How do you simplify $\frac{2}{5} + \frac{1}{2}$ $2/5+1/2$ ?

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How do you simplify $\frac{2}{5} + \frac{1}{2}$ $2/5+1/2$ ?

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Answer 1 · 2017-06-11T21:58:19

See a solution process below:

Explanation:

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

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

$\frac{2}{5} + \frac{1}{2} \Rightarrow (\frac{2}{2} \times \frac{2}{5}) + (\frac{5}{5} \times \frac{1}{2}) \Rightarrow \frac{4}{10} + \frac{5}{10}$ $2/5 + 1/2 => (2/2 xx 2/5) + (5/5 xx 1/2) => 4/10 + 5/10$

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

$\frac{4}{10} + \frac{5}{10} \Rightarrow \frac{4 + 5}{10} \Rightarrow \frac{9}{10}$ $4/10 + 5/10 => (4 + 5)/10 => 9/10$

Answer 2 · 2017-06-11T22:02:07

Choose 10 as the 'common denominator', so:

$(\frac{2}{5} \times \frac{2}{2}) + (\frac{1}{2} \times \frac{5}{5}) = \frac{4}{10} + \frac{5}{10} = \frac{9}{10}$ $(2/5xx2/2) + (1/2xx5/5) = 4/10+5/10=9/10$

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 $\frac{x}{x}$ $x/x$ , where $x$ $x$ is any number, since $\frac{x}{x} = 1$ $x/x=1$ .

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

To get $\frac{1}{2}$ $1/2$ to have 10 as the denominator, I will multiply it by $\frac{5}{5}$ $5/5$ , and get $\frac{5}{10}$ $5/10$ .

Now we can add the two fractions: $\frac{4}{10} + \frac{5}{10} = \frac{9}{10}$ $4/10 + 5/10 = 9/10$ .

We can't simplify that any further, so $\frac{9}{10}$ $9/10$ is our answer.

Answer 3 · 2017-06-11T22:04:27

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.

$\frac{2}{5} \cdot \frac{2}{2}$ $2/5*2/2$

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

$\frac{4}{10}$ $4/10$ 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.

$\frac{1}{2} \cdot \frac{5}{5}$ $1/2*5/5$

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

$\frac{5 + 4}{10}$ $(5+4)/10$ => $\frac{9}{10}$ $9/10$

However, the greatest common multiple of 9 and 10 is 1, so the fraction can't be simplified and $\frac{9}{10}$ $9/10$ is the final answer.

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