# Jon is making hamburgers for lunch. He has 422/3 lbs of ground beef. How many 1/3 pound hamburgers can he make using all the ground beef?

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6
Feb 12, 2017

We first convert the amount of ground beef into a non-mixed fraction.

#### Explanation:

$42 \frac{2}{3} = 42 \times \frac{3}{3} + \frac{2}{3} = \frac{126}{3} + \frac{2}{3} = \frac{128}{3} = 128 \times \frac{1}{3}$

So he can make $128$ hamburgers of $\frac{1}{3}$ pound each.

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Feb 12, 2017

$128$ hamburgers

#### Explanation:

The first decision is which operation is going to be done.

Students are often easily alarmed and confused when fractions appear in a question.

Consider the question "Tom has $450$ marbles and decides to sell them in bags of $10$. How many bags can he make to sell?"

Each bag will have $10$ marbles.
This will be solved by dividing: $450 \div 40 = 45$ bags.

The question with the hamburgers in this case is exactly the same...

Each hamburger uses $\frac{1}{3}$ pound of beef.
How many can be made from $42 \frac{2}{3}$ pounds of beef?

It is again a division: $\text{ } \textcolor{red}{42 \frac{2}{3}} \textcolor{b l u e}{\div \frac{1}{3}}$

$\textcolor{red}{\frac{128}{3}} \textcolor{b l u e}{\div \frac{1}{3}} \text{ } \leftarrow$ change to an improper fraction

$= \frac{128}{3} \textcolor{b l u e}{\times \frac{3}{1}} \text{ } \leftarrow$ multiply by the reciprocal

$= \frac{128}{\cancel{3}} \times \frac{\cancel{3}}{1} \text{ } \leftarrow$ simplify

$= 128$ hamburgers

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Feb 11, 2017

$128$

#### Explanation:

$\frac{42 \frac{2}{3}}{\frac{1}{3}}$

$\therefore = 42 \frac{2}{3} \div \frac{1}{3}$

$\therefore = 42 \frac{2}{3} \times \frac{3}{1}$

$\therefore = \frac{128}{\cancel{3}} ^ 1 \times {\cancel{3}}^{1} / 1$

$\therefore = 128 \times \frac{1}{3}$ pound hamburgers

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