Question

5 arturos backpack weighs $6\frac{3}{8}$ pounds. he removes a book that weighs $\frac{3}{4}$ pound. then he removes a book that weighs $\frac{1}{2}$ pound. how much does arturos backpack weigh now? show your work.

Explanation:

Step 1: Convert the mixed number to an improper fraction

The initial weight of the backpack is \( 6\frac{3}{8} \) pounds. To convert this mixed number to an improper fraction, we use the formula \( a\frac{b}{c}=\frac{a\times c + b}{c} \). So, \( 6\frac{3}{8}=\frac{6\times8 + 3}{8}=\frac{48 + 3}{8}=\frac{51}{8} \) pounds.

Step 2: Convert the weight of the book to eighths

The weight of the book is \( \frac{1}{2} \) pound. To subtract this from the backpack's weight, we need a common denominator. The denominator of the backpack's weight fraction is 8, so we convert \( \frac{1}{2} \) to eighths. We multiply the numerator and denominator by 4: \( \frac{1}{2}=\frac{1\times4}{2\times4}=\frac{4}{8} \) pounds.

Step 3: Subtract the weight of the book from the backpack's weight

Now we subtract the weight of the book from the initial weight of the backpack: \( \frac{51}{8}-\frac{4}{8}=\frac{51 - 4}{8}=\frac{47}{8} \) pounds.

Step 4: Convert the improper fraction back to a mixed number

To convert \( \frac{47}{8} \) back to a mixed number, we divide 47 by 8. 8 times 5 is 40, so the quotient is 5 and the remainder is \( 47-40 = 7 \). So, \( \frac{47}{8}=5\frac{7}{8} \) pounds.

Answer:

\( 5\frac{7}{8} \) pounds