Question

8/9:(3/4+1/2), (3/5-12/25):4/5, 4/15:(1 1/5-2/3)=

Answer 1

8/9:(3/4+1/2)= 8/9:(3/4+2/4)=8/9*4/5=

= 40/45*36/45=1440/45=32

(3/5-12/25):4/5=(15/25-12/25)*5/4=3/25*5/4= 3/20

4/15:(11/5-2/3)= 4/15:(33/15-10/15)= 4/15:23/15=4/15*15/23=4/23

Answer 2

$\frac{8}{9} \div (\frac{3}{4} + \frac{1}{2} ) = \\ \frac{3}{4} + \frac{1}{2} = \frac{3 + 2}{4} = \frac{6}{4} \\ \frac{8}{9} \div \frac{6}{4} = \frac{8}{9} \times \frac{4}{6} = \frac{32}{54}$

$( \frac{3}{5} - \frac{12}{25} ) \div \frac{4}{5} = \\ \frac{3}{5} - \frac{12}{25} = \frac{15 - 12}{25} = \frac{3}{25} \\ \frac{3}{25} \div \frac{4}{5} = \frac{3}{25} \times \frac{5}{4} = \frac{3 \times 25}{4} = \frac{75}{4} = 18 \times \frac{3}{4}$

$\frac{4}{15} \div (1 \times \frac{1}{5} - \frac{2}{3}) = \\ 1 \times \frac{1}{5} - \frac{2}{3} = \frac{6}{5} - \frac{2}{3} = \frac{18 - 10}{15} = \frac{8}{15} \\ \frac{4}{15} \div \frac{8}{15} = \frac{4}{15} \times \frac{15}{8} = 2$

Answer 3

To evaluate the given expressions, let's simplify each one:

1. 8/9 * (3/4 + 1/2):

To add the fractions inside the parentheses, we need a common denominator, which is 4. Rewriting the fractions:

(3/4 + 1/2) = (3/4 + 2/4) = 5/4

Now, we can multiply:

8/9 * 5/4 = (8 * 5) / (9 * 4) = 40/36

The fraction 40/36 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 4:

40/36 = (40 ÷ 4) / (36 ÷ 4) = 10/9

So, 8/9 * (3/4 + 1/2) simplifies to 10/9.

2. (3/5 - 12/25) : 4/5:

To subtract the fractions, we need a common denominator, which is 25. Rewriting the fractions:

(3/5 - 12/25) = (15/25 - 12/25) = 3/25

Now, we can divide:

(3/25) : (4/5) = (3/25) * (5/4) = (3 * 5) / (25 * 4) = 15/100

The fraction 15/100 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 5:

15/100 = (15 ÷ 5) / (100 ÷ 5) = 3/20

So, (3/5 - 12/25) : 4/5 simplifies to 3/20.

3. 4/15 : (1 1/5 - 2/3):

To subtract the mixed number (1 1/5) from the fraction (2/3), we need a common denominator, which is 15. Rewriting the mixed number:

1 1/5 = 6/5

Now, we can subtract:

(2/3 - 6/5) = (10/15 - 18/15) = -8/15

Now, we can divide:

4/15 : (-8/15) = 4/15 * (-15/8) = (4 * -15) / (15 * 8) = -60/120

The fraction -60/120 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 60:

-60/120 = (-60 ÷ 60) / (120 ÷ 60) = -1/2

So, 4/15 : (1 1/5 - 2/3) simplifies to -1/2.

To summarize:

1. 8/9 * (3/4 + 1/2) = 10/9
2. (3/5 - 12/25) : 4/5 = 3/20
3. 4/15 : (1 1/5 - 2/3) = -1/2