Answer:
[tex]\sf \dfrac{3}{4}[/tex]
Step-by-step explanation:
Given expression:
[tex]\implies \sf \left(\dfrac{-4}{9} \times \dfrac{63}{28}\right)-\left(\dfrac{33}{66} \times \dfrac{-51}{17}\right)+\left(\dfrac{5}{8} \times \dfrac{4}{10}\right)[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{b} \times \dfrac{c}{d}=\dfrac{a \times b}{c \times d}:[/tex]
[tex]\implies \sf \left(\dfrac{-4\times63}{9\times28} \right)-\left(\dfrac{33 \times -51}{66 \times 17}\right)+\left(\dfrac{5\times4}{8\times10} \right)[/tex]
Multiply the numbers:
[tex]\implies \sf \left(\dfrac{-252}{252} \right)-\left(\dfrac{-1683}{1122}\right)+\left(\dfrac{20}{80} \right)[/tex]
Reduce the fractions:
[tex]\implies \sf -1-\left(\dfrac{-3}{2}\right)+\left(\dfrac{1}{4} \right)[/tex]
[tex]\textsf{Apply rule}\quad \:a-\left(-b\right)=a+b:[/tex]
[tex]\implies \sf -1+\dfrac{3}{2}+\dfrac{1}{4}[/tex]
Adjust the fractions based on the LCM of 4:
[tex]\implies \sf \dfrac{-4}{4}+\dfrac{6}{4}+\dfrac{1}{4}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]
[tex]\implies \sf\dfrac{-4+6+1}{4}[/tex]
Add the numbers in the numerator:
[tex]\implies \sf \dfrac{3}{4}[/tex]
