Question

the sum of two numbers equals 5 1/2. If one of the numbers is 6 3/14, what is the other number? ( simplify if you can )

Answer 1

-5/7

Explanation:

A sum implies addition.

5 1/2 = A + 6 3/14

we need to put these as mixed numbers:

5 1/2= 11/2 6 3/14= 87/14

so then we have 5 1/2 = A + 87/14

If we multiply 2*7 then we put both fractions into equal terms:

11/2 * 7/7 = 77/14 (remember 7/7 is equal to one so your not actually changing anything)

then we have 77/14= A + 87/14

The we must isolate A by subtracting 87/14 from both sides -10/14 = A, which can be simplified to -5/7

(I'm calling the unknown number A)

Answer 2

`\sf - (5)/(7)`

Explanation:

Let the other number be x. We know that the sum of the two numbers is
`\sf 5 (1)/(2)`, so we can write the following equation:

`\sf x + 6 (3)/(14) = 5 (1)/(2)`

To simplify the equation, we can convert all of the numbers to fractions:

`\sf x + (14\cdot 6 + 3)/(14) = (2\cdot 5 + 1)/(2)`

`\sf x + (87)/(14) = (11)/(2)`

Subtracting
`\sf (87)/(14)` from both sides, we get:

`\sf x + (87)/(14) - (87)/(14) = (11)/(2)- (87)/(14)`

`\sf x = (11)/(2)- (87)/(14)`

`\sf x = (11 \cdot 7 - 87)/(14)`

`\sf x = (77 - 87)/(14)`

`\sf x = - (10)/(14)`

`\sf x =- \frac{\cancel{2}\cdot 5}{\cancel{2}\cdot 7 }`

`\sf x = - (5)/(7)`

Therefore, the other number is:

`\sf - (5)/(7)`