Question

A carpenter has a board that is 2/3 yard wide. He cuts the board into 5 pieces. If all the pieces are the same width, how wide is each piece?

Answer 1

Answer:

$\huge\boxed{\frac{2}{15} \text{ yards}}$

Step-by-step explanation:

We have a board that is $\frac{2}{3}$ yards long. If we want to cut the board into 5 equal pieces, we must divide $\frac{2}{3}$  by 5.

$\frac{2}{3} \div 5$

5 is the same thing as $\frac{5}{1}$, so:

$\frac{2}{3} \div \frac{5}{1}$

To divide a fraction by a fraction, we multiply by the reciprocal. This means we take the reciprocal of $\frac{5}{1}$ and multiply the two fractions.

The reciprocal of $\frac{5}{1}$  is $\frac{1}{5}$ - we swap the numerator and denominator.

$\frac{2}{3} \cdot \frac{1}{5}$

Multiply the numerator and denominators to get our final fraction:

$2\cdot 1 = 2\\3 \cdot 5 = 15\\\\\frac{2}{15}$

Hope this helped!