# SSAT Upper Level Math : How to find decimal fractions

## Example Questions

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### Example Question #1 : How To Find Decimal Fractions

Rewrite as a fraction with whole numerator and denominator in lowest terms:

None of the other responses is correct.

Explanation:

### Example Question #2 : How To Find Decimal Fractions

Rewrite as a fraction with whole numerator and denominator in lowest terms:

None of the other responses is correct.

Explanation:

Simplify as follows:

### Example Question #1 : How To Find Decimal Fractions

Simplify:

Explanation:

Begin by multiplying all of your decimal fractions by :

Simplify:

Now perform the multiplication:

The easiest thing to do next is to subtract  from :

Next, convert  into the fraction :

Now, the common denominator can be :

Simplify:

### Example Question #3 : How To Find Decimal Fractions

Rewrite the following fraction in simplest form:

Explanation:

In order to rewrite  in simplest form, multiply by a form of  that makes the fraction easier to reduce - in this case , :

### Example Question #4 : How To Find Decimal Fractions

What is the decimal fraction of

Explanation:

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

So

divided by

This results in

### Example Question #5 : How To Find Decimal Fractions

Convert  to a decimal to three decimal places.

Explanation:

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  can't divide into , add a decimal point after the  and however many s needed.

### Example Question #6 : How To Find Decimal Fractions

Convert  to a decimal. Answer to 3 decimal places.

Explanation:

See if you can reduce the fraction before converting to a decimal. They both are divisible by , so the new fraction becomes . 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  can't divide into , add a decimal point after the  and however many s needed.

### Example Question #7 : How To Find Decimal Fractions

Which of the following is the smallest?

I.

II.

III.

IV.

V.

III

I

V

IV.

II

IV.

Explanation:

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 . Even if you don't see that, first divide the numerator and denominator by , then , and you will see that it's  Choice is wrongChoice II is definitely bigger than . Reason is because if you look at the numerator, if I double it, that number is . Because this value is bigger than the denominator, this means the overall fraction is bigger than  Remember, the bigger the denominator, the smaller the fraction. ( is greater than   even though  is bigger than ) 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  with  which gives us . So we are comparing  with . Since  is greater than  this makes choice III bigger than  and therefore makes choice IV the smallest value.

### Example Question #8 : How To Find Decimal Fractions

Which of the following is the biggest?

I.

II.

III.

IV.

v.

II

V

I

IV

III

III

Explanation:

Convert the easy fractions to a decimal. Only choice IV is simple and that value is . 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 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 . This gives us a comparison of  to  which means choice III is clearly the biggest.

### Example Question #9 : How To Find Decimal Fractions

Which fraction is equivalent to the decimal of ?