Question

The sum of two like fractions is 8/11 and their difference is 2/11. Find these two like fractions.

Answer 1

Answer:

the two like fractions are 5/11 and 3/11

Answer 2

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split.

The two like fractions are 5/11 and 3/11, and their sum is 8/11, and their difference is 2/11.

Let's call the two like fractions x/y and z/y, where y is the common denominator.

From the problem, we know that:

$x/y + z/y = 8/11 ...(1)\\x/y - z/y = 2/11 ...(2)$

We can simplify equation (1) by combining the fractions on the left-hand side:

$(x + z) / y = 8/11$

Multiplying both sides by 11y gives:

$11(x + z) = 8y$

Similarly, we can simplify equation (2) by combining the fractions on the left-hand side:

$(x - z) / y = 2/11$

Multiplying both sides by 11y gives:

$11(x - z) = 2y$

Now we have two equations with two unknowns:

$11(x + z) = 8y ...(3)\\11(x - z) = 2y ...(4)$

We can solve this system of equations by eliminating z. To do this, we add equations (3) and (4):

$22x = 10y$

Simplifying, we get:

$11x = 5y$

Now we can substitute $5y/11 for x$ in either equation (3) or (4) and solve for y. Let's use equation (3):

$11(x + z) = 8y\\11((5y/11) + z) = 8y\\5y + 11z = 8y\\3y = 11z$

Substituting 5y/11 for x and 3y/11 for z, we get:

$5y/11 + 3y/11 = 8/11\\8y/11 = 8/11\\y = 1$

Now we can use this value of y to find x and z:

$11x = 5y\\11x = 5(1)\\x = 5/11$

And from equation (2):

$x - z = 2/11\\5/11 - z = 2/11\\z = 3/11$

Therefore, the two like fractions are 5/11 and 3/11, and their sum is 8/11, and their difference is 2/11.

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