# Ratio question

#### JeffM

##### Elite Member
Hi

I'm doing a maths reasoning practice question and I'm wondering why in the solution an eighth is translated as 1 1/8 instead of just 1/8. Please see enclosed.

Plus, can someone point me in the right direction where I can read up on this.

Many thanks

MView attachment 9234
If y is bigger than x by 1/8th of x, then

$$\displaystyle y = x + \dfrac{1}{8} * x \equiv \left (1 + \dfrac{1}{8} \right ) * x \equiv \dfrac{9x}{8}.$$

Just different ways to get the same arithmetic result. Really nothing to read up on.

#### Miles

##### New member
If y is bigger than x by 1/8th of x, then

$$\displaystyle y = x + \dfrac{1}{8} * x \equiv \left (1 + \dfrac{1}{8} \right ) * x \equiv \dfrac{9x}{8}.$$

Just different ways to get the same arithmetic result. Really nothing to read up on.
Thanks Jeff, but I need to practice more of these to get a better understanding, so what subject would this come under algebra?

#### Dr.Peterson

##### Elite Member
Thanks Jeff, but I need to practice more of these to get a better understanding, so what subject would this come under algebra?
This is the same concept as "percent increase". Reading about that may help.

Or, as Jeff showed, it just comes from applying algebra to the problem: "increase x by fraction m" means "add m times x to x itself" (start with x, and increase it by m times itself).

#### Miles

##### New member
This is the same concept as "percent increase". Reading about that may help.

Or, as Jeff showed, it just comes from applying algebra to the problem: "increase x by fraction m" means "add m times x to x itself" (start with x, and increase it by m times itself).
Ah! Now I get it. Thanks

#### stapel

##### Super Moderator
Staff member
Thanks Jeff, but I need to practice more of these to get a better understanding, so what subject would this come under algebra?
Fractions and percentages are usually pre-algebra, or before pre-algebra. 