math help

What is 7/16 + 10/12?

What is 7/16 + 10/12?

This is how we add

7
16
 +
10
12

Step 1

We still have different denominators (bottom numbers), though, so we need to get a common denominator. This will make the bottom numbers match. Multiply the denominators together first. Now, multiply each numerator by the other term's denominator.

Now we multiply 7 by 12, and get 84, then we multiply 16 by 12 and get 192.

7/16 times 12

Now for the second term. You multiply 10 by 16, and get 160, then multiply 16 by 12 and get 192.

10/12 times 16

This gives us a new problem that looks like so:

84
192
 +
160
192

Step 2

Since our denominators match, we can add the numerators.

84 + 160 = 244

So what's the answer so far?

244
192

Step 3

Can this fraction be reduced?

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

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

244
192
 ÷ 2 =
122
96

Let's try dividing by that again...

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

122
96
 ÷ 2 =
61
48

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...

No good. 53 is larger than 48. So we're done reducing.

There you have it! Here's the final answer to 7/16 + 10/12

7
16
 +
10
12
 =
61
48
© 2014 Randy Tayler

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