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question 26
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solve the following: 6\frac{1}{4} \div \frac{75}{8} = \frac{x}{y}
solve for x=
solve for y=
question 27
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solve the following: \frac{1}{100} \div \frac{1}{80} = \frac{x}{y}
solve for x=
solve for y=
question 28
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solve the following \frac{3}{8} \times \frac{4}{7} \times \frac{14}{9} = \frac{x}{y}
x =
y =

Explanation:

Question 26

Step1: Convert mixed number to improper fraction

$6\frac{1}{4}=\frac{6\times4 + 1}{4}=\frac{25}{4}$

Step2: Divide by multiplying reciprocal

$\frac{25}{4}\div\frac{75}{8}=\frac{25}{4}\times\frac{8}{75}$

Step3: Simplify the fraction

$\frac{25\times8}{4\times75}=\frac{200}{300}=\frac{2}{3}$
So, $\frac{x}{y}=\frac{2}{3}$, thus $x = 2$, $y = 3$

Step1: Divide by multiplying reciprocal

$\frac{1}{100}\div\frac{1}{80}=\frac{1}{100}\times\frac{80}{1}$

Step2: Simplify the fraction

$\frac{80}{100}=\frac{4}{5}$
So, $\frac{x}{y}=\frac{4}{5}$, thus $x = 4$, $y = 5$

Step1: Multiply the fractions

$\frac{3}{8}\times\frac{4}{7}\times\frac{14}{9}=\frac{3\times4\times14}{8\times7\times9}$

Step2: Simplify the numerator and denominator

$3\times4\times14 = 168$, $8\times7\times9 = 504$
$\frac{168}{504}=\frac{1}{3}$ (dividing numerator and denominator by 168)
So, $\frac{x}{y}=\frac{1}{3}$, thus $x = 1$, $y = 3$

Answer:

solve for x= $\boldsymbol{2}$
solve for y= $\boldsymbol{3}$

Question 27