### All SSAT Upper Level Math Resources

## Example Questions

### Example Question #322 : Number Concepts And Operations

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

**Possible Answers:**

None of the other responses is correct.

**Correct answer:**

### Example Question #31 : Decimals With Fractions

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

**Possible Answers:**

None of the other responses is correct.

**Correct answer:**

Simplify as follows:

### Example Question #1331 : Act Math

Simplify:

**Possible Answers:**

**Correct answer:**

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 #1 : How To Find Decimal Fractions

Rewrite the following fraction in simplest form:

**Possible Answers:**

**Correct answer:**

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

**Possible Answers:**

**Correct answer:**

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 #1 : How To Find Decimal Fractions

Convert to a decimal to three decimal places.

**Possible Answers:**

**Correct answer:**

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.

**Possible Answers:**

**Correct answer:**

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. **

**Possible Answers:**

**IV.**

**II**

**III**

**I**

**V**

**Correct answer:**

**IV.**

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 **I **is wrong**. **Choice **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. **

**Possible Answers:**

**I**

**II**

**III**

**V**

**IV**

**Correct answer:**

**III**

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 **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 . 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 ?

**Possible Answers:**

**Correct answer:**

By inspection, each answer choice has a denominator of with the exception of the fraction of . This can be fixed by dividing the fraction by which will be . To find the correct numerator value, just multiply by which is .

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