Describe how you would help your learner to add the following mixed fractions: a) 8 2/3 + 1 5/6 b) 5 2/5 + 9 3/7 c) 3 7/10 + 6 4/5

a)

Step 1: Convert the mixed number to an improper fraction.

$1 \frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{5}{3}$

Step 2: Add the fractions.

$\frac{5}{3} + \frac{5}{2}$

Step 3: Find the least common denominator (LCD), which is 6.

$\frac{5}{3} = \frac{5 \times 2}{3 \times 2} = \frac{10}{6}$

$\frac{5}{2} = \frac{5 \times 3}{2 \times 3} = \frac{15}{6}$

Step 4: Add the numerators.

$\frac{10 + 15}{6} = \frac{25}{6}$

Step 5: Convert to a mixed number.

$\frac{25}{6} = 4 \frac{1}{6}$

Final answer: $4 \frac{1}{6}$
4 \frac{1{6}}

b)

Step 1: Convert the mixed number to an improper fraction.

$6 \frac{3}{5} = \frac{6 \times 5 + 3}{5} = \frac{33}{5}$

Step 2: Add the fractions.

$\frac{33}{5} + \frac{9}{8}$

Step 3: Find the least common denominator (LCD), which is 40.

$\frac{33}{5} = \frac{33 \times 8}{5 \times 8} = \frac{264}{40}$

$\frac{9}{8} = \frac{9 \times 5}{8 \times 5} = \frac{45}{40}$

Step 4: Add the numerators.

$\frac{264 + 45}{40} = \frac{309}{40}$

Step 5: Convert to a mixed number.

$\frac{309}{40} = 7 \frac{29}{40}$

Final answer: $7 \frac{29}{40}$
7 \frac{29{40}}

c)

Step 1: Convert the mixed numbers to improper fractions.

$3 \frac{7}{10} = \frac{3 \times 10 + 7}{10} = \frac{37}{10}$

$6 \frac{5}{4} = \frac{6 \times 4 + 5}{4} = \frac{29}{4}$

Step 2: Add the fractions.

$\frac{37}{10} + \frac{29}{4}$

Step 3: Find the least common denominator (LCD), which is 20.

$\frac{37}{10} = \frac{37 \times 2}{10 \times 2} = \frac{74}{20}$

$\frac{29}{4} = \frac{29 \times 5}{4 \times 5} = \frac{145}{20}$

Step 4: Add the numerators.

$\frac{74 + 145}{20} = \frac{219}{20}$

Step 5: Convert to a mixed number.

$\frac{219}{20} = 10 \frac{19}{20}$

Final answer: $10 \frac{19}{20}$
10 \frac{19{20}}