The art teacher bought a box of special paper for the fifth grade classes to use. The table shows what fraction of a box of paper each class will need.

Question

Mr. Walker’s Class needs one-fourth of a box of paper, Ms. Smith’s Class needs one-fifth of a box of paper, and Mrs. Lawrence’s Class needs three-eighths of a box of paper.

How much paper will the classes need all together? Enter your answer as a fraction.

Answer 1

To find out how much paper the classes need together, we add the fractions corresponding to each class's needs:

• Mr. Walker’s Class: \(\frac{1}{4}\)
• Ms. Smith’s Class: \(\frac{1}{5}\)
• Mrs. Lawrence’s Class: \(\frac{3}{8}\)

First, we need to find a common denominator for the fractions. The denominators are 4, 5, and 8. The least common multiple (LCM) of these numbers will be our common denominator.

The multiples of each number are:

• Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, ...
• Multiples of 5: 5, 10, 15, 20, 25, 30, 35, ...
• Multiples of 8: 8, 16, 24, 32, ...

The LCM of 4, 5, and 8 is 40.

Next, we convert each fraction to have a denominator of 40:

1. For \(\frac{1}{4}\): \[ \frac{1}{4} = \frac{1 \times 10}{4 \times 10} = \frac{10}{40} \]

2. For \(\frac{1}{5}\): \[ \frac{1}{5} = \frac{1 \times 8}{5 \times 8} = \frac{8}{40} \]

3. For \(\frac{3}{8}\): \[ \frac{3}{8} = \frac{3 \times 5}{8 \times 5} = \frac{15}{40} \]

Now we can add all these fractions together:

\[ \frac{10}{40} + \frac{8}{40} + \frac{15}{40} = \frac{10 + 8 + 15}{40} = \frac{33}{40} \]

Thus, the total amount of paper needed for the classes all together is \(\frac{33}{40}\).