancel out the "x" on the right side:

3x - x = x - x + 12

We can see that on the right side of the equation, "x - x" can be simplified to equal 0, so we can cancel that out to get:

3x - x = + 12

or...

3x - x = 12

Also, we can simplify "3x - x" to give an  answer of "2x":

2x = 12

To simplify what we have now, we can divide each side by 2:

2x / 2 12 / 2

We can see that "2x / 2" is equal to "x" and that "12 / 2" is equal to 6, so we have a final answer of:

x = 6

Now that we know "x", all we have to do is find "y". This is really easy: we can just plug it into one of our first equations: "y = 3x" or "y = x+12". We'll do "y = 3x" for the sake of simplicity:

y = 3(6)

We can simplify "3(6)" by multiplying 3 and 6 to obtain an answer of 18, giving us our answer for "y":

y = 18

Points on a graph are shown as (x,y), so through using algebraic methods, we were able to find that the two equations intersect at the point (6,18).

If I didn't help you, I found a really helpful Purplemath page that further explains non-linear simultaneous equations you can see here.

-pokemonfan58

Jun 18, 2014