Question

4/45 : (12/25-4/15)+5/16×4/15=

Answer 1

$\frac{4}{45} : (\frac{12}{25} - \frac{4}{15}) + \frac{5}{16} * \frac{4}{15} = \frac{89}{300} \\\\1) \frac{12}{25} - \frac{4}{15} = \frac{36}{75} - \frac{20}{75} = \frac{16}{75} \\\\2) \frac{4}{45} : \frac{16}{75} = \frac{4*75}{45*16}= \frac{1*5}{3*4} = \frac{5}{12} \\\\3) \frac{5}{16} * \frac{4}{15} = \frac{5*4}{16*15} = \frac{1*1}{4*3} = \frac{1}{12} \\\\4) \frac{16}{75} + \frac{1}{12} = \frac{64}{300} + \frac{25}{300}= \frac{89}{300}$

Answer 2

To solve this expression, we can break it down step by step and simplify as we go along:

1. Start with the subtraction inside the parentheses: (12/25 - 4/15).

First, find a common denominator for 25 and 15, which is 75. Then, rewrite the fractions with this common denominator:

(12/25 - 4/15) = (12/25 * 3/3 - 4/15 * 5/5) = (36/75 - 20/75).

Now, subtract the fractions:

(36/75 - 20/75) = 16/75.

2. Next, multiply 5/16 by 4/15:

(5/16) * (4/15) = (5 * 4) / (16 * 15) = 20/240 = 1/12.

3. Now, we have the simplified values:

(12/25 - 4/15) + (5/16 * 4/15) = (16/75) + (1/12).

4. To add these fractions together, we need a common denominator, which is 300. Rewrite both fractions with this denominator:

(16/75) = (16/75 * 4/4) = (64/300),

(1/12) = (1/12 * 25/25) = (25/300).

Now, we can add them:

(64/300) + (25/300) = (64 + 25) / 300 = 89/300.

So, 4/45 : (12/25 - 4/15) + (5/16 * 4/15) = 89/300.