# A jug contains 2.45 liters of cranberry juice. A bottle contains 2 13/25 liters of grape juice. Which container holds less fruit juice? How much less?

Sep 11, 2017

The jug holds. 0.07 liters less

#### Explanation:

The jug contains 2.45 liters.

The bottle contains $2 \frac{13}{25}$ liters

convert $2 \frac{13}{25}$ into a single fraction 2 x 25 + 13 = $\frac{63}{25}$

$\frac{63}{25}$ of $1$ liter:

$\left(\frac{63}{25}\right) \cdot 1$

i.e $\frac{63}{25} = \textcolor{b l u e}{2.52}$ liters

Amount in bottle - amount in jug:

$2.52 - 2.45 = \textcolor{b l u e}{0.07}$

$\textcolor{b l u e}{0.07}$ liters less

Sep 11, 2017

The jug holds $0.07$ litres less than the bottle.

#### Explanation:

We can see that $0.45$ is less than $\frac{1}{2} \text{ } \left(0.45 < 0.50\right)$

while $\frac{13}{25}$ is slightly more than $\frac{1}{2} \text{ } \left(\frac{12 \frac{1}{2}}{25} < \frac{13}{25}\right)$.

Therefore the jug contains less juice, but by how much?

Numbers have to be in the same form to be accurately compared.

Convert the mixed number into a decimal by making the denominator $100$

$2 \frac{13}{25} = 2 \frac{13 \times 4}{25 \times 4} = 2 \frac{52}{100} = 2.52$

The measurements are both in litres, so now we can find the difference.

$2.52 - 2.45 = 0.07$ litres