*Contributor: Joanna D'Orazio Mignella. Lesson ID: 14181*

Magic tricks can be really neat! Numbers can do magic tricks, too! Jump in to discover the magic of the multiplicative inverse, a special trick that you can use when solving equations.

categories

subject

Math

learning style

Auditory, Visual

personality style

Lion, Otter

Grade Level

Intermediate (3-5)

Lesson Type

Quick Query

Magic tricks can be fascinating! Imagine impressing your family and friends with a mind-blowing magic trick that seems impossible!

- Have you ever tried to do a magic trick?

Check out the video below to see a stunning magic trick in action. You can even try it at home with just a few cups and small balls you can find around the house.

Wow, what a cool trick!

Just like magic, numbers have their own tricks, too!

- For instance, have you ever heard of the multiplicative inverse?

It's like the secret to making equations balance, just like a magician makes things disappear and reappear!

Jump in to discover a special number trick that will help you solve one-step equations like a pro!

Magic tricks are pretty neat. So are number tricks!

The multiplicative inverse is a special number trick you can use to solve equations.

Imagine you have 1 cupcake to share with 4 friends. You want to share it equally.

You can set up an equation to figure out how much of the cupcake each friend will get.

4x = 1

Here, *x* is the fraction of the cupcake each friend receives.

To solve for *x*, you can use a cool number trick called the *multiplicative inverse* or reciprocal. It helps you isolate *x* so that you can solve for it.

Think of 4 as a fraction.

4 | |

1 |

To find the multiplicative inverse, flip the fraction.

1 | |

4 |

When you multiply 4 by its multiplicative inverse, you get 1!

4 | x | 1 | = | 1 | ||

4 |

Now, you can solve the equation and discover that each person will get ^{1}/_{4} of the cupcake!

The multiplicative inverse is also known as a number's reciprocal. It's a number that, when multiplied by another number, equals 1.

So, for example, the multiplicative inverse of 4 is ^{1}/_{4} because 4 x ^{1}/_{4} = 1

Check out the video below to learn how to find the multiplicative inverse of any number!

Now, it’s your turn! Find the multiplicative inverse of each number.

Nice work!

- Why is the multiplicative inverse important?

Imagine you and two friends are splitting the total cost of dinner.

So, three of you are sharing the bill. You can use the multiplicative inverse of 3 to figure out how much each person should pay.

The multiplicative inverse of 3 is ^{1}/_{3}. That means each of you will pay ^{1}/_{3} of the total cost.

Abracadabra! Now that you know about the multiplicative inverse, you can use it to solve equations!

Look at the equation below.

12x = 48

The multiplicative inverse of 12 will help you isolate x and solve for it.

First, find the multiplicative inverse.

1 | |

12 |

Multiply both sides by the multiplicative inverse.

12x | x | 1 | = | 1x | |

12 |

48 | x | 1 | = | 48 | = | 4 | |

12 | 12 |

That means x = 4.

Follow along with the video below to dive deeper into solving equations using the multiplicative inverse. Grab a piece of paper or a notebook to jot down notes as you watch!

Great job!

Now, pretend you’re going on a road trip with your family. You drive at a speed of 50 miles per hour, and after a certain number of hours, you cover a distance of 100 miles.

- How many hours did you spend in the car?

You can use the multiplicative inverse to solve this.

Your equation is 50x = 100.

Here, x represents the number of hours you traveled.

First, find the multiplicative inverse.

1 | |

50 |

Multiply both sides by the multiplicative inverse.

50x | x | 1 | = | 1x | |

50 |

100 | x | 1 | = | 100 | = | 2 | |

50 | 50 |

So, x = 2, which means you traveled for 2 hours in the car!

The multiplicative inverse is a helpful number trick!

Next, imagine you’re packing boxes for a charity event. Each box contains the same number of canned goods. You have 60 canned goods and are packing them into 5 boxes.

- How many canned goods are in each box?

You can solve this using the multiplicative inverse!

Your equation is 5x = 60.

Here, x represents the number of canned goods in each box.

First, find the multiplicative inverse.

1 | |

5 |

Multiply both sides by the multiplicative inverse.

5x | x | 1 | = | 1x | |

5 |

60 | x | 1 | = | 60 | = | 12 | |

5 | 5 |

Wow, there are 12 canned goods in each box!

Give it a try.

Nicely done!

Now, head to the *Got It?* section to continue practicing!