Problem:
4y divided by 3 plus 3 divided by 5 = 4 divided by 9?

Solution:

To determine whether the given equation is true or false, we need to evaluate both sides of the equation separately and compare the results.

Evaluating the left side:
The left side of the equation is: 4y/3 + 3/5

To add fractions, we need to have a common denominator. In this case, the common denominator is 15.

- The first fraction, 4y/3, can be multiplied by 5/5 to get a denominator of 15: (4y * 5)/(3 * 5) = (20y)/15.
- The second fraction, 3/5, can be multiplied by 3/3 to get a denominator of 15: (3 * 3)/(5 * 3) = 9/15.

Now that both fractions have the same denominator, we can add them together: (20y/15) + (9/15) = (20y + 9)/15.

Evaluating the right side:
The right side of the equation is: 4/9.

Both sides of the equation now have a common denominator of 15, so we can compare them directly.

Comparing both sides:

The left side of the equation is (20y + 9)/15, and the right side is 4/9.

To compare them, we can cross-multiply and check if the resulting equation is true:

(20y + 9) * 9 = 4 * 15

180y + 81 = 60

Subtracting 81 from both sides:

180y = -21

Dividing by 180:

y = -21/180

Simplifying the fraction:

y = -7/60

Conclusion:

After evaluating both sides of the equation, we find that the value of y is -7/60. Therefore, the given equation 4y/3 + 3/5 = 4/9 is false.

4y/3+3/5=4/9