Question

(42 5/7 - 4 2/5) - (23 - 15 9/14)

Answer 1

(42 5/7 - 4 2/5) - (23 - 15 9/14) = 30 67/70

1) 42 5/7 - 4 2/5 = 42 25/35 - 4 14/35 = 38 11/35

2) 23 - 15 9/14 = 22 14/14 - 15 9/14 = 7 5/14

3) 38 11/35 - 7 5/14 = 38 22/70 - 7 25/70 = 37 92/70 - 7 25/70 = 30 67/70

Ответ: 30 целых 67/70.

Answer 2

To simplify the expression (42 5/7 - 4 2/5) - (23 - 15 9/14), let's start by converting the mixed numbers into improper fractions:

42 5/7 = (7 * 42 + 5)/7 = 295/7 4 2/5 = (5 * 4 + 2)/5 = 22/5 15 9/14 = (14 * 15 + 9)/14 = 219/14

Now we can substitute these values back into the expression:

(295/7 - 22/5) - (23 - 219/14)

To simplify further, we need to find a common denominator for the fractions involved:

Common denominator for 7 and 5 is 7 * 5 = 35 Common denominator for 14 and 35 is 14 * 35 = 490

Now we can rewrite the expression with the common denominators:

((295/7) * (5/5) - (22/5) * (7/7)) - ((23 * 14/14) - (219/14 * 35/35))

Simplifying the expression inside the parentheses:

(1475/35 - 154/35) - (322/14 - 7665/490)

Combining like terms within each parentheses:

(1321/35) - (23 - 1573/490)

Subtracting the remaining values:

1321/35 - 23 + 1573/490

To combine the fractions, we need to find a common denominator for 35 and 490, which is 35 * 490 = 17,150.

Now we can rewrite the expression with the common denominator:

(1321/35) * (490/490) - (23 * 490/490) + (1573/490)

Simplifying further:

(647,690/17,150) - (11,270/17,150) + (1573/490)

Combining like terms:

(647,690 - 11,270 + 1573) / 17,150

Calculating the numerator:

(635,993) / 17,150

Now we can simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD), which is 7:

635,993 ÷ 7 / 17,150 ÷ 7

91,141 / 2,450

Therefore, the final simplified expression is 91,141/2,450.