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**Set 2: Addition and Subtraction of Fractions**

**Example:**

[tex]
\[
\begin{array}{l}
10 \frac{2}{5} - 4 \frac{3}{4} + 2 \frac{2}{3} \\
= 10 \frac{24}{60} - 4 \frac{45}{60} + 2 \frac{40}{60} \\
= 9 \frac{84}{60} - 4 \frac{45}{60} + 2 \frac{40}{60} \\
= 5 \frac{39}{60} + 2 \frac{40}{60} \\
= 7 \frac{79}{60} = 8 \frac{19}{60}
\end{array}
\]
[/tex]

**Problems:**

1. [tex]\(6 \frac{2}{5} + 4 \frac{2}{3} - 7 \frac{3}{4} \quad \text{lcm} = 60\)[/tex]

[tex]
\[
\begin{array}{l}
= 6 \frac{24}{60} + 4 \frac{40}{60} - 7 \frac{45}{60} \\
= \frac{10 \frac{64}{60} - 7 \frac{45}{60}}{3 \frac{14}{60}}
\end{array}
\]
[/tex]

[tex]\(=\)[/tex]

2. [tex]\(6 \frac{2}{9} - 3 \frac{5}{6} + 1 \frac{1}{4} \quad \text{lcm} = 36\)[/tex]

[tex]
\[
= 6 \frac{36}{36}
\]
[/tex]

3. [tex]\(9 \frac{5}{8} - 4 \frac{3}{4} + 2 \frac{5}{6}\)[/tex]

[tex]
\[
=
\]
[/tex]

4. [tex]\(4 \frac{1}{4} - 2 \frac{5}{7} + 6 \frac{4}{14}\)[/tex]

[tex]
\[
= \quad
\]
[/tex]

5. [tex]\(3 \frac{1}{8} - 1 \frac{5}{12} + 4 \frac{17}{18}\)[/tex]

[tex]
\[
= \quad
\]
[/tex]

Answer :

Certainly! Let's go through the process of solving the problem step by step.

We need to solve the expression:

[tex]\[ 6 \frac{2}{5} + 4 \frac{2}{3} - 7 \frac{3}{4} \][/tex]

Step 1: Convert each mixed number to an improper fraction.
- For [tex]\(6 \frac{2}{5}\)[/tex]:
[tex]\[
6 \times 5 + 2 = 30 + 2 = 32 \quad \text{so it's } \frac{32}{5}
\][/tex]
- For [tex]\(4 \frac{2}{3}\)[/tex]:
[tex]\[
4 \times 3 + 2 = 12 + 2 = 14 \quad \text{so it's } \frac{14}{3}
\][/tex]
- For [tex]\(7 \frac{3}{4}\)[/tex]:
[tex]\[
7 \times 4 + 3 = 28 + 3 = 31 \quad \text{so it's } \frac{31}{4}
\][/tex]

Step 2: Find the least common denominator (LCM) for the fractions.
- The denominators are 5, 3, and 4.
- The LCM of 5, 3, and 4 is 60.

Step 3: Convert each fraction to have the common denominator of 60.
- Convert [tex]\(\frac{32}{5}\)[/tex] to a denominator of 60:
[tex]\[
\frac{32}{5} = \frac{32 \times 12}{60} = \frac{384}{60}
\][/tex]
- Convert [tex]\(\frac{14}{3}\)[/tex] to a denominator of 60:
[tex]\[
\frac{14}{3} = \frac{14 \times 20}{60} = \frac{280}{60}
\][/tex]
- Convert [tex]\(\frac{31}{4}\)[/tex] to a denominator of 60:
[tex]\[
\frac{31}{4} = \frac{31 \times 15}{60} = \frac{465}{60}
\][/tex]

Step 4: Perform the addition and subtraction.
[tex]\[
\frac{384}{60} + \frac{280}{60} - \frac{465}{60} = \frac{384 + 280 - 465}{60}
\][/tex]

Calculate the numerator:
[tex]\[
384 + 280 = 664
\][/tex]
[tex]\[
664 - 465 = 199
\][/tex]

So our expression now is:
[tex]\[
\frac{199}{60}
\][/tex]

Step 5: Convert the improper fraction back to a mixed number.
- Divide 199 by 60 to find the whole number part:
[tex]\[
199 \div 60 = 3 \quad \text{with a remainder of } 19
\][/tex]

Therefore, the mixed number is:
[tex]\[
3 \frac{19}{60}
\][/tex]

So, the final answer is:

[tex]\[ 3 \frac{19}{60} \][/tex]

Thanks for taking the time to read Set 2 Addition and Subtraction of Fractions Example tex begin array l 10 frac 2 5 4 frac 3 4 2 frac 2 3 10. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

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