How many gallons does a full tank hold?

If 24 gallons of water are poured into an empty tank, then 3/4 of the tank is filled. How many gallons does a full tank hold?

Let V be the full volume of tank.
3/4 of tank = 24 gallons
3/4 * V = 24
V = 24 * 4/3 = 32

The full tank will hold 32 gallons of water.

With how much money did she start?

A woman spent two-thirds of her money. She lost two-thirds of the remainder and then had $4 left. With how much money did she start?

Let M be the money the woman had with her initially.

The money she spent = \(\dfrac{2}{3}\) * M
Remaining = M -  \(\dfrac{2}{3}\) * M =  \(\dfrac{1}{3}\) * M
The money she lost =  \(\dfrac{2}{3}\) * ( \(\dfrac{1}{3}\) * M ) = \(\dfrac{2}{9}\) * M
Remaining = \(\dfrac{1}{3}\) * M - \(\dfrac{2}{9}\) * M= \(\dfrac{1}{9}\) * M

=> \(\dfrac{1}{9}\) * M = 4
=> M = 9 * 4 = 36

She had $36 at the start. 

Simple fraction in lowest terms

Express the extended fraction at the right as a simple fraction in lowest terms.\(\dfrac{1}{2+\dfrac{1}{2+\dfrac{1}{2+\dfrac{1}{2}}}}\)

Start working from inside.

\(\dfrac{1}{2+\dfrac{1}{2+\dfrac{1}{2+\dfrac{1}{2}}}}\) = \(\dfrac{1}{2+\dfrac{1}{2+\dfrac{1}{\dfrac{5}{2}}}}\) = \(\dfrac{1}{2+\dfrac{1}{2+\dfrac{2}{5}}}\) = \(\dfrac{1}{2+\dfrac{1}{\dfrac{12}{5}}}\) = \(\dfrac{1}{2+\dfrac{5}{12}}\) = \(\dfrac{1}{\dfrac{29}{12}}\) = \(\dfrac{12}{29}\)

Find the values of A and B in the sum of fractions

If  \(\dfrac{1}{3}\) = \(\dfrac{1}{A}\) + \(\dfrac{1}{B}\) where A and B are different whole numbers.Find the values of A and B.


MetroEye: As per Fractions01

\(\dfrac{1}{3}\) = \(\dfrac{1}{3+1}\) + \(\dfrac{1}{3*(3+1)}\)

\(\dfrac{1}{3}\) = \(\dfrac{1}{4}\) + \(\dfrac{1}{12}\)  

So A = 4 and B=12

Simple fraction in lowest terms?

Express the following sum as a simple fraction in lowest terms.

MetroEye:   The given fractions can be represented as below:




So the sum becomes



The sum in the simplest fraction is 5/6.