Question

which of the following fractions is equivalent to the fraction 6/16?
A.) 4/14
B.) 1/10
C.) 3/8
D.) 2/8

Answer 1

So we want to simplify the fraction. It helps to write out the numerator and the denominator as products - like prime factorize them both. What are the prime factorizations of 6 and 16?

Answer 2

Do u know how to prime factorize?

Answer 3

for example:
The prime factors of 9 are 3 and 3

Answer 4

What are the prime factorization of 6 and 16?

Answer 5

c)

Answer 6

3/8

Answer 7

to simplify 6/16
you should write 6 as 2*3
notice 16 can be divide by 2: 2*8
but 8 can be divided by 2: 2*2*4, and so on
you get 16=2*2*2*2

the fraction
\[ \frac{6}{16}= \frac{2 \cdot 3}{ 2\cdot 2\cdot 2\cdot 2} \]
now look for the same number in the top and bottom. They "cancel out", which means they = 1, and 1 times anything does not change the answer
\[ \frac{6}{16}= \frac{\cancel{2} \cdot 3}{ \cancel{2}\cdot 2\cdot 2\cdot 2} \]
now multiply the bottom 2's to get the final answer.

Of course, in this case, we know 16 (or 8) is not divisible by 3 so we could have been smart an written the bottom as 2*8

btw, to do these problems you should learn the "divisibility rules"
http://math.about.com/library/bldivide.htm

and memorize the first few prime numbers
http://primes.utm.edu/lists/small/1000.txt

(1000 is overkill, but the first line would be great)

Answer 8

C 3/8