Find the fraction and colon notation for the ratio 3.8 to 7.4.

Fraction notation:

$\frac{3.8}{7.4}$

multiply numerator and denominator by 10

then divide numerator and denominator by 2

$\frac{38}{74}$

$\frac{19}{37}$

Fraction notation: $\frac{19}{37}$

Colon notation: $19:37$

Ling and Taylor took 12 days and 2 weeks respectively to complete the task. Find the ratio of Ling to Taylor in terms of time it took to complete the task.

For ratios, we have to convert them to the same unit.

2 weeks equals to 14 days.

$\frac{12}{14}$

$\frac{12}{14}=\frac{6}{7}$

An airplane traveled 2514 kilometers in 3 hours. What was the rate per hour (or speed)?

To find km per hour, divide the total distance traveled by the total time taken to travel that distance.

$\frac{2514\mathrm{ km}}{3\mathrm{ hrs}}=\frac{838\mathrm{ km}}{1\mathrm{ hr}}$

The airplane is travelling at 838 km/hr.

The heart of an elephant, at rest, beats an average of 1500 beats in 60 minutes. What is the rate in beats per minute?

To find beats per minute, divide the total number of beats by the time (in minutes) it took to reach that count.

$\frac{1500\mathrm{ beats}}{60\mathrm{ minutes}}=\frac{25\mathrm{ beats}}{1\mathrm{ minute}}$

The elephant at rest has a heart rate of 25 beats/minute.

$\frac{6.3}{0.9}=\frac{0.7}{n}$

To solve the proportion, cross multiply (multiply the denominator to the other side of the equation).

Steps to cross-multiplication:

1. Multiply both sides by 0.9
2. 0.9 gets cancelled out on the left side
3. Multiply both sides by n
4. n gets cancelled out on the right side

   $\frac{6.3}{0.9}=\frac{0.7}{n}$

$0.9\times \frac{6.3}{0.9}=\frac{0.7}{n}\times 0.9$

$0.9\times \frac{6.3}{0.9}=\frac{0.7}{n}\times 0.9$

   $6.3=\frac{0.7}{n}\times 0.9$

$n\times 6.3=\frac{0.7}{n}\times 0.9\times n$

$n\times 6.3=\frac{0.7}{\text{n}}\times 0.9\times \text{n}$

$n\times 6.3=0.7\times 0.9$

Now solve for the unknown by dividing the coefficient (number in front of the variable) back to the other side of the equation.

$\frac{n\times 6.3}{6.3}=\frac{0.7\times 0.9}{6.3}$

$n=\frac{0.7\times 0.9}{6.3}$

$n=0.1$

$\frac{y}{\frac{3}{5}}=\frac{\frac{7}{12}}{\frac{14}{15}}$

cross multiply

$\frac{y}{\frac{3}{5}}\times \frac{14}{15}=\frac{7}{12}$

$y\times \frac{14}{15}=\frac{7}{12}\times \frac{3}{5}$

now solve for the unknown $y$ by dividing the coefficient (number in front of the variable) back to the other side of the equation.

$\frac{y\times \frac{14}{15}}{\frac{14}{15}}=\frac{\frac{7}{12}\times \frac{3}{5}}{\frac{14}{15}}$

   $y=\frac{\frac{7}{12}\times \frac{3}{5}}{\frac{14}{15}}$

$y=\frac{3}{8}$

A serving of fish steak (cross section) is generally $\frac{1}{2}$ lb. How many servings can be prepared from a cleaned $18\frac{3}{4}$ lb tuna?

cross multiply

then solve for the variable

$\frac{1 serving}{\frac{1}{2}lb}=\frac{x servings}{18\frac{3}{4}lbs}$

$1\times 18\frac{3}{4}=\frac{1}{2}\times x$

$x=\frac{1\times 18\frac{3}{4}}{\frac{1}{2}}$

$x=37\frac{1}{2}$

The cleaned $18\frac{3}{4}$ lb tuna could prepare $37\frac{1}{2}$ servings.