Decimals with Fractions - SSAT Upper Level Quantitative (Math)

Simplify as follows:

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:

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

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

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.

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.

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 Vcan 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.

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.

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 .

Lets try to get these values into whole numbers. To do that, we need to make sure both numerator and denominator are whole numbers and we will look for the number with the most decimal places. This is found in the numerator. To get it into a whole number, we will multiply by or move the decimal places to the right. When you do that for the numerator, the same applies for the denominator. The new fraction is . Just reduce the fraction by factoring out a and the answer is shown.

Convert each fraction to decimal. We have and . Add these values. Remember when adding decimals, make sure the decimal places are all lined up.

Lets place a under the decimal. We are going to make a fraction. Essentially, it's still the same value. Now, we want a whole number in the numerator and what we do to the numerator is done to the denominator as well. Lets multiply the top by or move the decimal place spots to the right. Now we have . This needs to be reduced, so divide by twice until it can't be reduced any further. The answer should be .

First, lets convert the exponent into a fraction. Any negative exponent means it's the reciprocal of the positive exponent. So means . Now lets multiply it with the . This means or or .

Let be .

Lets multiply by . Now we have:

Lets subtract this equation with the first one and we get:

We do this because we want to get rid of the repeating decimals and now we have a simple equation, isolate and we arrive at the final answer.

Let be .

Lets multiply by . I chose , because there is a set of numbers that make the repeating decimal. To determine the value to multiply the repeating decimal, we do to the power of number in a set before it repeats.

Now we have:

Lets subtract this equation with the first one and we get:

We do this because we want to get rid of the repeating decimals and now we have a simple equation, isolate and we arrive at the final answer.

For each fraction, divide each numerator by its denominator to get its decimal representation, then subtract to find its difference from 0.6.

is the closest to 0.6 of the five.

Divide 8 by 15:

The 3 repeats, so the correct choice is .

Divide 11 by 18:

The 1 repeats infinitely, so this can be rewritten as .

Divide 5 by 27:

The group "185" repeats infinitely, so this can be written as .