*Contributor: Lanette Judy . Lesson ID: 14183*

Recipes frequently use mixed numbers to indicate ingredient amounts. How do you adjust these quantities if you need to make more? Learn how to calculate and modify your recipe ingredients with ease!

categories

subject

Math

learning style

Visual

personality style

Beaver

Grade Level

Intermediate (3-5)

Lesson Type

Skill Sharpener

Picture this: you’re a math chef in your very own kitchen, and you have a tasty chocolate chip cookie recipe that calls for 2 ^{1}/_{2} cups of sugar and 2 ^{1}/_{2} cups of flour.

But uh-oh! The recipe only makes enough cookies for a few friends.

- How can you use your math skills to multiply those ingredients and whip up a batch that will satisfy everyone?

Get ready to dive into the delicious world of multiplying mixed numbers to create the perfect treat for all your buddies!

Welcome to a math adventure where you will master multiplying mixed numbers—those awesome combinations of whole numbers and fractions.

Think of it as mixing ingredients for a delicious recipe. By following a few simple steps, you can tackle even the trickiest math recipes with confidence!

Say you’re making chocolate chip cookies for a party and need to make 1 ^{1}/_{2} times the original recipe.

- If the recipe calls for 2
^{3}/_{4}cups of flour, how much do you need?

First, set up your problem.

2 | 3 | x | 1 | 1 | = | |

4 | 2 |

To multiply mixed numbers, you need to change them into improper fractions. Here’s how.

- Change 2
^{3}/_{4}to an improper fraction.

Multiply the whole number (2) by the denominator (4): 4 x 2 = 8.

Then, add the numerator (3): 8 + 3 = 11.

So, 2 ^{3}/_{4} becomes ^{11}/_{4}.

- Change 1 1/2 to an improper fraction.

Multiply the whole number (1) by the denominator (2): 2 x 1 = 2.

Then, add the numerator (1): 2 + 1 = 3.

So, 1 ^{1}/_{2} becomes ^{3}/_{2}.

Now, your problem looks like this.

11 | x | 3 | = | |

4 | 2 |

Next, multiply straight across.

11 x 3 = 33

4 x 2 = 8

So, you get ^{33}/_{8}.

But wait! You need to convert that back into a mixed number.

33 | = | 4 | 1 | ||

8 | 8 |

When you divide 33 by 8, you get 4 ^{1}/_{8}. That means you’ll need 4 ^{1}/_{8} cups of flour for your cookies!

Just like following a recipe, multiplying mixed numbers involves a few important steps.

- Set up the problem.

- Change the mixed numbers to improper fractions.

- Write the new problem with improper fractions.

- Multiply straight across.

- Convert the answer back to a mixed number.

Grab a notecard or piece of paper and jot down these steps to keep handy while you learn to multiply mixed numbers.

Then, watch the video below for another example. You can refer to your note card to follow along!

- Ready to try another challenge?

Imagine it takes you 2 ^{1}/_{2} hours to make those cookies. Your friend John takes 1 ^{3}/_{4} times as long as you, and Sally takes 2 ^{1}/_{3} times as long as John.

- How long does it take Sally to make the cookies?

You’ll need to multiply 2 ^{1}/_{2} x 1 ^{3}/_{4} x 2 ^{1}/_{3}. Break it down.

- Set up the problem.

2 | 1 | x | 1 | 3 | x | 2 | 1 | = | |

2 | 4 | 3 |

- Change to improper fractions.

2 | 1 | = | 5 | |

2 | 2 |

1 | 3 | = | 7 | |

4 | 4 |

2 | 1 | = | 7 | |

3 | 3 |

- Write the new problem.

5 | x | 7 | x | 7 | = | |

2 | 4 | 3 |

- Multiply across.

5 | x | 7 | x | 7 | = | 245 |

2 | x | 4 | x | 3 | = | 24 |

- Convert back to a mixed number.

245 | = | 10 | 5 | |

24 | 24 |

Great job!

- Are you feeling hungry yet?
- How about a quick cookie break?

Once you’re ready, cook up some more tasty math in the *Got It?* section!