Answer:
[tex]84\frac{5}{9}[/tex] ↔ [tex]45\frac{2}{9}+39\frac{3}{9}[/tex]
[tex]6\frac{2}{9}[/tex] ↔ [tex]-24\frac{5}{9} + 30\frac{7}{9}[/tex]
[tex]-23.24[/tex] ↔ [tex]28.98+(-52.22)[/tex]
[tex]131.87[/tex] ↔ [tex]56.7+75.12[/tex]
Step-by-step explanation:
[tex]84\frac{5}{9}[/tex] and [tex]45\frac{2}{9}+39\frac{3}{9}[/tex]
Convert [tex]84\frac{5}{9}[/tex] to an improper fraction.
To write 84 as a fraction with a common denominator, multiply by [tex]\frac{9}{9}[/tex]
Combine the numerators over the common denominator.
[tex]\frac{84*9+5}{9}[/tex]
[tex]\frac{756+ 5}{9}[/tex]
[tex]\frac{761}{9}[/tex] = [tex]45\frac{2}{9}+39\frac{3}{9}[/tex]
covert [tex]45\frac{2}{9}[/tex] to an improper fraction
Combine the numerators over the common denominator.
[tex]\frac{761}{9}[/tex] = [tex]\frac{45*9+2}{9}[/tex] + [tex]39\frac{3}{9}[/tex]
[tex]\frac{761}{9}[/tex] = [tex]\frac{407}{9}[/tex] + [tex]39\frac{3}{9}[/tex]
covert [tex]39\frac{3}{9}[/tex] to an improper fraction
Combine the numerators over the common denominator.
[tex]\frac{761}{9}[/tex] = [tex]\frac{407}{9}[/tex] + [tex]\frac{39*9+3}{9}[/tex]
[tex]\frac{761}{9}[/tex] = [tex]\frac{407}{9}[/tex] + [tex]\frac{354}{9}[/tex] →[tex]\frac{407+354}{9}[/tex]
[tex]\frac{761}{9}[/tex] = [tex]\frac{761}{9}[/tex]
therefore the statement[tex]84\frac{5}{9}[/tex] = [tex]45\frac{2}{9}+39\frac{3}{9}[/tex] is true
[tex]6\frac{2}{9}[/tex] and [tex]-24\frac{5}{9} + 30\frac{7}{9}[/tex]
Convert [tex]6\frac{2}{9}[/tex] to an improper fraction.
To write 6 as a fraction with a common denominator, multiply by [tex]\frac{9}{9}[/tex]
[tex]\frac{6*9}{9} +\frac{2}{9}[/tex] →[tex]\frac{54+2}{9}[/tex] → [tex]\frac{56}{9}[/tex]
Convert [tex]-24\frac{5}{9}[/tex] and [tex]30\frac{7}{9}[/tex] an improper fraction
[tex]-24\frac{5}{9}[/tex] → [tex]-(\frac{24*9}{9} + \frac{5}{9} )[/tex] → [tex]-\frac{24*9+5}{9}[/tex] → [tex]-\frac{221}{9}[/tex]
[tex]30\frac{7}{9}[/tex] → [tex]\frac{30*9}{9} +\frac{7}{9}[/tex] → [tex]\frac{30*9+7}{9}[/tex]→ [tex]\frac{277}{9}[/tex]
[tex]\frac{56}{9}[/tex] = [tex]-\frac{221}{9}[/tex] + [tex]\frac{277}{9}[/tex] →
[tex]\frac{56}{9}[/tex] = [tex]\frac{56}{9}[/tex]
therefore the statement [tex]6\frac{2}{9}[/tex] = [tex]-24\frac{5}{9} + 30\frac{7}{9}[/tex] is true
[tex]28.98+(-52.22)[/tex] and [tex]-23.24[/tex]
[tex]28.98 - 52.22[/tex] → [tex]-23.24[/tex]
[tex]-23.24[/tex] = [tex]-23.24[/tex]
therefore the statement [tex]28.98+(-52.22)[/tex] = [tex]-23.24[/tex] is true
[tex]131.87[/tex] and [tex]56.7+75.12[/tex]
[tex]56.7+75.12[/tex] → [tex]131.872[/tex]
[tex]131.87[/tex] ≠ [tex]131.872[/tex]
therefore the statement [tex]131.87[/tex] = [tex]56.7+75.12[/tex] is False
