simplify the following fractions by rewriting them in factored form and finding all the "ones" you can....plis help..
42/60, 16/80, 51/17, 7/33...
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42/60 = 21/30 = 7/10
16/80 = 8/40 = 4/20 = 2/10 = 1/5
51/17 = 3
7/33 cannot be reduced.
To simplify these fractions by rewriting them in factored form and finding all the "ones," you can follow these steps:
1. The first fraction is 42/60. To factorize the numerator and the denominator, you need to find their prime factors.
Start with the numerator, 42:
- Divide 42 by the first prime number, 2, to get 42/2 = 21.
- Divide 21 by 3, a prime number, to get 21/3 = 7.
So the prime factorization of 42 is 2 * 3 * 7 = 2^1 * 3^1 * 7^1.
Now find the prime factorization of the denominator, 60:
- Divide 60 by 2 to get 60/2 = 30.
- Divide 30 by 2 again to get 30/2 = 15.
- Divide 15 by 3, a prime number, to get 15/3 = 5.
So the prime factorization of 60 is 2^2 * 3^1 * 5^1.
Next, look for the common factors between the numerator and denominator and cancel them out to simplify the fraction:
42/60 = (2^1 * 3^1 * 7^1)/(2^2 * 3^1 * 5^1)
Here, you can cancel out the common factors of 2 and 3:
= (2^1 * 7^1)/(2^2 * 5^1)
= (2/2) * (7/5)
= 1 * 7/5
= 7/5
So the simplified fraction for 42/60 in factored form with all "ones" is 7/5.
2. The second fraction is 16/80. Let's factorize the numerator and denominator:
The prime factorization of 16 is 2^4.
The prime factorization of 80 is 2^4 * 5^1.
Now cancel out the common factor of 2:
16/80 = (2^4)/(2^4 * 5^1)
= (2^4)/(2^4 * 5)
= 1/5
So the simplified fraction for 16/80 in factored form with all "ones" is 1/5.
3. The third fraction is 51/17. Prime factorize both the numerator and the denominator:
The prime factors of 51 are 3 * 17.
The prime factorization of 17 is 17 itself.
There are no common factors to cancel here. So the simplified fraction for 51/17 in factored form with all "ones" remains as it is, i.e., 51/17.
4. The fourth fraction is 7/33. Prime factorize the numerator and the denominator:
The prime factorization of 7 is 7 itself.
The prime factors of 33 are 3 * 11.
Again, there are no common factors to cancel out in this case. So the simplified fraction for 7/33 in factored form with all "ones" remains 7/33.
To summarize:
42/60 = 7/5
16/80 = 1/5
51/17 = 51/17
7/33 = 7/33