Question

word problems (show your work)

1. the rope was 4 7/8 feet long. after cutting off 1 1/4 feet, how much remains?
2. a container held 3 2/5 liters of water. 1 1/10 liters were used. how much is left?

criteria for success (cfs)
section 4: multiplying fractions / mixed numbers
rewrite mixed numbe

Explanation:

Problem 1: The rope was \( 4\frac{7}{8} \) feet long. After cutting off \( 1\frac{1}{4} \) feet, how much remains?

Step 1: Convert mixed numbers to improper fractions

Convert \( 4\frac{7}{8} \) to improper fraction: \( 4\frac{7}{8}=\frac{4\times8 + 7}{8}=\frac{39}{8} \)
Convert \( 1\frac{1}{4} \) to improper fraction: \( 1\frac{1}{4}=\frac{1\times4+1}{4}=\frac{5}{4} \)

Step 2: Find a common denominator

The common denominator of 8 and 4 is 8. Rewrite \( \frac{5}{4} \) with denominator 8: \( \frac{5}{4}=\frac{5\times2}{4\times2}=\frac{10}{8} \)

Step 3: Subtract the fractions

Subtract \( \frac{10}{8} \) from \( \frac{39}{8} \): \( \frac{39}{8}-\frac{10}{8}=\frac{39 - 10}{8}=\frac{29}{8} \)

Step 4: Convert back to mixed number

Convert \( \frac{29}{8} \) to mixed number: \( \frac{29}{8}=3\frac{5}{8} \)

Problem 2: A container held \( 3\frac{2}{5} \) liters of water. \( 1\frac{1}{10} \) liters were used. How much is left?

Step 1: Convert mixed numbers to improper fractions

Convert \( 3\frac{2}{5} \) to improper fraction: \( 3\frac{2}{5}=\frac{3\times5 + 2}{5}=\frac{17}{5} \)
Convert \( 1\frac{1}{10} \) to improper fraction: \( 1\frac{1}{10}=\frac{1\times10 + 1}{10}=\frac{11}{10} \)

Step 2: Find a common denominator

The common denominator of 5 and 10 is 10. Rewrite \( \frac{17}{5} \) with denominator 10: \( \frac{17}{5}=\frac{17\times2}{5\times2}=\frac{34}{10} \)

Step 3: Subtract the fractions

Subtract \( \frac{11}{10} \) from \( \frac{34}{10} \): \( \frac{34}{10}-\frac{11}{10}=\frac{34 - 11}{10}=\frac{23}{10} \)

Step 4: Convert back to mixed number

Convert \( \frac{23}{10} \) to mixed number: \( \frac{23}{10}=2\frac{3}{10} \)

Answer:

\( 3\frac{5}{8} \) feet