Question

1.(–2 1/6 – 3 1/4) : 2 3/5 + 2/3 ∙ 2 1/4 – 5 1/6 ; 2.(–1 1/10 – 7 : (3 1/12 – 1 5/8)) ∙ 1 1/59 .

Answer 1

Ответ:

Пошаговое объяснение:

1.(–2 1/6 – 3 1/4) : 2 3/5 + 2/3 ∙ 2 1/4 – 5 1/6 =-5 3/4

-2 1/6-3 1/4=-2 2/12-3 3/12=-5 5/12

-5 5/12:2 3/5=-65/12*5/13=-25/12=-2 1/12

2/3*2 1/4=2/3*9/4=3/2=1 1/2

-2 1/12+1 1/2=-2 1/12+1 6/12=-7/12

-7/12-5 1/6=-7/12-5 2/12=-5 3/4

2.(–1 1/10 – 7 : (3 1/12 – 1 5/8)) ∙ 1 1/59 =-6

3 1/12-1 5/8=3 2/24-1 15/24=1 11/24

7:1 11/24=7*24/35=24/5=4 4/5

-1 1/10-4 4/5=-1 1/10-4 8/10=-5 9/10

-5 9/10*1 1/59=-59/10*60/59=-6

Answer 2

To solve these mathematical expressions, let's take them one by one:

1. (–2 1/6 – 3 1/4) : 2 3/5 + 2/3 ∙ 2 1/4 – 5 1/6

Step 1: Convert all mixed numbers to improper fractions. (-2 1/6) = (-13/6) (3 1/4) = (13/4) (2 3/5) = (13/5) (2 1/4) = (9/4) (5 1/6) = (31/6)

Step 2: Perform the operations according to the order of operations (PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).

(-13/6 - 13/4) / (13/5) + (2/3) * (9/4) - 31/6

Step 3: Perform the operations inside the parentheses first.

((-13/6) - (13/4)) / (13/5) + (2/3) * (9/4) - 31/6 (-13/6 - 39/12) / (13/5) + (2/3) * (9/4) - 31/6 ((-13 - 39)/6) / (13/5) + (2/3) * (9/4) - 31/6 (-52/6) / (13/5) + (2/3) * (9/4) - 31/6

Step 4: Simplify the division.

(-26/3) / (13/5) + (2/3) * (9/4) - 31/6

Step 5: Divide by a fraction is the same as multiplying by its reciprocal.

(-26/3) * (5/13) + (2/3) * (9/4) - 31/6

Step 6: Simplify the multiplication.

(-130/39) + (6/4) - 31/6

Step 7: Convert the mixed number back to an improper fraction.

(-130/39) + (3/2) - 31/6

Step 8: Find a common denominator and perform addition.

To add fractions with different denominators, we need to find a common denominator. The least common multiple (LCM) of 39 and 6 is 78.

(-130/39) + (3/2) - (31/6) = (-130/39) + (3 * 39/78) - (31/6) = (-130/39) + (117/78) - (31/6)

Step 9: Continue with the addition.

(-130/39) + (117/78) - (31/6) = (-130/39) + (117/78) - (13 * 6/6) = (-130/39) + (117/78) - (13/1) = (-130/39) + (117/78) - 13

Step 10: Convert the whole numbers to fractions.

(-130/39) + (117/78) - 13 = (-130/39) + (117/78) - (13 * 78/78) = (-130/39) + (117/78) - (1014/78)

Step 11: Continue with the addition.

(-130/39) + (117/78) - (1014/78) = (-130/39) + (117/78) - (1014/78) = (-130/39) + (117/78) - (1014/78) = (-130/39) + (117/78) - (169/78)

Step 12: Continue with the addition.

(-130/39) + (117/78) - (169/78) = (-130/39) + (117/78) - (169/78) = (-130/39) + (117/78) - (169/78) = (-130/39) - (52/78)

Step 13: Continue with the subtraction.

(-130/39) - (52/78) = (-130/39) - (26/39)

Step 14: Combine the fractions.

(-130/39) - (26/39) = -156/39

Step 15: Simplify the fraction.

-156/39 = -4

So, the value of the expression is -4.

2. (–1 1/10 – 7 : (3 1/12 – 1 5/8)) ∙ 1 1/59

Step 1: Convert all mixed numbers to improper fractions. (-1 1/10) = (-11/10) (3 1/12) = (37/12) (1 5/8) = (13/8) (1 1/59) = (60/59)

Step 2: Perform the operations inside the parentheses first.

(-11/10) - 7 / (37/12 - 13/8)

Step 3: Simplify the subtraction inside the parentheses.

(-11/10) - 7 / (37/12 - 13/8) = (-11/10) - 7 / (37/12 - 13/8) = (-11/10) - 7 / (37/12 - 39/24) = (-11/10) - 7 / (37/12 - 39/24) = (-11/10) - 7 / (1/24)

Step 4: Invert and multiply to divide by a fraction.

(-11/10) - 7 / (1/24) = (-11/10) - 7 * (24/1)

Step 5: Simplify the multiplication.

(-11/10) - 7 * (24/1) = (-11/10) - (7 * 24) = (-11/10) - 168

Step 6: Convert the whole number to a fraction.

(-11/10) - 168 = (-11/10) - (168 * 10/10) = (-11/10) - 1680/10

Step 7: Continue with the subtraction.

(-11/10) - 1680/10 = (-11 - 1680)/10 = (-1691)/10

Step 8: Simplify the fraction.

(-1691)/10 = -169.1

So, the value of the expression is approximately -169.1.