To convert fractions (and ratios) and decimals to a percent:

• Without a calculator - the word “percent” means “per 100”. Therefore, if the fraction (or ratio) already has 100 in the denominator, the numerator is your percent value.

• Without a calculator - if the fraction is easily manipulated to a fraction with 100 in the denominator, you can do this and refer to the previous point

• With a calculator - if the fraction is messy, you can complete the division of the fraction (the fraction ⅔ means 2 ÷ 3) to obtain a decimal, then multiply the decimal by 100

• Without a calculator - any decimal can be converted to a percent by multiplying the decimal by 100

And like fractions, we can have equivalent ratios:

Lastly, we can also express ratios using words or by writing a fraction.

Ratios and fractions are sometimes the same (⅖ is both a fraction and a ratio).

However, ratios - unlike fractions, decimals, and percents - are interesting in that they can help us compare separate quantities. For example, you can use a ratio (and a fraction, decimal, or percent) to compare the shaded squares to total squares like we do below, but you can also use a ratio to compare separate quantities of another "type". To illustrate this, consider the following examples of ratios being used in this way:

• For every breakfast special ordered at a diner, 2 jams are given

The ratio for breakfast order to jams is 1 : 2

• For a salad dressing recipe, you can make as much salad as you want, keeping the following ratio in mind when scaling the recipe larger or smaller

3 parts vinegar to 2 parts olive oil

In these scenarios, ratios are not referring to parts of a whole in the same way that fractions do. Instead, we are comparing two quantities (and we can compare more than 2 if we want) of different objects. Further, ratios can be used to compare more than two quantities. Consider the following example:

• To make a homemade face mask, mix the ingredients according to the following ratio (measurements in tablespoons)

The ratio for olive oil to lemon juice to honey is 3 : 4 : 2

We'll look at ratios more in the sub-module on ratios, unit rates, and proportions.

You can also have a decimal with 0 as the whole number before the decimal. This means we are only dealing with a fractional component, and we are referring to a part of a whole.

To convert fractions (and ratios) and percents to a decimal:

• Without a calculator - to convert a percent to a decimal, divide the percent by 100

• Without a calculator - by knowing common fraction-decimal equivalents

• With a calculator - complete the division of a fraction (or ratio) to obtain a decimal

We can describe the number of boxes shaded in orange compared to the total number of boxes using percents, fractions, decimals, and ratios. We can also describe the number of unshaded, or white, boxes compared to the total number of boxes.

Common Fraction and Decimal Equivalents to Know

Check Your Understanding

(1) Fill out the following table by converting the given figures to percents, ratios, fractions, and decimals as needed.

Extra Practice - with solutions