Question
Adding \& Subtracting Fractions Bertha Songolo \( \begin{array}{ll}\text { a. } \frac{5}{8}+\frac{1}{4}= & \text { b. } \frac{6}{10}-\frac{2}{5}= \\ \text { c. } \frac{8}{12}-\frac{3}{6}= & \text { d. } \frac{2}{3}+\frac{4}{9}= \\ \text { e. } \frac{4}{5}+\frac{8}{10}= & \text { f. } \frac{3}{4}-\frac{2}{3}= \\ \text { g. } \frac{4}{9}-\frac{1}{3}= & \text { h. } \frac{1}{4}+\frac{4}{12}= \\ \text { i. } \frac{3}{5}+\frac{1}{3}= & \text { j. } \frac{1}{2}-\frac{1}{5}= \\ \text { k. } \frac{5}{6}-\frac{1}{2}= & \text { I. } \frac{1}{2}+\frac{1}{3}=\end{array} \)
Ask by Gordon Bowman. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Here are the solutions to the fraction addition and subtraction problems:
a. \(\frac{5}{8} + \frac{1}{4} = \frac{7}{8}\)
b. \(\frac{6}{10} - \frac{2}{5} = \frac{1}{5}\)
c. \(\frac{8}{12} - \frac{3}{6} = \frac{1}{6}\)
d. \(\frac{2}{3} + \frac{4}{9} = 1 \frac{1}{9}\) or \(\frac{10}{9}\)
e. \(\frac{4}{5} + \frac{8}{10} = 1 \frac{3}{5}\) or \(\frac{8}{5}\)
f. \(\frac{3}{4} - \frac{2}{3} = \frac{1}{12}\)
g. \(\frac{4}{9} - \frac{1}{3} = \frac{1}{9}\)
h. \(\frac{1}{4} + \frac{4}{12} = \frac{7}{12}\)
i. \(\frac{3}{5} + \frac{1}{3} = \frac{14}{15}\)
j. \(\frac{1}{2} - \frac{1}{5} = \frac{3}{10}\)
k. \(\frac{5}{6} - \frac{1}{2} = \frac{1}{3}\)
l. \(\frac{1}{2} + \frac{1}{3} = \frac{5}{6}\)
Solution
Sure, let's solve each of the addition and subtraction fraction problems step by step.
### a. \(\frac{5}{8} + \frac{1}{4}\)
**Step 1:** Find a common denominator. The least common denominator (LCD) of 8 and 4 is 8.
\[
\frac{1}{4} = \frac{2}{8}
\]
**Step 2:** Add the fractions.
\[
\frac{5}{8} + \frac{2}{8} = \frac{7}{8}
\]
**Answer:** \(\frac{7}{8}\)
---
### b. \(\frac{6}{10} - \frac{2}{5}\)
**Step 1:** Find a common denominator. The LCD of 10 and 5 is 10.
\[
\frac{2}{5} = \frac{4}{10}
\]
**Step 2:** Subtract the fractions.
\[
\frac{6}{10} - \frac{4}{10} = \frac{2}{10} = \frac{1}{5}
\]
**Answer:** \(\frac{1}{5}\)
---
### c. \(\frac{8}{12} - \frac{3}{6}\)
**Step 1:** Simplify the fractions.
\[
\frac{8}{12} = \frac{2}{3}, \quad \frac{3}{6} = \frac{1}{2}
\]
**Step 2:** Find a common denominator. The LCD of 3 and 2 is 6.
\[
\frac{2}{3} = \frac{4}{6}, \quad \frac{1}{2} = \frac{3}{6}
\]
**Step 3:** Subtract the fractions.
\[
\frac{4}{6} - \frac{3}{6} = \frac{1}{6}
\]
**Answer:** \(\frac{1}{6}\)
---
### d. \(\frac{2}{3} + \frac{4}{9}\)
**Step 1:** Find a common denominator. The LCD of 3 and 9 is 9.
\[
\frac{2}{3} = \frac{6}{9}
\]
**Step 2:** Add the fractions.
\[
\frac{6}{9} + \frac{4}{9} = \frac{10}{9} = 1 \frac{1}{9}
\]
