Question

1. $\frac{x}{6}=10.2$
2. $\frac{2}{3}m=\frac{20}{27}$
3. $3.14r=7.85$
4. $\frac{9}{100}+h=\frac{1}{10}$
5. $-0.5v=-9$

Explanation:

Problem 5: Solve for $x$

Step1: Multiply both sides by 6
$\frac{x}{6} \times 6 = 10.2 \times 6$
Step2: Calculate the product
$x = 61.2$

Problem 7: Solve for $m$

Step1: Multiply by reciprocal $\frac{3}{2}$
$\frac{2}{3}m \times \frac{3}{2} = \frac{20}{27} \times \frac{3}{2}$
Step2: Simplify the fraction
$m = \frac{60}{54} = \frac{10}{9}$

Problem 9: Solve for $r$

Step1: Divide both sides by 3.14
$\frac{3.14r}{3.14} = \frac{7.85}{3.14}$
Step2: Compute the quotient
$r = 2.5$

Problem 11: Solve for $h$

Step1: Subtract $\frac{9}{100}$ from both sides
$h = \frac{1}{10} - \frac{9}{100}$
Step2: Convert and subtract fractions
$h = \frac{10}{100} - \frac{9}{100} = \frac{1}{100}$

Problem 13: Solve for $v$

Step1: Divide both sides by -0.5
$\frac{-0.5v}{-0.5} = \frac{-9}{-0.5}$
Step2: Calculate the quotient
$v = 18$

Answer:

1. $x = 61.2$
2. $m = \frac{10}{9}$
3. $r = 2.5$
4. $h = \frac{1}{100}$
5. $v = 18$