Question

1) |- 4/9| + |5/6|2) | 4 ,8|*|-1,75|.​

Answer 1

Відповідь:

Покрокове пояснення:

1) $|-\frac{4}{9}| + |\frac{5}{6} |= \frac{4}{9} + \frac{5}{6}= \frac{23}{18} = 1\frac{5}{18}$

2) $| 4 ,8|*|-1,75|= 4,8*1,75= 8,4$

Answer 2

Let's calculate each expression step by step:

1. |-4/9| + |5/6|:

The absolute value of a fraction is calculated by taking the absolute value of the numerator and the absolute value of the denominator separately, and then dividing the numerator by the denominator.

|-4/9| = 4/9 |5/6| = 5/6

Now we can add them together:

4/9 + 5/6

To add these fractions, we need a common denominator. The least common multiple of 9 and 6 is 18, so let's rewrite the fractions with that denominator:

(4/9)(2/2) + (5/6)(3/3) (8/18) + (15/18)

Now we can add the numerators:

8/18 + 15/18 = (8 + 15)/18 = 23/18

So, the value of |-4/9| + |5/6| is 23/18.

2. |4, 8| * |-1, 75|:

The notation |a, b| represents the Euclidean norm or magnitude of a vector with components a and b. For a two-dimensional vector (a, b), the Euclidean norm is calculated as:

|a, b| = √(a^2 + b^2)

In this case, we have two vectors: (4, 8) and (-1, 75). Let's calculate their Euclidean norms separately:

For (4, 8): |4, 8| = √(4^2 + 8^2) = √(16 + 64) = √80

For (-1, 75): |-1, 75| = √((-1)^2 + 75^2) = √(1 + 5625) = √5626

So, the value of |4, 8| * |-1, 75| is √80 * √5626, which simplifies to √(80 * 5626).