Answer:
[tex]4\frac{1}{3}[/tex]
Step-by-step explanation:
Apply PEMDAS order of operations:
→ Parentheses
→ Exponents
→ Multiplication
→ Division
→ Addition
→ Subtraction
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[tex]\frac{3}{5}+2^2-\frac{2}{5}\left(8-6\right)\div \:3=4\frac{1}{3}[/tex]
1) Parentheses:
[tex]\left(8-6\right)[/tex]
[tex]8-6[/tex]
[tex]=2[/tex]
[tex]\frac{3}{5}+2^2-\frac{2}{5}\times \:2\div \:3[/tex]
2) Exponents:
[tex]2^2[/tex]
[tex]=4[/tex]
[tex]\frac{3}{5}+4-\frac{2}{5}\cdot \:2\div \:3[/tex]
3) Multiplication/Division:
[tex]\frac{2}{5}\times \:2\div \:3[/tex]
[tex]\frac{2}{5}\times \:2[/tex]
Convert to fraction:
[tex]2=\frac{2}{1}[/tex]
[tex]\frac{2}{5}\times \frac{2}{1}[/tex]
Multiply 2 × 2, and 5 × 1:
[tex]=\frac{4}{5}[/tex]
[tex]\frac{4}{5}\div \:3[/tex]
Convert to fraction:
[tex]3=\frac{3}{1}[/tex]
[tex]\frac{4}{5}\div \frac{3}{1}[/tex]
Apply fraction rule: [tex]\frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}[/tex]
[tex]\frac{4}{5}\times \frac{1}{3}[/tex]
Multiply 4 × 1 and 5 × 3:
[tex]\frac{4}{15}[/tex]
[tex]\frac{3}{5}+4-\frac{4}{15}[/tex]
4) Addition/ Subtraction:
[tex]\frac{3}{5}+4[/tex]
[tex]=\frac{23}{5}[/tex]
[tex]\frac{23}{5}-\frac{4}{15}[/tex]
[tex]=\frac{13}{3}[/tex]
Finally, Convert fraction to mixed number:
[tex]\frac{13}{3}=4\frac{1}{3}[/tex]
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