Question

(5/6-2/3):8/9 ; 3/10:(2/5+3/15) ; 10:2/5-3/10; (1 1/2-3/8):3.

Answer 1

(5/6-2/3):8/9=1.                                                                                                         3/10:(2/5+3/15)=2.4                                                                                                    10:2/5-3/10=2.31                                                                                                      (1 1/2-3/8):3=0.7051




  

Answer 2

Let's solve each of these expressions step by step:

1. (5/6 - 2/3) : (8/9) To simplify this expression, we need to find a common denominator for the fractions involved. The least common multiple of 6 and 3 is 6. So, we rewrite the expression as follows: (5/6 - 4/6) : (8/9)

Now, we subtract the numerators and keep the common denominator: (1/6) : (8/9)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction: (1/6) * (9/8)

Multiplying the numerators and denominators, we get: 9/48

Simplifying the fraction, we divide both the numerator and denominator by their greatest common divisor, which is 3: 3/16

Therefore, (5/6 - 2/3) : (8/9) simplifies to 3/16.

2. 3/10 : (2/5 + 3/15) First, we need to find a common denominator for the fractions involved. The least common multiple of 10 and 15 is 30. So, we rewrite the expression as follows: 3/10 : (12/30 + 6/30)

Now, we add the fractions in the parentheses: 3/10 : 18/30

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction: (3/10) * (30/18)

Multiplying the numerators and denominators, we get: 90/180

Simplifying the fraction, we divide both the numerator and denominator by their greatest common divisor, which is 90: 1/2

Therefore, 3/10 : (2/5 + 3/15) simplifies to 1/2.

3. 10 : (2/5 - 3/10) First, we need to subtract the fractions in the parentheses: 10 : (4/10 - 3/10)

Simplifying the numerator, we get: 10 : 1/10

To divide by a fraction, we multiply the first number by the reciprocal of the fraction: 10 * (10/1)

Multiplying the numerators and denominators, we get: 100/1

Therefore, 10 : (2/5 - 3/10) simplifies to 100.

4. (1 1/2 - 3/8) : 3 First, we need to convert the mixed number to an improper fraction: (3/2 - 3/8) : 3

To subtract the fractions, we need to find a common denominator. The least common multiple of 2 and 8 is 8. So, we rewrite the expression as follows: (12/8 - 3/8) : 3

Now, we subtract the numerators and keep the common denominator: 9/8 : 3

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction: (9/8) * (1/3)

Multiplying the numerators and denominators, we get: 9/24

Simplifying the fraction, we divide both the numerator and denominator by their greatest common divisor, which is 3: 3/8

Therefore, (1 1/2 - 3/8) : 3 simplifies to 3/8.