# Converting Decimals, Improper Fractions, and Mixed Numbers

We use fractions and decimals daily. All our money transactions are done in decimal form. When we bake, we use half cups and one-third cups. Being able to convert between a decimal and a fraction is a math skill you will use every single day.

The table shows a decimal, an improper fraction, and a mixed number that are all equivalent.

Decimal | \(3.25\) |

Improper fraction | \(\frac{13}{4}\) |

Mixed number | \(3\frac{1}{4}\) |

**Converting a Decimal to a Fraction:**

When converting a decimal to a fraction, we start by multiplying the decimal by a fraction that is equivalent to 1, so the value of the decimal does not change. For example, if there is only one number after the decimal (in other words, a number in the tenths place), the number would be multiplied by \(\frac{10}{10}\). If there are two numbers after the decimal (the last digit is in the hundredths place), we would multiply the number by \(\frac{100}{100}\), and so on. After multiplying, we simplify the fraction.

Let’s take a look at an example.

We will convert 5.85 into fraction form. Since there are 2 numbers after the decimal, we will multiply 5.85 by \(\frac{100}{100}\).

\(5.58\times \frac{100}{100}=\frac{585}{100}\)

To simplify the fraction, we will start by breaking down the number into its factors. Then we will cancel out the common factors in the numerator and denominator. Both numbers have a factor of 5, so \(\frac{585}{100}\) can be simplified to \(\frac{117}{20}\).

\(\frac{585}{100}=\frac{5\times 3\times 3\times 13}{5\times 5\times 2\times 2}=\frac{117}{20}\)

The fraction equivalent to 5.85 is \(\frac{117}{20}\), which is also called an improper fraction. We will now convert the improper fraction into a mixed number.

**Converting an Improper Fraction to a Mixed Number:**

We will convert the improper fraction, \(\frac{117}{20}\), to a mixed number by first dividing the numerator by the denominator. The whole number becomes the number in the front of the fraction, the remainder becomes the numerator of the fraction, and the denominator of the fraction remains the same. Therefore, \(\frac{117}{20}\), converted to a mixed number is \(5\frac{17}{20}\).

Here’s an example of how we use conversions in real life.

Samm owns a bakery. She has \(5\frac{3}{4}\) kg of sugar. She buys another bag with 10.75 kg of sugar. What is the total amount of sugar, in kilograms, that Samm has for baking? Give your answer in fraction form.

First, we will start by converting 10.75 to fraction form by multiplying it by \(\frac{100}{100}\), which is \(\frac{1,075}{100}\). Once the fraction is simplified, we get \(\frac{43}{4}\), which when converted to a mixed number is \(10\frac{3}{4}\).

Now that both numbers are in mixed number form, we can easily combine to find the total amount of sugar that Samm has for her baking. So all we’re gonna do is add, \(5\frac{3}{4}+10\frac{3}{4}\). When we add mixed numbers, we want to start by adding the fractional parts, so let’s do \(\frac{3}{4}+\frac{3}{4}\). That gives us \(\frac{6}{4}\) because we add our numerators and our denominator stays the same. Now, if you notice, we have an improper fraction. So let’s convert that to a mixed number. If we divide the numerator by the denominator, we’ll get \(1\frac{2}{4}\), which can be simplified to \(1\frac{1}{2}\). Now we’re gonna add this part to our whole number parts from earlier. So \(5+10=15+1\frac{1}{2}=16\frac{1}{2}\). So Samm has \(16\frac{1}{2}\) kg of sugar for baking.

I hope this video on converting decimals, improper fractions, and mixed numbers was helpful. Thanks for watching, and happy studying!