Can you please show me the steps as to how the problem `1/2 + 3/8` equals to `4/8+3/8` as the answer.

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nathanshields's profile pic

nathanshields | High School Teacher | (Level 1) Associate Educator

Posted on

You want to add 1/2 and 3/8.

Imagine a pie cut into eight pieces.  Half of the pie (1/2) is equal to 4 pieces, and three eighths of the pie (3/8) is equal to 3 pieces.  So together you have 7 pieces, or 7/8 of the pie.

But to add fractions in general, you do stuff like this:

1. Find a common denominator.  Here, 2 and 8 both go into 8, so the common denominator is 8.

2. Transform one or both fractions to have that common denominator.  Here, we just need to fix up the 1/2:

`1/2 + 3/8 = `

`4/4*1/2+3/8=`

`4/8+3/8=`

3.  Just add up the numerators! (Reduce if you need to, write as a mixed number if you want to.)

`7/8`

txmedteach's profile pic

txmedteach | High School Teacher | (Level 3) Associate Educator

Posted on

It looks like the question you're asking about looks like this:

`1/2+3/8 = 4/8+3/8`

If this is true, here is how and why you convert the 1/2 to 4/8.

When adding fractions, you can only add them if they have the same denominator (bottom). It's kind of like money, you can't pay for things with both dollars and pesos, you have to convert one to the other depending on whether you're in Mexico or the U.S. In the same way, you can't straight-up add 1/2 and 3/8 without making one or the other fraction have the same denominator.

The way you convert denominators is by multiplying fractions by 1. Keep in mind, when you multiply by 1, you don't change anything. Here's the catch, though: When you multiply by 1, you actually multiply by some number over itself. For example:

`1 = 2/2 = 3/3 = 4/4 = 5/5`

This means that we can multiply the numerator and denomintor (top and bottom) of any fraction by the same number and we haven't messed with the problem at all!

In our case, we want to make the denominator of 1/2 or the denominator of 3/8 equal to the other denominator. For simplicity, we're going to convert 1/2 to a number with an 8 in the denominator. To do this, we're going to have to multiply by 4/4. Again, if we want to change a number on the bottom by multiplying, we need to multiply by the same number on top so we don't change the problem.

Here's how that'll look:

`1/2 * 4/4 = (1*4)/(2*4) = 4/8`

and that's where the 4/8 came from. To complete the problem, we'll just subsitute 4/8 for the 1/2 in the original problem and solve:

`4/8 + 3/8 = 7/8`

And we're done! Good luck!

The link below gives some other examples of how to add fractions with unequal denominators.

Sources:

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