I am a fraction equivalent to 45/60. If you were to multiply my denominator by my numerator the product would be 192. What fraction am I?

i am a fraction. the numerator is 6 less than denominator. if 1 subtracted from numerator and 1 added to denominator the denominator b

To find the fraction that is equivalent to 45/60 and has a numerator multiplied by the denominator resulting in a product of 192, we can follow these steps:

Step 1: Simplify the fraction 45/60
To simplify the fraction, we find the greatest common divisor (GCD) of the numerator and denominator, which is 15. So, we divide both the numerator and denominator by 15:
45 ÷ 15 = 3
60 ÷ 15 = 4

So, the simplified fraction is 3/4.

Step 2: Find the missing numerator
Since multiplying the denominator by the numerator results in a product of 192, we can write an equation as: 4 * x = 192.
To solve for x (the missing numerator), we divide both sides of the equation by 4:
x = 192 ÷ 4
x = 48

Therefore, the missing numerator is 48.

Step 3: Determine the fraction
Now that we know the numerator is 48 and the denominator is 4, we can conclude that the fraction is 48/4.

In summary, the fraction equivalent to 45/60 with a numerator multiplied by the denominator resulting in a product of 192 is 48/4.

To find the fraction equivalent to 45/60, we need to simplify it by finding the greatest common divisor (GCD) of the numerator and denominator.

Step 1: Find the GCD of 45 and 60.
The factors of 45 are 1, 3, 5, 9, 15, and 45.
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
The GCD of 45 and 60 is 15.

Step 2: Divide both the numerator and denominator of 45/60 by 15 to simplify the fraction:
45 ÷ 15 = 3
60 ÷ 15 = 4

Therefore, the simplified fraction equivalent to 45/60 is 3/4.

Now, let's check if this is the correct fraction by multiplying its numerator and denominator:

3 (numerator) × 4 (denominator) = 12.

Since the product of the numerator and denominator is not 192, the fraction 3/4 is not the correct answer.

To find the fraction that satisfies the given condition (numerator multiplied by denominator equals 192), we need to list all possible factors of 192 and see which pairs of numbers multiply to give this product.

The factors of 192 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, and 192.

Let's check each factor to see if it satisfies the condition:

1 × 192 ≠ 192
2 × 96 ≠ 192
3 × 64 ≠ 192
4 × 48 ≠ 192
6 × 32 ≠ 192
8 × 24 ≠ 192
12 × 16 ≠ 192

None of the factors satisfy the given condition. Therefore, there is no fraction that fits the given criteria (numerator multiplied by denominator equals 192).

a/b is the fraction.

ab=192
a/b=45/60
a= 45b/60

45b/60 * b= 192
b^2=4*192/3=4*64=16^2
b=16