-2/5 + 7/8, and -3/7 + 2/5 - 1/2?

Question

-2/5 + 7/8, and -3/7 + 2/5 - 1/2?

Answer 1

-2/5 + 7/8 = -16/40 + 35/40 = 19/40

The lcm (lowest common multiple) of 5 and 8 is 40, so convert each fraction to be over that, then it's simply addition.

-3/7 + 2/5 - 1/2 = -30/70 + 28/70 - 35/70 = -37/70

The lcm of 7, 5, and 2 is 70, so once again convert each fraction to be over that, then solve.

Answer 2

To work those problems, you first have to find a common denominator for the fractions involved.   The common denom. is a number that all the other denominators will divide into, without a remainder.  One way to find a common denominator is to multiply the original denoms together.   For example, in the first problem, the two denominators are 5 and 8, and if you multiply them together you will get 5 x 8 = 40, so 40 would be a common denominator.  

Let's use 40 for your first problem.   We'll convert both of those fractions, -2/5 and +7/8, into fractions with a denominator of 40.  

With the first fraction, -2/5, we divide the denom, 5, into 40 and multiply the result times our numerator, which is 2, and make that product our new numerator, with our new denom of 40.    Here's how that goes:   5 into 40 goes 8 times, and 8 times 2 equals 16, so that our original fraction, -2/5, gets converted to -16/40.

Then with the second fraction, +7/8, we divide the denom, 8, into 40 and multiply the result times our numerator, which is 7, and make that product our new numerator, with our new denom of 40.  Here's how that goes:  8 into 40 goes 5 times, and 5 times 7 equals 35, so that our original fraction, +7/8, gets converted to +35/40.

OK, so now we have the two fractions, -16/40 and +35/40.  Let's rearrange the terms to +35/40 and -16/40.   Combining those two equals (35 minus 16)/40, and since 35 - 16 = 19, our answer is 19/40.

In the second problem we can again get a common denominator by multiplying all our original denominators together.   In this case our original denoms are 7, 5, and 2.   And, multiplying them together, we get 7 x 5 = 35, and 35 x 2 = 70, so 70 is a common denominator.

Then going through the same kinds of paces that we did above, the three fractions convert to the following:

-3/7 =  -30/70

+2/5 = +28/70

-1/2  =  -35/70

And when we combine these, our problem becomes ...

-30/70 + 28/70 - 35/70.

Then simplifying by combining the negative terms, the problem reduces to  ....

+28/70 - 65/70

which equals   -37/70.

.

Answer 3

-2/5 +7/8

40 is the lcd

-2/5=-16/40

7/8=35/40

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       19/40

-3/7+2/5-1/2

70 is the lcd

-3/7=-21/70

2/5= 28/70

-1/2=-35/70

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   -28/70=-2/5