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3-34.

As you have discovered, any fraction can be rewritten in many equivalent ways. When choosing a denominator that will work to add two fractions, there is no single correct choice. Often, people find it convenient to use the smallest whole number that all denominators divide into evenly. This number is called the lowest common denominator.

For example, when adding the fractions $\frac { 2 } { 3 } + \frac { 5 } { 6 } + \frac { 3 } { 8 }$, you could choose to rewrite each fraction with $48$ or $96$ in the denominator. However, the numbers will stay smaller if you choose to rewrite each fraction with a denominator of $24$, since $24$ is the lowest number that $3$, $6$, and $8$ divide into evenly. (Dividing into a number evenly means that there is no remainder.)

For each of the following sums, first rewrite each fraction using the lowest common denominator. Then add. Read the Math Notes box in this lesson for additional help. Homework Help ✎

1. $\quad \frac { 5 } { 12 } + \frac { 1 } { 3 }$

• Notice that $3$ is a factor of $12$.

1. $\quad \frac { 4 } { 5 } + \frac { 3 } { 4 }$

• Write the first few multiples of $4$ and $5$. What is the first number that appears on both lists?

• Find the lowest common denominator.

• $(4)(5)=20$

• Use Giant Ones to rewrite each fraction with the lowest common denominator.

• $\left(\frac{4}{5}\right) \! \left(\frac{4}{4}\right) \! = \frac{16}{20}$

• $\left(\frac{3}{4}\right) \! \left(\frac{5}{5}\right) \! =\frac{15}{20}$

• Find the sum of the fractions.

• $\frac{16}{20}+\frac{15}{20}=\frac{31}{20}=1\frac{11}{20}$