How do you simplify #2/5+1/2#?

3 Answers
Jun 11, 2017

Answer:

See a solution process below:

Explanation:

To add two fractions they must be over a common denominator, which for this problem is #10#.

To put each fraction over a common denominator we must multiply each fraction by the appropriate form of #1#:

#2/5 + 1/2 => (2/2 xx 2/5) + (5/5 xx 1/2) => 4/10 + 5/10#

We can now add the numerators of the two fractions over the common denominator:

#4/10 + 5/10 => (4 + 5)/10 => 9/10#

Jun 11, 2017

Answer:

Choose 10 as the 'common denominator', so:

#(2/5xx2/2) + (1/2xx5/5) = 4/10+5/10=9/10#

Explanation:

You need a 'common denominator': the number at the bottom of each fraction must be the same. To get that, we can multiply a fraction by #x/x#, where #x# is any number, since #x/x=1#.

Since our denominators are 2 and 5, we need a common denominator that both of those will divide into equally. I'm going to choose 10. It's true that 20 or 100 or 1 000 000 would also work, but we usually try to use the 'least common denominator' or 'lowest common denominator' (both are abbreviated as LCD).

To get #2/5# to have 10 as the denominator, I will multiply it by #2/2#, and get #4/10#. (we've really just multiplied it by 1, since #2/2 = 1#)

To get #1/2# to have 10 as the denominator, I will multiply it by #5/5#, and get #5/10#.

Now we can add the two fractions: #4/10 + 5/10 = 9/10#.

We can't simplify that any further, so #9/10# is our answer.

Jun 11, 2017

Start by finding the least common multiple of 5 and 2, the denominators. Their lcm is 10. Now we have to make the denominators both 10.

#2/5*2/2#

Since 2/2 is one, you aren't really changing the fraction. Either way, we end up with

#4/10# as our first fraction. Now for the second one, we make its denominator 10 as well, by multiplying by 5/5. Since 5/5=1, the fraction isn't changing.

#1/2*5/5#

The final fraction is 5/10. Now that the denominators are the same, simply add the numerators and simplify the fraction.

#(5+4)/10# => #9/10#

However, the greatest common multiple of 9 and 10 is 1, so the fraction can't be simplified and #9/10# is the final answer.