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Bumek [7]
3 years ago
9

Find both the sum and difference of the following rational numbers. 3/11, 13/5

Mathematics
2 answers:
anzhelika [568]3 years ago
8 0
For 3/11 the difference is 8 the sum is 14.the difference of 13/5 is 8 the sum is 18
weqwewe [10]3 years ago
3 0

Sum:

\dfrac{3}{11} + \dfrac{13}{5}

  • Set up

\dfrac{15}{55} + \dfrac{143}{55}

  • Find common denominator (55)

\dfrac{15 + 143}{55} = \boxed{\dfrac{158}{55}}

  • Add numerators over common denominator

Difference:

\dfrac{3}{11} - \dfrac{13}{5}

  • Set up

\dfrac{15}{55} - \dfrac{143}{55}

  • Find common denominator (55)

\dfrac{15 - 143}{55} = \boxed{-\dfrac{128}{55}}

  • Subtract numerators over common denominator
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Read 2 more answers
Solve by using Pythagorean Theorem, a= 5, b= x-1, and c=x
charle [14.2K]

The value of x is 13, from the values of x the values of a,b and c becomes 5, 12 and 13, which is obtained by using Pythagorean theorem.

Step-by-step explanation:

The given is,

             a = 5

             b = x - 1

             c = x

Step:1

      Pythagorean theorem is,

              a^{2} + b^{2} = c^{2}................................(1)

      (  It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides )

      From the given values the equation (1) becomes,

                       5^{2} + (x-1) ^{2} = x^{2}

                             ( (a-b)^{2} = a^{2}  + b^{2} -2ab )

               25 + ( x^{2} + 1 - 2x ) = x^{2}

                           25 + 1 -2x = 0               ( ∵ Eliminate x^{2} in both sides)

                                     26 = 2x

                                       x = 13

Step:2

        From the values of x,

                   a = 5

                    b = ( 13 - 1 ) = 12

                   c = 13

Result:

            The value of x is 13, from the values of x the values of a,b and c becomes 5, 12 and 13, which is obtained by using Pythagorean theorem.

3 0
3 years ago
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