Question

3 3/7 + 2 1/5 + 5 4/7 : 5/6

Answer 1

$3 \frac{3}{7} + 2 \frac{1}{5} + 5 \frac{4}{7} \div \frac{5}{6} = 3 \frac{3}{7} + 2 \frac{1}{5} + 6 \frac{24}{35 } = 5 \frac{22}{35} + 6 \frac{24}{35} = 12 \frac{11}{35}$

(1)

$5 \frac{4}{7} \div \frac{5}{6} = \frac{5 \times 7 + 4}{7} \div \frac{5}{6} = \frac{39}{7} \times \frac{6}{5} = \frac{234}{35} = 6 \frac{24}{35}$

(2)

$3 \frac{3}{7} + 2 \frac{1}{5} = \frac{3 \times 7 + 3}{7} + \frac{2 \times 5 + 1}{5} = \frac{24}{7} + \frac{11}{5} = \frac{120 + 77}{35} = 5 \frac{22}{35}$

(3)

$5 \frac{22}{35} + 6 \frac{24}{35} = 11 \frac{22}{35} + \frac{24}{35} = 11 \frac{46}{35} = 12 \frac{11}{35}$

Answer 2

To solve the expression, we'll first convert all mixed numbers to improper fractions and then perform the calculations. Here's the step-by-step solution:

Step 1: Convert mixed numbers to improper fractions 3 3/7 can be written as (7 * 3 + 3) / 7 = 24/7 2 1/5 can be written as (5 * 2 + 1) / 5 = 11/5 5 4/7 can be written as (7 * 5 + 4) / 7 = 39/7

Step 2: Perform the addition operation (24/7) + (11/5) + (39/7)

Step 3: Find a common denominator for the fractions The least common multiple of 7 and 5 is 35.

Step 4: Convert all fractions to the common denominator (24/7) can be converted to (24/7) * (5/5) = 120/35 (11/5) can be converted to (11/5) * (7/7) = 77/35 (39/7) can be converted to (39/7) * (5/5) = 195/35

Step 5: Perform the addition operation (120/35) + (77/35) + (195/35) = (120 + 77 + 195) / 35 = 392/35

Step 6: Divide the result by 5/6 To divide by a fraction, we multiply by its reciprocal (invert it): (392/35) ÷ (5/6) = (392/35) * (6/5)

Step 7: Simplify the result (392/35) * (6/5) = (392 * 6) / (35 * 5) = 2352/175 = 1344/100

Step 8: Simplify the fraction further, if needed 1344/100 can be simplified to 672/50, which can also be written as 13 22/50.

So, the final result of the expression 3 3/7 + 2 1/5 + 5 4/7 ÷ 5/6 is 13 22/50.