math help

What is 6/19 + 4/10?

What is 6/19 + 4/10?

Here's how we add

6
19
 +
4
10

Step 1

Can you add yet? Nope! The denominators don't match. We need a common denominator. So next we take both denominators and multiply them. Next, take each numerator and multiply it by the denominator of the other term.

So, we multiply 6 by 10, and get 60, then we multiply 19 by 10 and get 190.

6/19 times 10

Now for the second term. You multiply 4 by 19, and get 76, then multiply 19 by 10 and get 190.

4/10 times 19

We now have a new problem, that looks like this:

60
190
 +
76
190

Step 2

Since our denominators match, we can add the numerators.

60 + 76 = 136

That gives us the sum, which is

136
190

Step 3

Now, do we need to simplify this fraction?

First, we attempt to divide it by 2...

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

136
190
 ÷ 2 =
68
95

Let's try dividing by that again...

Nope! So now we try the next greatest prime number, 3...

Nope! So now we try the next greatest prime number, 5...

Nope! So now we try the next greatest prime number, 7...

Nope! So now we try the next greatest prime number, 11...

Nope! So now we try the next greatest prime number, 13...

Nope! So now we try the next greatest prime number, 17...

Nope! So now we try the next greatest prime number, 19...

Nope! So now we try the next greatest prime number, 23...

Nope! So now we try the next greatest prime number, 29...

Nope! So now we try the next greatest prime number, 31...

Nope! So now we try the next greatest prime number, 37...

Nope! So now we try the next greatest prime number, 41...

Nope! So now we try the next greatest prime number, 43...

Nope! So now we try the next greatest prime number, 47...

Nope! So now we try the next greatest prime number, 53...

Nope! So now we try the next greatest prime number, 59...

Nope! So now we try the next greatest prime number, 61...

Nope! So now we try the next greatest prime number, 67...

Nope! So now we try the next greatest prime number, 71...

No good. 71 is larger than 68. So we're done reducing.

There you have it! Here's the final answer to 6/19 + 4/10

6
19
 +
4
10
 =
68
95
© 2014 Randy Tayler

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