Question

4/5:3/10+1/9, 4/15+3/18:5/16, 1 1/2-1/6:4/21, 2 1/4:15/16-1/4

Answer 1

ответ см на фото.Я исправила последние 2 примера

Answer 2

To solve the given expressions, let's simplify each expression step by step:

1. 4/5 : 3/10 + 1/9

To add fractions, we need a common denominator. In this case, the least common multiple (LCM) of 10 and 9 is 90.

(4/5) : (3/10) + (1/9) = (4/5) : (27/90) + (10/90) = (4/5) : (27/90 + 10/90) = (4/5) : (37/90)

To divide fractions, we multiply by the reciprocal of the divisor:

= (4/5) * (90/37) = (4 * 90) / (5 * 37) = 360/185 = 72/37

Therefore, 4/5 : 3/10 + 1/9 = 72/37.

2. 4/15 + 3/18 : 5/16

First, let's simplify the division by multiplying the second fraction by its reciprocal:

4/15 + (3/18) * (16/5) = 4/15 + (3 * 16) / (18 * 5) = 4/15 + 48/90 = 4/15 + 8/15 = (4 + 8)/15 = 12/15 = 4/5

Therefore, 4/15 + 3/18 : 5/16 = 4/5.

3. 1 1/2 - 1/6 : 4/21

Let's first convert the mixed number into an improper fraction:

1 1/2 = (2 * 1 + 1)/2 = 3/2

Now, let's simplify the division by multiplying the second fraction by its reciprocal:

(3/2) - (1/6) * (21/4) = 3/2 - (1 * 21) / (6 * 4) = 3/2 - 21/24 = 3/2 - 7/8

To subtract fractions, we need a common denominator. In this case, the LCM of 2 and 8 is 8.

= (3/2 * 4/4) - (7/8 * 1/1) = 12/8 - 7/8 = (12 - 7)/8 = 5/8

Therefore, 1 1/2 - 1/6 : 4/21 = 5/8.

4. 2 1/4 : 15/16 - 1/4

Let's first convert the mixed number into an improper fraction:

2 1/4 = (4 * 2 + 1)/4 = 9/4

Now, let's simplify the division by multiplying the first fraction by the reciprocal of the second fraction:

(9/4) * (16/15) - 1/4 = (9 * 16) / (4 * 15) - 1/4 = 144/60 - 15/60 = (144 - 15)/60 = 129/60

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 3:

(129/3) / (60/3) = 43/20

Therefore, 2 1/4 : 15/16 - 1/4 = 43/20.