**Answer:** \(1 \frac{1}{9}\) or \(\frac{10}{9}\)
---
### e. \(\frac{4}{5} + \frac{8}{10}\)
**Step 1:** Simplify \(\frac{8}{10}\).
\[
\frac{8}{10} = \frac{4}{5}
\]
**Step 2:** Add the fractions.
\[
\frac{4}{5} + \frac{4}{5} = \frac{8}{5} = 1 \frac{3}{5}
\]
**Answer:** \(1 \frac{3}{5}\) or \(\frac{8}{5}\)
---
### f. \(\frac{3}{4} - \frac{2}{3}\)
**Step 1:** Find a common denominator. The LCD of 4 and 3 is 12.
\[
\frac{3}{4} = \frac{9}{12}, \quad \frac{2}{3} = \frac{8}{12}
\]
**Step 2:** Subtract the fractions.
\[
\frac{9}{12} - \frac{8}{12} = \frac{1}{12}
\]
**Answer:** \(\frac{1}{12}\)
---
### g. \(\frac{4}{9} - \frac{1}{3}\)
**Step 1:** Find a common denominator. The LCD of 9 and 3 is 9.
\[
\frac{1}{3} = \frac{3}{9}
\]
**Step 2:** Subtract the fractions.
\[
\frac{4}{9} - \frac{3}{9} = \frac{1}{9}
\]
**Answer:** \(\frac{1}{9}\)
---
### h. \(\frac{1}{4} + \frac{4}{12}\)
**Step 1:** Simplify \(\frac{4}{12}\).
\[
\frac{4}{12} = \frac{1}{3}
\]
**Step 2:** Find a common denominator. The LCD of 4 and 3 is 12.
\[
\frac{1}{4} = \frac{3}{12}, \quad \frac{1}{3} = \frac{4}{12}
\]
**Step 3:** Add the fractions.
\[
\frac{3}{12} + \frac{4}{12} = \frac{7}{12}
\]
**Answer:** \(\frac{7}{12}\)
---
### i. \(\frac{3}{5} + \frac{1}{3}\)
**Step 1:** Find a common denominator. The LCD of 5 and 3 is 15.
\[
\frac{3}{5} = \frac{9}{15}, \quad \frac{1}{3} = \frac{5}{15}
\]
**Step 2:** Add the fractions.
\[
\frac{9}{15} + \frac{5}{15} = \frac{14}{15}
\]
**Answer:** \(\frac{14}{15}\)
---
### j. \(\frac{1}{2} - \frac{1}{5}\)
**Step 1:** Find a common denominator. The LCD of 2 and 5 is 10.
\[
\frac{1}{2} = \frac{5}{10}, \quad \frac{1}{5} = \frac{2}{10}
\]
**Step 2:** Subtract the fractions.
\[
\frac{5}{10} - \frac{2}{10} = \frac{3}{10}
\]
**Answer:** \(\frac{3}{10}\)
---
### k. \(\frac{5}{6} - \frac{1}{2}\)
**Step 1:** Find a common denominator. The LCD of 6 and 2 is 6.
\[
\frac{1}{2} = \frac{3}{6}
\]
**Step 2:** Subtract the fractions.
\[
\frac{5}{6} - \frac{3}{6} = \frac{2}{6} = \frac{1}{3}
\]
**Answer:** \(\frac{1}{3}\)
---
### l. \(\frac{1}{2} + \frac{1}{3}\)
**Step 1:** Find a common denominator. The LCD of 2 and 3 is 6.
\[
\frac{1}{2} = \frac{3}{6}, \quad \frac{1}{3} = \frac{2}{6}
\]
**Step 2:** Add the fractions.
\[
\frac{3}{6} + \frac{2}{6} = \frac{5}{6}
\]
**Answer:** \(\frac{5}{6}\)
---
If you need further explanations or assistance with any of these problems, feel free to ask!
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
Did you know that fractions have a historical connection to ancient civilizations? The Egyptians were among the first to use fractions, representing them as sums of unit fractions. Their numeral system had different ways of expressing fractions based on their unique needs for trade and engineering. So next time you add or subtract fractions, just think of how far we've come since the days of the pyramids! When adding or subtracting fractions, remember the golden rule: find a common denominator! This means you'll want to convert each fraction to have the same bottom number (denominator) before performing any math. A common mistake is forgetting to simplify your final answer. Always check if you can reduce your fraction to its simplest form for the best result—no one likes a fraction that's too complicated!
