Answers & Step-by-step explanation:
#1. Insert given values:
[tex]16*\frac{1}{4} -4*6[/tex]
Simplify multiplication from left to right. Use the rule [tex]\frac{a}{b}*c =\frac{ac}{b}[/tex]:
[tex]\frac{16}{4}-4*6\\\\ 4-4*6[/tex]
Simplify multiplication:
[tex]4-24[/tex]
Simplify subtraction:
[tex]-20\\\\16a-4b=-20[/tex]
#2. Insert given values:
[tex]\frac{5*6}{32*\frac{1}{4} }[/tex]
Simplify multiplication:
[tex]\frac{30}{32*\frac{1}{4} }[/tex]
Simplify multiplication. Use the rule [tex]\frac{a}{b} *c=\frac{ac}{b}[/tex]:
[tex]\frac{30}{\frac{32}{4} }[/tex]
Simplify division:
[tex]\frac{30}{8}[/tex]
Simplify fraction:
[tex]\frac{15}{4} \\\\\frac{5b}{32a}=\frac{15}{4}[/tex]
#3. Insert given values:
[tex]12*\frac{1}{4} +(6-\frac{1}{4} -4)[/tex]
Simplify subtraction within parentheses. Convert to fractions. Use the rule [tex]a=\frac{a}{1}[/tex]:
[tex]\frac{6}{1} -\frac{1}{4} -\frac{4}{1}[/tex]
Make all denominators the same. Multiply top and bottom by 4 (only do this to the fractions with 1 as the denominator):
[tex]\frac{24}{4}-\frac{1}{4}-\frac{16}{4}[/tex]
Simplify subtraction. Subtract the numerators. The denominator will stay the same:
[tex]\frac{24}{4}-\frac{1}{4}-\frac{16}{4}=\frac{7}{4}[/tex]
Insert:
[tex]12*\frac{1}{4} +\frac{7}{4}[/tex]
Simplify multiplication. Use the rule [tex]\frac{a}{b} *c=\frac{ac}{b}[/tex]:
[tex]\frac{12}{4} =3[/tex]
Insert:
[tex]3+\frac{7}{4}[/tex]
Simplify addition. Convert the whole number to a fraction. Use the rule [tex]a=\frac{a}{1}[/tex]:
[tex]\frac{3}{1} +\frac{7}{4}[/tex]
Multiply top and bottom of the first term by 4:
[tex]\frac{12}{4}+\frac{7}{4}=\frac{19}{4} \\\\12a+(b-a-4)=\frac{19}{4}[/tex]
:Done
