Question

adding and subtracting mixed numbers
subtracting mixed fractions with unlike denominators may seem impossible, but if you follow these three simple steps, you will be a pro!
-first, convert your mixed fraction to an improper fraction.
-next, find a common denominator and add or subtract the fractions.
-last, convert the answer back to a mixed fraction.
quick reminder: an improper fraction has a numerator that is greater than or equal to the denominator.
example: ( 3\frac{1}{4} + 2\frac{1}{2} = ? )

1. convert to an improper fraction: ( 3\frac{1}{4} = \frac{13}{4} ), ( 2\frac{1}{2} = \frac{5}{2} )
2. find a common denominator: ( \frac{13}{4} ), ( \frac{10}{4} )
3. now, add them: ( \frac{13}{4} + \frac{10}{4} = \frac{23}{4} )
4. convert back to a mixed fraction: ( 5\frac{3}{4} )

for each problem below, follow the steps used in the example to find your solution. be sure to show all your work in the space provided.

1. ( 3\frac{5}{8} + 1\frac{3}{4} = ? )
2. ( 6\frac{5}{6} - 3\frac{1}{4} = ? )
3. ( 4\frac{1}{3} + 3\frac{2}{5} = ? )
4. ( 7\frac{7}{8} - 6\frac{1}{4} = ? )
5. ( 3\frac{2}{3} + 2\frac{5}{7} = ? )
6. ( 5\frac{4}{5} - 3\frac{1}{3} = ? )
7. ( 4\frac{1}{4} + 1\frac{1}{3} = ? )
8. ( 11\frac{5}{6} - 5\frac{1}{2} = ? )

Explanation:

Problem 1: \( 3\frac{5}{8} + 1\frac{3}{4} \)

Step 1: Convert to improper fractions

\( 3\frac{5}{8} = \frac{3\times8 + 5}{8} = \frac{29}{8} \)
\( 1\frac{3}{4} = \frac{1\times4 + 3}{4} = \frac{7}{4} \)

Step 2: Find a common denominator

The common denominator of 8 and 4 is 8. So, \( \frac{7}{4} = \frac{7\times2}{4\times2} = \frac{14}{8} \)

Step 3: Add the fractions

\( \frac{29}{8} + \frac{14}{8} = \frac{29 + 14}{8} = \frac{43}{8} \)

Step 4: Convert back to a mixed number

\( \frac{43}{8} = 5\frac{3}{8} \)

Step 1: Convert to improper fractions

\( 6\frac{5}{6} = \frac{6\times6 + 5}{6} = \frac{41}{6} \)
\( 3\frac{1}{4} = \frac{3\times4 + 1}{4} = \frac{13}{4} \)

Step 2: Find a common denominator

The common denominator of 6 and 4 is 12. So, \( \frac{41}{6} = \frac{41\times2}{6\times2} = \frac{82}{12} \) and \( \frac{13}{4} = \frac{13\times3}{4\times3} = \frac{39}{12} \)

Step 3: Subtract the fractions

\( \frac{82}{12} - \frac{39}{12} = \frac{82 - 39}{12} = \frac{43}{12} \)

Step 4: Convert back to a mixed number

\( \frac{43}{12} = 3\frac{7}{12} \)

Step 1: Convert to improper fractions

\( 4\frac{1}{3} = \frac{4\times3 + 1}{3} = \frac{13}{3} \)
\( 3\frac{2}{5} = \frac{3\times5 + 2}{5} = \frac{17}{5} \)

Step 2: Find a common denominator

The common denominator of 3 and 5 is 15. So, \( \frac{13}{3} = \frac{13\times5}{3\times5} = \frac{65}{15} \) and \( \frac{17}{5} = \frac{17\times3}{5\times3} = \frac{51}{15} \)

Step 3: Add the fractions

\( \frac{65}{15} + \frac{51}{15} = \frac{65 + 51}{15} = \frac{116}{15} \)

Step 4: Convert back to a mixed number

\( \frac{116}{15} = 7\frac{11}{15} \)

Answer:

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

Problem 2: \( 6\frac{5}{6} - 3\frac{1}{4} \)