Question

3. Обчисліть значення виразу, спростивши запис: a) 7+ (-8) - (12) - (-7) + 13-20; B) -0,96+ (-5,37 + 1,03) - (6,03 -2,7). 4. Скільки цілих чисел розташовано на координатнiй прямій між числа ми -34 та 36. Обчисліть суму цих чисел найзручнішим способом. б) 6) 23-(-1;)+(-5)-(-3)-43;​

Answer 1

Ответ:

a) 7+(-8)-(12)-(-7)+13-20 = 7-8-12+7+13-20 = -13

b) -0.96+(-5.37+1.03)-(6.03-2.7) = -0.96-4.34+3.33-3.33 = -5.3

Для визначення кількості цілих чисел між -34 та 36, потрібно відняти -34 від 36 і додати одиницю: 36-(-34)+1 = 71. Отже, на координатній прямій між числами -34 та 36 розташовано 71 цілих чисел.

Суму цих чисел можна обчислити, використовуючи формулу для суми арифметичної прогресії: S = (n/2) * (a1+an), де n - кількість чисел, а1 - перше число, аn - останнє число. У даному випадку n=71, а1=-33, аn=35, тому S = (71/2) * (-33+35) = 71.

23-(-1)+(-5)-(-3)-43 = 23+1-5+3-43 = -21

Answer 2

a) 7 + (-8) - (12) - (-7) + 13 - 20

First, let's simplify the expression inside the parentheses: 7 + (-8) - (12) - (-7) + 13 - 20 = 7 - 8 - 12 + 7 + 13 - 20

Next, combine the like terms: = (7 + 7) - 8 - 12 + 13 - 20 = 14 - 8 - 12 + 13 - 20

Now, perform the subtraction: = 6 - 12 + 13 - 20 = -6 + 13 - 20

Continue the subtraction: = 7 - 20 = -13

Therefore, the value of the expression is -13.

b) -0.96 + (-5.37 + 1.03) - (6.03 - 2.7)

First, simplify the expression inside the parentheses: -0.96 + (-5.37 + 1.03) - (6.03 - 2.7) = -0.96 + (-4.34) - (3.33)

Next, perform the addition and subtraction: = -0.96 - 4.34 - 3.33 = -5.30 - 3.33

Now, subtract: = -8.63

Therefore, the value of the expression is -8.63.

4. To find the number of integers between -34 and 36 on the number line, we can count them one by one. However, it would be more convenient to use the formula for the number of integers between two values.

The formula is: Number of integers = (largest integer - smallest integer) + 1

In this case, the largest integer is 36, and the smallest integer is -34. Number of integers = (36 - (-34)) + 1 = 70 + 1 = 71

So, there are 71 integers between -34 and 36.

To find the sum of these integers, we can use the formula for the sum of an arithmetic series: Sum = (Number of terms / 2) * (First term + Last term)

In this case, the first term is -34 and the last term is 36. Sum = (71 / 2) * (-34 + 36) = 35.5 * 2 = 71

Therefore, the sum of the integers between -34 and 36 is 71.

б) 6 * (23 - (-1)) + (-5) - (-3) - 43

First, simplify the expression inside the parentheses: 6 * (23 - (-1)) + (-5) - (-3) - 43 = 6 * (23 + 1) + (-5) - (-3) - 43 = 6 * 24 + (-5) - (-3) - 43

Next, perform the multiplication and subtraction: = 144 + (-5) - (-3) - 43 = 144 - 5 - (-3) - 43 = 144 - 5 + 3 - 43

Now, perform the addition and subtraction: = 142 - 43 = 99

Therefore, the value of the expression is 99.