We will look at addition and subtraction of fractions using pie slices.
In this lesson, we will use partially filled circles to represent
fractions. For example, the
circle to the left is divided into 5 slices, and three of those slices are filled in with
green. So it represents the fraction $$3/5$$.
(If they were filled in with pink, it would
represent the fraction $$-3/5$$.)
What fractions are represented by each of the pie diagrams to the left? Do the
problems in the left-hand table below first, then continue to the right-hand table. Do not
reduce these answers to lowest terms.
If we want to represent a fraction that’s greater than 1 or less than $-1$, we’ll put
several pies next to each other to get enough total slices. For instance, there are two pairs of
pies to the left, each representing $$-7/4$$. In this course, we write
improper fractions (like $$3/2$$), instead of “mixed” fractions (like
Click the first Next button below, and then look at
the top pie diagram to the left. Type the fraction that it represents into the table below.
Your answer will be illustrated in the bottom pie diagram. Do this for each row of the tables
When two fractions have the same denominator (bottom part), their
pie slices are the same size. This means the fractions can be added or subtracted by adding or
subtracting their numerators (top parts).
Two fractions which represent the same number (cover the same amount of pie) are called
equivalent. For example, $$1/2$$ and $$3/6$$ are equivalent
Look at the first row of the table from fracEqQ. Notice
that you have to multiply the first denominator ($2$) by $3$ in order to get the second
denominator ($6$). Similarly, you have to multiply the first numerator
($1$) by $3$ in order to get the second numerator ($3$).
Now look at the second row of the table from fracEqQ.
Now look at the last row of the table from fracEqQ.
Notice that any time you multiply or divide both the numerator and the denominator of a
fraction by the same number, you get an equivalent fraction.
Writing a fraction in lowest terms means finding the equivalent fraction with
the smallest possible denominator.
From now on, unless a question asks you to give a version of a fraction with a specific
denominator, you should always write the fraction in lowest terms.
You already know how to add and subtract fractions with the same denominator. You can combine
this with the idea of equivalence to add and subtract any fractions you want.
Each row of the table below has two fractions in it. Find fractions that are
equivalent to each of these two fractions, and have the same denominator as each other.
For each of the arithmetic problems listed below, make it so the two fractions
have the same denominator by replacing one or both of them with an equivalent fraction. Then
solve the arithmetic problem.
You can add or subtract any two fractions by following this process:
For each of the arithmetic problems listed below, turn it into a problem where
the fractions have the same denominator. Then perform the addition, and write the result in