Question

If the quotient of a number and 8 is added to 1/4 the result is 7/8. Find the number.

Answer 1

5

Explanation:

Let n be the unknown number.

The quotient is the result obtained by dividing one number by another.

Therefore, the quotient of a number and 8 is ⁿ/₈.

If the quotient of a number and 8 is added to 1/4 the result is 7/8:

`\implies (n)/(8)+(1)/(4)=(7)/(8)`

To solve, make the denominators of all the fractions the same:

`\implies (n)/(8)+(1 \cdot 2)/(4 \cdot 2)=(7)/(8)`

`\implies (n)/(8)+(2)/(8)=(7)/(8)`

`\textsf{Apply the fraction rule} \quad (a)/(c)+(b)/(c)=(a+b)/(c):`

`\implies (n+2)/(8)=(7)/(8)`

Multiply both sides by 8:

`\implies (8(n+2))/(8)=(7 \cdot 8)/(8)`

`\implies n+2=7`

Subtract 2 from both sides:

`\implies n+2-2=7-2`

`\implies n=5`

Therefore, the number is 5.