# Fraction Frog

 1 1 + 2 2 3

## Step 1: Analyze the operation

This is an addition problem, so we need to find two equivalent fractions that have the same denominators. Then we can add the numerators together.

 1 1 + 2 2 3

## Step 2: Convert to improper form

It's difficult to perform arithmetic on mixed numbers, so we want to convert them to improper fractions. Use this formula for the conversion:

Whole × Denominator + Numerator = New Numerator

The first fraction needs to be converted to improper form. Plug in the values of the first fraction into the formula:

1 × 2 + 1 = 3

Re-writing the first fraction, we get 3/2.

 3 + 2 2 3

## Step 3: Find a common denominator

List the multiples of each denominator until a common number is found.

Multiples of 2: 2, 4, 6

Multiples of 3: 3, 6

Now we know 6 is the least common denominator of 3/2 and 2/3.

 3 + 2 2 3

## Step 4: Write each fraction with the common denominator

We want the denominator of each fraction to be 6. But we can't change the denominator without changing the numerator too. To find the new numerator of each fraction, use this formula:

(Common Denominator ÷ Denominator) x Numerator = New Numerator

Plug in the values of the first fraction into the formula:

(6 ÷ 2) × 3 = 9

Re-writing the first fraction, we get 9/6.

Plug in the values of the second fraction into the formula:

(6 ÷ 3) × 2 = 4

Re-writing the second fraction, we get 4/6.

 9 + 4 6 6

## Step 5: Add the numerators and write over common denominator

Add the first numerator and the second numerator together:

 9 + 4 = 13 6 6 6
 13 6

## Step 6: Convert to mixed number

13/6 is improper because the numerator is greater than or equal to the denominator. We need to turn it into a mixed number. Divide the denominator into the numerator:

 2 6 13 - 12 1

The quotient, 2, is the whole part of the mixed number. The remainder, 1, is the numerator of the fraction. Putting it all together, we get:

2 1/6