math help

What is 78/92 + 10/12?

What is 78/92 + 10/12?

This is how we add

78
92
 +
10
12

Step 1

We can't add two fractions with different denominators (the bottom number). So you need to get a common denominator - both bottom numbers need to match. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we multiply 78 by 12, and get 936, then we multiply 92 by 12 and get 1104.

78/92 times 12

Do the same for the second term. We multiply 10 by 92, and get 920, then multiply 92 by 12 and get 1104.

10/12 times 92

So now our fractions look like this:

936
1104
 +
920
1104

Step 2

Since our denominators match, we can add the numerators.

936 + 920 = 1856

So the answer is:

1856
1104

Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

To find out, we try dividing it by 2...

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

1856
1104
 ÷ 2 =
928
552

Let's try dividing by that again...

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

928
552
 ÷ 2 =
464
276

Let's try dividing by that again...

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

464
276
 ÷ 2 =
232
138

Let's try dividing by that again...

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

232
138
 ÷ 2 =
116
69

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 69. So we're done reducing.

There you have it! Here's the final answer to 78/92 + 10/12

78
92
 +
10
12
 =
116
69
© 2014 Randy Tayler

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