Question

( 6 1/24 - 2/3) : ( 3 1/2 + 7/8)

Answer 1

Ответ:

$(6 \frac{1}{24} - \frac{2}{3} ) \div (3 \frac{1}{2} + \frac{7}{8} ) = 1 \frac{8}{35}$

Пошаговое объяснение:

$1) \: 6 \frac{1}{24} - \frac{2}{3} = 5 \frac{3}{8}$

$2) \: 3 \frac{1}{2} + \frac{7}{8} = 4 \frac{3}{8}$

$3) \: 5 \frac{3}{8} \div 4 \frac{3}{8} = 1 \frac{8}{35}$

Answer 2

To solve this expression, we'll first convert the mixed numbers into improper fractions and then perform the operations.

1. Convert mixed numbers to improper fractions:

   • 6 1/24 = (6 * 24 + 1) / 24 = 145/24
   • 3 1/2 = (3 * 2 + 1) / 2 = 7/2

2. Now, rewrite the expression: (145/24 - 2/3) / (7/2 + 7/8)

3. Perform the subtractions and additions: Numerator: (145/24 - 2/3) = [(145/24) * (8/8) - (16/24)] = (1160/192 - 16/24)

   Denominator: (7/2 + 7/8) = [(7/2) * (4/4) + (7/8) * (1/1)] = (28/8 + 7/8)

4. Continue simplifying: Numerator: (1160/192 - 16/24) = (1160/192 - 128/192) = (1032/192)

   Denominator: (28/8 + 7/8) = (35/8)

5. Now, divide the numerator by the denominator: (1032/192) / (35/8)

6. To divide fractions, multiply by the reciprocal of the second fraction: (1032/192) * (8/35)

7. Simplify the result: (1032/192) * (8/35) = (54/10) * (8/35)

8. Reduce the fraction: (54/10) * (8/35) = (27/5) * (8/35)

9. Multiply the numerators and denominators: (27 * 8) / (5 * 35) = 216 / 175

So, the final result is 216/175.