# Converting 500 grams to Kilograms: How-to & Steps

Instructor: Stephanie Matalone

Stephanie taught high school science and math and has a Master's Degree in Secondary Education.

In this lesson, we will go over the steps of converting 500 grams to kilograms by setting up fractions and cross multiplying in order to get an equation where we can solve for the unknown.

## Steps to Solving the Problem

You decide to mail your sister a nice present for her birthday. You weigh your package at home and know it is 500 grams, then look up the cost online. Small problem... all the costs online are listed in kilograms!

In order to figure out how much your package will cost to ship, you need to convert the weight of 500 grams into kilograms. In order to do so, you must know that there are 1,000 grams in a kilogram. 'Kilo' will always indicate 1,000 and can help with measurements like this!

Knowing that 1 kilogram is equal to 1,000 grams, we can set up our first fraction:

Next, we will set up an equivalent ratio, or a fraction that is equal to the original. In order to do this, we must put the units in the correct spot. If kilograms are on top of the first fraction, they must also be on top of the equivalent fraction.

Our equivalent fraction will consist of an unknown number of kilograms, which we will represent with x. In this case, x is simply a variable that stands for a number we do not know. This variable x will go on top of the fraction because it is a measurement in kilograms, which was on top of the original fraction. The 500 grams which we are trying to convert will go on the bottom of the fraction because grams were on bottom of the original fraction.

Equivalent ratio:

Since the two fractions we wrote are equal, we will set them equal to each other:

In order to solve for the unknown number of kilograms, we must cross multiply the two equal fractions. In order to do this, we multiply the top of the first fraction with the bottom of the second fraction. In our problem, we will multiply 1 kilogram times 500 grams and x kilograms by 1,000 grams.

We will end up with this equation:

1 kilogram x 500 grams = x kilograms x 1,000 grams

Since we are trying to solve for x, we need to get that variable by itself. We need to divide both sides by 1,000 grams to leave x kilograms isolated. When we do this, we will divide the 500 on the left by 1,000 to get .5. The unit grams will cancel out on both sides, leaving the solution:

.5 kilograms = x kilograms

## Solution

500 grams are equal to .5 kilograms. This means that your package weighs .5 kilograms and now you can see how much it will cost.

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