Question

learning goal 1.2:
students will
solve real - world
problems
involving adding
and subtracting
fractions.

1. $6\frac{1}{8}-2\frac{3}{5}=$
2. $4\frac{1}{4}+6\frac{7}{10}=$
3. $2\frac{1}{9}-\frac{4}{7}=$

Explanation:

Problem 8: \( 6\frac{1}{8} - 2\frac{3}{5} \)

Step 1: Convert mixed numbers to improper fractions

\( 6\frac{1}{8} = \frac{6 \times 8 + 1}{8} = \frac{49}{8} \)
\( 2\frac{3}{5} = \frac{2 \times 5 + 3}{5} = \frac{13}{5} \)

Step 2: Find a common denominator

The least common denominator of 8 and 5 is 40.
\( \frac{49}{8} = \frac{49 \times 5}{8 \times 5} = \frac{245}{40} \)
\( \frac{13}{5} = \frac{13 \times 8}{5 \times 8} = \frac{104}{40} \)

Step 3: Subtract the fractions

\( \frac{245}{40} - \frac{104}{40} = \frac{245 - 104}{40} = \frac{141}{40} \)

Step 4: Convert back to a mixed number

\( \frac{141}{40} = 3\frac{21}{40} \)

Step 1: Convert mixed numbers to improper fractions

\( 4\frac{1}{4} = \frac{4 \times 4 + 1}{4} = \frac{17}{4} \)
\( 6\frac{7}{10} = \frac{6 \times 10 + 7}{10} = \frac{67}{10} \)

Step 2: Find a common denominator

The least common denominator of 4 and 10 is 20.
\( \frac{17}{4} = \frac{17 \times 5}{4 \times 5} = \frac{85}{20} \)
\( \frac{67}{10} = \frac{67 \times 2}{10 \times 2} = \frac{134}{20} \)

Step 3: Add the fractions

\( \frac{85}{20} + \frac{134}{20} = \frac{85 + 134}{20} = \frac{219}{20} \)

Step 4: Convert back to a mixed number

\( \frac{219}{20} = 10\frac{19}{20} \)

Step 1: Convert the mixed number to an improper fraction

\( 2\frac{1}{9} = \frac{2 \times 9 + 1}{9} = \frac{19}{9} \)

Step 2: Find a common denominator

The least common denominator of 9 and 7 is 63.
\( \frac{19}{9} = \frac{19 \times 7}{9 \times 7} = \frac{133}{63} \)
\( \frac{4}{7} = \frac{4 \times 9}{7 \times 9} = \frac{36}{63} \)

Step 3: Subtract the fractions

\( \frac{133}{63} - \frac{36}{63} = \frac{133 - 36}{63} = \frac{97}{63} \)

Step 4: Convert back to a mixed number

\( \frac{97}{63} = 1\frac{34}{63} \)

Answer:

\( 3\frac{21}{40} \)

Problem 9: \( 4\frac{1}{4} + 6\frac{7}{10} \)