Answer:
part 1) [tex]13[/tex]
part 2) [tex]\frac{119}{45}[/tex]
part 3) [tex]2[/tex]
part 4) [tex]\frac{1,958,309}{128}[/tex]
part 5) [tex]4\ yd^2[/tex]
Step-by-step explanation:
The complete question in the attached figure
we know that
Applying PEMDAS
P ----> Parentheses first
E -----> Exponents (Powers and Square Roots, etc.)
MD ----> Multiplication and Division (left-to-right)
AS ----> Addition and Subtraction (left-to-right)
Part 1) we have
[tex]\frac{2}{3}(6)+\frac{3}{4}(12)[/tex]
Remember that when multiply a fraction by a whole number, multiply the numerator of the fraction by the whole number and maintain the same denominator
so
[tex]\frac{12}{3}+\frac{36}{4}[/tex]
[tex]4+9=13[/tex]
Part 2) we have
[tex]2\frac{1}{3}(3\frac{2}{5}:3)[/tex]
Convert mixed number to an improper fraction
[tex]2\frac{1}{3}=2+\frac{1}{3}=\frac{2*3+1}{3}=\frac{7}{3}[/tex]
[tex]3\frac{2}{5}=3+\frac{2}{5}=\frac{3*5+2}{5}=\frac{17}{5}[/tex]
substitute
[tex]\frac{7}{3}(\frac{17}{5}:3)[/tex]
Solve the division in the parenthesis (applying PEMDAS)
[tex]\frac{7}{3}(\frac{17}{15})[/tex]
[tex]\frac{119}{45}[/tex]
Part 3) we have
[tex]\frac{7}{8}:(1\frac{1}{4}:4)[/tex]
Convert mixed number to an improper fraction
[tex]1\frac{1}{4}=1+\frac{1}{4}=\frac{1*4+1}{4}=\frac{5}{4}[/tex]
substitute
[tex]\frac{7}{8}:(\frac{5}{4}:4)[/tex]
Solve the division in the parenthesis (applying PEMDAS)
[tex]\frac{7}{8}:(\frac{5}{16})[/tex]
Multiply in cross
[tex]\frac{80}{40}=2[/tex]
Part 4) we have
[tex]18:(\frac{2}{3})^2+25:(\frac{2}{5})^7[/tex]
exponents first
[tex]18:(\frac{4}{9})+25:(\frac{128}{78,125})[/tex]
Solve the division
[tex](\frac{162}{4})+(\frac{1,953,125}{128})[/tex]
Find the LCD
LCD=128
so
[tex]\frac{32*162+1,953,125}{128}[/tex]
[tex]\frac{1,958,309}{128}[/tex]
Part 5) Find the area of triangle
The area of triangle is equal to
[tex]A=\frac{1}{2}(b)(h)[/tex]
substitute the given values
[tex]A=\frac{1}{2}(6)(1\frac{1}{3})[/tex]
Convert mixed number to an improper fraction
[tex]1\frac{1}{3}=1+\frac{1}{3}=\frac{1*3+1}{3}=\frac{4}{3}[/tex]
substitute
[tex]A=\frac{1}{2}(6)(\frac{4}{3})=4\ yd^2[/tex]
