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 รท 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`

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