*Contributor: Erika Wargo. Lesson ID: 12843*

Sharing is a good thing, yes? What if you have to share something weird, like 1-2/3 of leftover birthday cakes? How do six people do that? Learn to divide mixed numbers like that so you can be fair!

categories

subject

Math

learning style

Visual

personality style

Otter

Grade Level

Middle School (6-8)

Lesson Type

Quick Query

Mike, Sarah, Lisa, and Mary arrived at the party late, so there were only 1-½ pizzas left. Each pizza had 8 slices. If they each eat the same number of slices, how many slices of pizza will each person be able to eat?

Dividing mixed numbers is similar to multiplying mixed numbers and fractions.

*Fractions* are parts of a whole, and they represent an amount less than one. *Mixed numbers* are used to represent a value larger than one. When dividing mixed numbers, you are figuring out how many ways an amount, such as a fraction or mixed number, can be divided into another amount, such as a whole number or a mixed number.

Watch a video to help you learn more about dividing mixed numbers and fractions. Respond to the following questions in your math journal:

- What is the first step when dividing a mixed number and a fraction, as shown in the video?
- How do you change a mixed number to an improper fraction?
- What does “keep, change, flip” mean when talking about dividing fractions?

Discuss the questions above with a parent or teacher after watching the Anywhere Math video, *Dividing Mixed Numbers*:

As you saw in the video above, the steps needed to divide mixed numbers and fractions are:

- Convert all mixed numbers or whole numbers to improper fractions.
- Follow the KCF method (Keep, Change, Flip).
- Keep the first fraction the same.
- Change the division sign to multiplication.
- Flip the second fraction. When you flip the second fraction, you are finding the
*reciprocal*of the fraction.

- Multiply the numerators and denominators.
- Reduce your answer and convert back to a mixed number, if necessary.

Mixed numbers need to be changed to an improper fraction before you can begin dividing mixed numbers. To do this, multiply the denominator by the whole number and add the numerator. The denominator stays the same and the new numerator is written on top to form an equivalent improper fraction. For example, 1-½ becomes ^{3}⁄_{2}.

If you have a whole number, write the whole number as the numerator and a 1 as the denominator. All whole numbers have one as a denominator when changed into a fraction. For example, 7 as an improper fraction is written as ^{7}⁄_{1}.

Example: At the beginning of the lesson, you were presented with this word problem:

*Mike, Sarah, Lisa, and Mary arrived at the party late, so there were only 1-½ pizzas left. Each pizza had 8 slices. If they each eat the same number of slices, how many slices of pizza will each person be able to eat?*

In this problem, you are looking for how many groups or parts of a group can be made from another whole and parts. Since there are four people and 1-½ pizzas, you want to divide 1-½ by 4.

1 | 1 | ÷ | 4 | = | |

2 |

**Step 1** Convert all mixed numbers or whole numbers to improper fractions.

1 | 1 | ÷ | 4 | = | becomes | 3 | ÷ | 4 | |

2 | 2 | 1 |

**Step 2** Follow the KCF method (Keep, Change, Flip). Keep the first fraction the same, change the division sign to multiplication, flip the second fraction. When you flip the second fraction, you are finding the reciprocal of the fraction.

3 | ÷ | 4 | = | |

2 | 1 |

3 | x | 1 | = | |

2 | 4 |

**Step 3** Multiply the numerators and denominators.

3 | x | 1 | = | 3 | |

2 | 4 | 8 |

**Step 4**: Reduce your answer and convert back to a mixed number, if necessary. ^{3}/_{8} is a proper fraction, so it does not need to be reduced or changed into a mixed number. Each person would eat 3 slices of pizza.

In your math journal, write a response to the following questions:

- How is dividing mixed numbers different from multiplying mixed numbers?
- How is dividing mixed numbers the same as multiplying mixed numbers?
- Where else might you see a problem like the example above in everyday life?

Now you will move on to the *Got It?* section to play interactive games to practice dividing mixed numbers.

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