$\displaystyle \frac{3.5}{2.1} = \frac{3.5 \times 10}{2.1 \times 10} = \frac{35}{21} = \frac{35 \div 7}{21\div 7} = \frac{5}{3}$

Simplify as follows:

$\displaystyle \frac{1.28}{0.4} = \frac{1.28 \times 100}{0.4 \times 100} = \frac{128}{40} = \frac{128 \div 8}{40 \div 8} = \frac{16}{5}$

Begin by multiplying all of your decimal fractions by $\displaystyle \frac{100}{100}$:

$\displaystyle 0.35+\frac{0.75}{0.2}*\frac{100}{100}-0.4*\frac{0.5}{0.1}*\frac{100}{100}$

Simplify:

$\displaystyle 0.35+\frac{75}{20}-0.4*\frac{50}{10}=0.35+\frac{15}{4}-0.4*5$

Now perform the multiplication:

$\displaystyle 0.35+\frac{15}{4}-2$

The easiest thing to do next is to subtract $\displaystyle 2$ from $\displaystyle 0.35$:

$\displaystyle 0.35+\frac{15}{4}-2=\frac{15}{4}-1.65$

Next, convert $\displaystyle 1.65$ into the fraction $\displaystyle \frac{165}{100}$:

$\displaystyle \frac{15}{4}-\frac{165}{100}$

Now, the common denominator can be $\displaystyle 100$:

$\displaystyle \frac{15}{4}*\frac{25}{25}-\frac{165}{100}=\frac{375}{100}-\frac{165}{100}$

Simplify:

$\displaystyle \frac{375}{100}-\frac{165}{100}=\frac{210}{100}=\frac{21}{10}$

In order to rewrite $\displaystyle \frac{0.42}{0.84}$ in simplest form, multiply by a form of $\displaystyle 1$ that makes the fraction easier to reduce - in this case , $\displaystyle \frac{100}{100}$:

$\displaystyle \frac{0.42\times 100}{0.84\times 100}=\frac{42}{84}=\frac{1}{2}$

To find the decimal equivalent of a fraction, we just apply long division. We divide the numerator by the denominator.

So

$\displaystyle 1.000$

divided by

$\displaystyle 8$

This results in

$\displaystyle 0.125$

To convert any fraction to a decimal, the numerator is in the dividend and the denominator is the divisor. Then divide as you would normally. Just remember that since $\displaystyle 7$ can't divide into $\displaystyle 1$, add a decimal point after the $\displaystyle 1$ and however many $\displaystyle 0$s needed. 

See if you can reduce the fraction before converting to a decimal. They both are divisible by $\displaystyle 5$, so the new fraction becomes $\displaystyle \frac{7}{8}$. To convert any fraction to a decimal, the numerator is in the dividend and the denominator is the divisor. Then divide as you would normally. Just remember that since $\displaystyle 8$ can't divide into $\displaystyle 7$, add a decimal point after the $\displaystyle 7$ and however many $\displaystyle 0$s needed. 

There is no other way but to analyze each answer choice. We do have a decimal choice so lets compare the decimal to all of the fractions. Choice I. is $\displaystyle 0.5$. Even if you don't see that, first divide the numerator and denominator by $\displaystyle 9$, then $\displaystyle 11$, and you will see that it's $\displaystyle 0.5.$ Choice I is wrong. Choice II is definitely bigger than $\displaystyle 0.49$. Reason is because if you look at the numerator, if I double it, that number is $\displaystyle 202$. Because this value is bigger than the denominator, this means the overall fraction is bigger than $\displaystyle 0.5$ Remember, the bigger the denominator, the smaller the fraction. ($\displaystyle \frac{1}{2}$ is greater than $\displaystyle \frac{1}{3}$  even though $\displaystyle 3$ is bigger than $\displaystyle 2$) The converse is the same. If apply this reasoning to both Choice III and V, only choice V can be eliminated. Choice III is hard to figure out the exact decimal value but if we didn't have a calculator, we can surely compare their values. Let's force choice IV into a fraction. The only way to compare these fractions easily is by having the same denominator. So, lets multiply $\displaystyle 0.49$ with $\displaystyle 195$ which gives us $\displaystyle 95.55$. So we are comparing $\displaystyle 95.55$ with $\displaystyle 97$. Since $\displaystyle 97$ is greater than $\displaystyle 95.55$ this makes choice III bigger than $\displaystyle 0.49$ and therefore makes choice IV the smallest value. 

Convert the easy fractions to a decimal. Only choice IV is simple and that value is $\displaystyle 0.99$. Lets compare to choice III which also has a decimal. Choice III is greater than choice IV so thats elminated. Lets apply a techique to determine the strengths of fractions. Lets compare choice I and II. We will cross-multiply these values but when we cross-multiply, multiply the denominator of the left fraction with the numerator of the right fraction and the product will be written next to the numerator of the right fraction. Same is done with multiplying the denominator of the right fraction with the numerator of the left fraction and the product will be written next to the numerator of the left fraction. Whichever product is greater means that fraction is greater than the other. So with choice I and II, we have products of 10200 versus 10201. Clearly 10201 is greater and that corresponds to choice II so choice I is eliminated. Lets compare now choice II and choice V. Applying this method, gives choice II the edge here. So now lets compare choice III and II. Lets convert the decimal to a fraction with a denominator of $\displaystyle 102$. This gives us a comparison of $\displaystyle 101.082$ to $\displaystyle 101$ which means choice III is clearly the biggest.  

By inspection, each answer choice has a denominator of $\displaystyle 150$ with the exception of the fraction of $\displaystyle \frac{200}{300}$. This can be fixed by dividing the fraction by $\displaystyle 2$ which will be $\displaystyle \frac{100}{150}$. To find the correct numerator value, just multiply $\displaystyle 0.4$ by $\displaystyle 150$ which is $\displaystyle 60$.