Write the fraction in the simplest form.
12/56:
3/30:
5/25:
9/39:
6/54:
2/100:
8/18:
THANKS
write each number as a product of prime factors. Then cancel factors that appear in both the numerator and denominator.
12/56 = 2*2*3/2*2*2*7
Now cancel the 2*2 that appears in both top and bottom:
12/56 = 3/2*7 = 3/14
work the others the same way.
To write a fraction in the simplest form, you need to find the greatest common divisor (GCD) of the numerator and the denominator and then divide both the numerator and the denominator by the GCD.
Let's simplify the fractions you mentioned:
1) 12/56:
To find the GCD of 12 and 56, you can factorize each number:
12 = 2 * 2 * 3
56 = 2 * 2 * 2 * 7
The common factors are 2 and 2. So, the GCD is 2.
Dividing both numerator and denominator by the GCD (2), we get:
12/2 = 6
56/2 = 28
Therefore, the simplest form of 12/56 is 6/28.
2) 3/30:
To find the GCD of 3 and 30, we can factorize each number:
3 = 3
30 = 2 * 3 * 5
The common factor is 3. So, the GCD is 3.
Dividing both numerator and denominator by the GCD (3), we get:
3/3 = 1
30/3 = 10
Therefore, the simplest form of 3/30 is 1/10.
3) 5/25:
To find the GCD of 5 and 25, we can see that both numbers share the common factor 5. So, the GCD is 5.
Dividing both numerator and denominator by the GCD (5), we get:
5/5 = 1
25/5 = 5
Therefore, the simplest form of 5/25 is 1/5.
4) 9/39:
To find the GCD of 9 and 39, we can factorize each number:
9 = 3 * 3
39 = 3 * 13
The common factor is 3. So, the GCD is 3.
Dividing both numerator and denominator by the GCD (3), we get:
9/3 = 3
39/3 = 13
Therefore, the simplest form of 9/39 is 3/13.
5) 6/54:
To find the GCD of 6 and 54, we can factorize each number:
6 = 2 * 3
54 = 2 * 3 * 3 * 3
The common factors are 2 and 3. So, the GCD is 6.
Dividing both numerator and denominator by the GCD (6), we get:
6/6 = 1
54/6 = 9
Therefore, the simplest form of 6/54 is 1/9.
6) 2/100:
To find the GCD of 2 and 100, we can see that both numbers are divisible by 2. So, the GCD is 2.
Dividing both numerator and denominator by the GCD (2), we get:
2/2 = 1
100/2 = 50
Therefore, the simplest form of 2/100 is 1/50.
So, the simplified forms of the fractions are:
12/56 = 6/28
3/30 = 1/10
5/25 = 1/5
9/39 = 3/13
6/54 = 1/9
2/100 = 1/50.