Question

2целых2/3÷2+(4/15+2/5)÷(3целых1/3×3/5); 2÷1/4+((1целая1/2+2целых2/3)÷3целых3/4-2/3)÷8целых8/9

Answer 1

А) 2 2/3 : 2 + (4/15 + 2/5) : (3 1/3 * 3/5) = 8/3 * 1/2 + (4+6)/15 : (10/3 * 3/5) = 4/3 + 10/15 : 2 = 4/3 + 10/15 * 1/2 = 4/3 + 5/15 = (20+5)/15 = 25/15 = 1 10/15 = 1 2/3
б) 2 : 1/4 + ((1 1/2 + 2 2/3) : 3 3/4 - 2/3) : 8 8/9 = 2/1 * 4/1 + ((3/2 + 8/3) : 15/4) : 80/9 = 8 + ((9+16)/6 : 15/4) : 80/9 = 8 + (25/6 * 4/15) : 80/9 = 8 + (5/3*2/3) : 80/9 = 8 + 10/9 * 9/80 = 8 + 1/8 = 8 1/8

Answer 2

To solve these expressions, we need to use the order of operations, also known as PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Let's solve the first expression:

2целых2/3 ÷ 2 + (4/15 + 2/5) ÷ (3целых1/3 × 3/5)

= (2*3 + 2)/3 ÷ 2 + (4/15 + 6/15) ÷ (10/15)

= 8/3 ÷ 2 + 2/5 ÷ (2/3)

= 8/3 ÷ 2 + (2/5 × 3/2)

= 8/3 ÷ 2 + 3/5

= (8/3) ÷ (2/1) + (3/5)

= 8/3 * 1/2 + 3/5

= 4/3 + 3/5

= (20/15 + 9/15)

= 29/15

Therefore, the value of the first expression is 29/15.

Now let's solve the second expression:

2 ÷ 1/4 + ((1целая1/2 + 2целых2/3) ÷ 3целых3/4 - 2/3) ÷ 8целых8/9

= 2 ÷ (1/4) + ((3/2 + 8/3) ÷ (15/4) - 2/3) ÷ (89/98)

= 2 ÷ (1/4) + ((9/6 + 16/6) ÷ (15/4) - 2/3) ÷ (8/9)

= 2 ÷ (1/4) + (25/6 ÷ 15/4 - 2/3) ÷ (8/9)

= 2 ÷ (1/4) + (5/2 - 2/3) ÷ (8/9)

= 2 ÷ (1/4) + (15/6 - 4/6) ÷ (8/9)

= 2 ÷ (1/4) + 11/6 ÷ (8/9)

= 2 ÷ (1/4) + 11/6 × (9/8)

= 2 ÷ (1/4) + 33/48

= 2 ÷ (1/4) + (11/16 × 3/3)

= 2 ÷ (1/4) + 33/48

= 8 ÷ 1 + 11/16

= 8 + 11/16

= (128/16 + 11/16)

= 139/16

Therefore, the value of the second expression is 139/16.