math help

What is 7/10 + 10/12?

What is 7/10 + 10/12?

Here's how we add

7
10
 +
10
12

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 7 by 12, and get 84, then we multiply 10 by 12 and get 120.

7/10 times 12

Now for the second term. You multiply 10 by 10, and get 100, then multiply 10 by 12 and get 120.

10/12 times 10

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

84
120
 +
100
120

Step 2

Since our denominators match, we can add the numerators.

84 + 100 = 184

That gives us the sum, which is

184
120

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:

184
120
 ÷ 2 =
92
60

Let's try dividing by that again...

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

92
60
 ÷ 2 =
46
30

Let's try dividing by that again...

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

46
30
 ÷ 2 =
23
15

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...

No good. 17 is larger than 15. So we're done reducing.

There you have it! Here's the final answer to 7/10 + 10/12

7
10
 +
10
12
 =
23
15
© 2014 Randy Tayler

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