Question

2) (5/12-x) : 1/2 = 2/94) 4/15 - (y+3/25) = 1/256) 3 1/16 : (x-5/16) = 7/8​

Answer 1

Решение во вложении

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Answer 2

Let's solve each equation step by step:

1. (5/12 - x) : (1/2) = 2/9

To simplify the equation, we need to find the reciprocal of (1/2), which is 2. So the equation becomes:

(5/12 - x) * 2 = 2/9

Now, let's distribute the 2 to both terms inside the parentheses:

(10/12 - 2x) = 2/9

Next, we can simplify the fractions:

(5/6 - 2x) = 2/9

To eliminate the fractions, we can multiply both sides of the equation by the least common denominator (LCD) of 6 and 9, which is 18:

18 * (5/6 - 2x) = 18 * (2/9)

After simplifying, we have:

15 - 36x = 4

Now, let's isolate the term with x by subtracting 15 from both sides:

-36x = 4 - 15

-36x = -11

Finally, divide both sides by -36 to solve for x:

x = (-11) / (-36)

Simplifying the fraction gives:

x = 11/36

So the solution to the equation is x = 11/36.

2. 4/15 - (y + 3/25) = 1/25

Let's simplify the equation by removing the parentheses:

4/15 - y - 3/25 = 1/25

To combine the fractions, we need to find a common denominator, which is 75 in this case:

(4/15) - (3/25) - y = 1/25

Multiplying each fraction by the necessary factors, we get:

(4/15)(5/5) - (3/25)(3/3) - y = 1/25

(20/75) - (9/75) - y = 1/25

Now, let's combine the fractions:

(20 - 9) / 75 - y = 1/25

11/75 - y = 1/25

To get rid of the fraction, we can multiply both sides by the least common denominator (LCD) of 75 and 25, which is 1875:

1875 * (11/75 - y) = 1875 * (1/25)

After simplifying, we have:

11 * 25 - 1875y = 75

275 - 1875y = 75

Next, let's isolate the term with y by subtracting 275 from both sides:

-1875y = 75 - 275

-1875y = -200

Finally, divide both sides by -1875 to solve for y:

y = (-200) / (-1875)

Simplifying the fraction gives:

y = 8/75

So the solution to the equation is y = 8/75.

3. (3 1/16) : (x - 5/16) = 7/8

First, let's convert the mixed number into an improper fraction:

3 1/16 = (3 * 16 + 1) / 16 = 49/16

Now, let's substitute the values into the equation:

(49/16) : (x - 5/16) = 7/8

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

(49/16) * (16 / (x - 5/16)) = 7/8

The 16 in the numerator and denominator cancels out:

49 / (x - 5/16) = 7/8

Next, we cross-multiply:

49 * 8 = 7 * (x - 5/16)

392 = 7x - 35/16

Now, let's convert the mixed number (-35/16) into an improper fraction:

-35/16 = (-2 * 16 + 1) / 16 = -33/16

Substituting this into the equation, we have:

392 = 7x - 33/16

To eliminate the fraction, let's multiply both sides of the equation by the least common denominator (LCD) of 16:

16 * 392 = 16 * (7x - 33/16)

6272 = 112x - 33

Now, let's isolate the term with x by adding 33 to both sides:

6272 + 33 = 112x

6305 = 112x

Finally, divide both sides by 112 to solve for x:

x = 6305 / 112

Simplifying the fraction gives:

x = 5635/112

So the solution to the equation is x = 5635/112.