Adding & Subtracting Fractions - Pre Algebra

1. What is $\frac{5}{6} - \frac{1}{4}$?

   $\frac{7}{12}$. Rewrite as $\frac{10}{12} - \frac{3}{12}$.

2. What is $\frac{1}{3} + \frac{1}{4}$?

   $\frac{7}{12}$. Rewrite as $\frac{4}{12} + \frac{3}{12}$.

3. What is $2\frac{1}{2} + 1\frac{3}{4}$?

   $4\frac{1}{4}$. Add $2\frac{2}{4} + 1\frac{3}{4} = 3\frac{5}{4}$, and $\frac{5}{4} = 1\frac{1}{4}$.

4. What is the error in writing $\frac{1}{2} + \frac{1}{3} = \frac{2}{5}$?

   The denominators were added. Only numerators are added once the denominators match: $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$.

5. What is $\frac{2}{5} + \frac{3}{10}$?

   $\frac{7}{10}$. Rewrite $\frac{2}{5}$ as $\frac{4}{10}$, then add.

6. What is $\frac{1}{6} + \frac{1}{3}$ in simplest form?

   $\frac{1}{2}$. The sum $\frac{1}{6} + \frac{2}{6} = \frac{3}{6}$ simplifies to $\frac{1}{2}$.

7. What must be true of two fractions' denominators before you add or subtract their numerators?

   The denominators must be equal. Rewrite each fraction as an equivalent fraction with a common denominator, then combine the numerators and keep that denominator.

8. What is $3\frac{1}{4} - 1\frac{3}{4}$?

   $1\frac{1}{2}$. Regroup $3\frac{1}{4}$ as $2\frac{5}{4}$, then $2\frac{5}{4} - 1\frac{3}{4} = 1\frac{2}{4}$.

9. What is the least common denominator of $\frac{3}{8}$ and $\frac{5}{12}$?

   $24$. It is the least common multiple of $8$ and $12$.

10. What is $3 - \frac{2}{5}$?

    $2\frac{3}{5}$ (or $\frac{13}{5}$). Write $3$ as $\frac{15}{5}$, then subtract.

11. What is $\frac{7}{8} - \frac{1}{2}$?

    $\frac{3}{8}$. Rewrite $\frac{1}{2}$ as $\frac{4}{8}$, then subtract.

12. A pizza has $\frac{1}{4}$ eaten by one person and $\frac{1}{3}$ eaten by another. What fraction of the pizza is left?

    $\frac{5}{12}$. Eaten: $\frac{3}{12} + \frac{4}{12} = \frac{7}{12}$, so $1 - \frac{7}{12} = \frac{5}{12}$ remains.

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