Question
The total weight of 5 science textbooks is 6 2/3 pounds. How much does each book weigh? Your answer should be written as a mixed number.
Answers
Answered by
GPT-4o mini
To find the weight of each textbook, we begin by dividing the total weight of the textbooks by the number of textbooks.
The total weight of the 5 textbooks is \( 6 \frac{2}{3} \) pounds. First, we need to convert this mixed number into an improper fraction.
1. Convert \( 6 \frac{2}{3} \) into an improper fraction:
\[
6 \frac{2}{3} = \frac{6 \times 3 + 2}{3} = \frac{18 + 2}{3} = \frac{20}{3}
\]
2. Now, we will divide this fraction by the number of textbooks, which is 5:
\[
\text{Weight of each book} = \frac{20/3}{5}
\]
3. Dividing by a whole number is the same as multiplying by the reciprocal:
\[
\frac{20}{3} \div 5 = \frac{20}{3} \times \frac{1}{5} = \frac{20 \times 1}{3 \times 5} = \frac{20}{15}
\]
4. Now, we simplify \( \frac{20}{15} \):
\[
\frac{20}{15} = \frac{4}{3}
\]
5. Finally, we convert \( \frac{4}{3} \) back into a mixed number:
\[
\frac{4}{3} = 1 \frac{1}{3}
\]
Thus, the weight of each textbook is \( \boxed{1 \frac{1}{3}} \) pounds.
The total weight of the 5 textbooks is \( 6 \frac{2}{3} \) pounds. First, we need to convert this mixed number into an improper fraction.
1. Convert \( 6 \frac{2}{3} \) into an improper fraction:
\[
6 \frac{2}{3} = \frac{6 \times 3 + 2}{3} = \frac{18 + 2}{3} = \frac{20}{3}
\]
2. Now, we will divide this fraction by the number of textbooks, which is 5:
\[
\text{Weight of each book} = \frac{20/3}{5}
\]
3. Dividing by a whole number is the same as multiplying by the reciprocal:
\[
\frac{20}{3} \div 5 = \frac{20}{3} \times \frac{1}{5} = \frac{20 \times 1}{3 \times 5} = \frac{20}{15}
\]
4. Now, we simplify \( \frac{20}{15} \):
\[
\frac{20}{15} = \frac{4}{3}
\]
5. Finally, we convert \( \frac{4}{3} \) back into a mixed number:
\[
\frac{4}{3} = 1 \frac{1}{3}
\]
Thus, the weight of each textbook is \( \boxed{1 \frac{1}{3}} \) pounds.