Fractions

Episode #4 of the course Everyday math by Jenn Schilling

 

Today, we will explore fractions in more detail. We’ve already discussed fractions a few times in this course, but this is our deep dive.

 

The Math

Fractions can be thought of as a type ratio that represents a comparison between a part and a whole. The fraction 1/4 represents 1 part of the whole (4 equal parts). The top number of a fraction is called the numerator, and it represents the number of parts we have (in the case of 1/4, 1). The bottom number of a fraction is called the denominator, and it represents the number of equal parts in the whole (in the case of 1/4, 4).

Fractions are simple to add and subtract as long as they have the same denominator, then you just add or subtract the numerators and keep the denominator. For example, 1/4 + 2/4 = 3/4. You can create equal denominators in fractions by multiplying the numerator and denominator by the same whole number. For instance, to add 1/3 and 1/4, you could multiply the numerator and denominator of 1/3 by 4 and 1/4 by 3 to create 4/12 and 3/12. Then adding those fractions together, you would get 7/12.

To multiply fractions, you multiply the numerators and the denominators together. For example, 1/4 × 2/4 = 2/16 because 1 × 2 = 2 and 4 × 4 = 16. Fractions can be simplified by dividing the numerator and denominator by the same number. For example, the previous answer, 2/16, can be simplified to 1/8 by dividing both the numerator and denominator by 2. These two fractions (2/16 and 1/8) are called equivalent fractions.

Dividing fractions is slightly more complicated. A fraction can actually be thought of as a division problem. For instance, the fraction 1/4 is the same as “1 divided by 4.” Say we want to divide 1/2 by 1/4 (1/2 ÷ 1/4). The opposite of division is multiplication, and division by 1/4 is basically division by 1 divided by 4. This double division then turns into multiplication by the reciprocal of 1/4, which is 4 or 4/1. So, we calculate 1/2 divided by 1/4 by multiplying 1/2 and 4. Therefore, 1/2 ÷ 1/4 = 1/2 × 4 = 2. The general rule for dividing fractions is to keep the first fraction (the dividend), turn the division sign into a multiplication sign, and flip the second fraction (the divisor).

 

Everyday Applications

Fractions are super useful in our everyday lives! Fractions show up in time, money, cooking, and more!

When telling time, we often refer to fractions of an hour. For example, you might work on something for 90 minutes, or an hour and a half. One half of an hour is 30 minutes. We say a quarter past the hour to mean 15 minutes past the hour.

The denominations of currency are often fractions of a whole. For example, an American quarter represents 25 cents, or 1/4 of a dollar. An American dime is 1/10 of a dollar, and an American nickel is 1/20 of a dollar. An American penny is 1/100 of a dollar.

Fractions show up frequently in cooking. Recipes often call for fractions of a cup (or teaspoon) of an ingredient, and it is useful to be able to compute calculations with fractions when scaling a recipe up or down. For instance, if a recipe calls for 1/2 cup of flour, and you want to make half of the recipe, you will need to divide 1/2 by 2, which will give you 1/4 cup of flour.

I hope you’ve enjoyed our deep dive into fractions! Tomorrow, we will explore common concepts and applications of geometry.

 

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