First of all, you can simplify the 4 at the numerator and the 14 at the denominator (they're both multiple of 2):
Now, rationalize a denominator means that you have to get rid of the square root, in order to have an integer denominator.
To do so, remember that you can always multiply any number by 1 without changing its value, and you can always think of 1 as a fraction where numerator and denominator are equal:
Answer:
Gina is 12 years old
Step-by-step explanation:
First, we will have to write these statements mathematically and then solve.
Let Gina's age be x, let Gina's brother's age be y and let Gina's sister's age be z.
The second statement"Gina's older sister is twice Gina's age" can be mathematically written as: z =2 x ---------------------------(1)
The next statement "Gina's brother is half Gina's age" can be mathematically written as y = ---------------------------------------(2)
Then the next statement "the sum of their ages is 42" can be mathematically written as: x + y + z = 42 ----------------------------(3)
We can now proceed to solve;
Substitute equation (1) and equation(2) into equation (3)
x + y + z = 42
x + + 2x = 42
Multiply through by 2
2x + x + 4x = 84
7x = 84
Divide both-side of the equation by 7
=
x = 12
Therefore, Gina is 12 years old