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Example Questions
Example Question #14 : Decimals With Fractions
What is the fractional equivalent of the sum 
First simplify 
Since 
This fraction can be reduced fully by using common factors. Simplify.
Example Question #1511 : Act Math
An acid-water solution is made in which 65% of the solution is water by volume. How many liters of acid are there in 50 liters of the solution?
17.5
38.5
12.5
32.5
17.5
35% of the solution is acid, therefore 0.35 * 50 = 17.5.
Example Question #1 : Fractions
0.3 < 1/3
4 > √17
1/2 < 1/8
–|–6| = 6
Which of the above statements is true?
0.3 < 1/3
1/2 < 1/8
4 > √17
–|–6| = 6
0.3 < 1/3
The best approach to this equation is to evaluate each of the equations and inequalities. The absolute value of –6 is 6, but the opposite of that value indicated by the “–“ is –6, which does not equal 6.
1/2 is 0.5, while 1/8 is 0.125 so 0.5 > 0.125.
√17 has to be slightly more than the √16, which equals 4, so“>” should be “<”.
Finally, the fraction 1/3 has repeating 3s which makes it larger than 3/10 so it is true.
Example Question #1 : Decimals With Fractions
How much less is 
Example Question #2 : Decimals With Fractions
The ogre under the bridge eats 
1/5 of the pizza is left after the ogre eats his share. The rats eat 3/4 of that, so 1/4 of 1/5 of the pizza is left.
1/4 * 1/5 = 1/20 = 5%
Example Question #3 : Decimals With Fractions
Which of the following numbers is between 1/5 and 1/6?
0.19
0.22
0.25
0.16
0.13
0.19
Long division shows that 1/5 = 0.20 and 1/6 = 0.16666... 0.13 < 0.16 < 1/6 < 0.19 < 1/5 < 0.22 < 0.25.
Example Question #4 : Decimals With Fractions
Trevor, James, and Will were each given a candy bar. Trevor ate 7/12 of his and Will ate 20% of his. If James ate more than Will and less than Trevor, what amount could James have eaten?
8/9
9/15
2/7
3/5
1/10
2/7
Turn Trevor and Will’s amounts into decimals to compare: 20% = 0.20 and 7/12 = 0.5083 rounded. When the answer choices are converted into decimals, 2/7 = 0.2871 is the only value between 0.20 and 0.5083.
Example Question #1516 : Act Math
Write the following fraction as a decimal rounded to three decimal places:
This is a problem best solved with a calculator, but we will also cover how to work it out by hand, as well as how to eliminate a few answers.
The given fraction is very close to 
To work this out by hand, set the problem up as division problem with 
Example Question #2 : Decimals
0.10
0.07
0.05
0.04
0.01
0.07
Multiply numerator by the other numerator and multiply the denominator by the other denominator for multiplication. To divide fractions, switch numerator and denominator and treat it as multiplication. The answer is 0.07.
Example Question #1 : How To Find The Amount Of Rational Numbers Between Two Numbers
How many rational numbers are there between 0 and 5?
6
0
Infinitely many
5
Infinitely many
Rational numbers are written in the form 
where 
; therefore, we can write infinitely many combinations of rational numbers between 0 and 1, e.g. 1/2, 1/3, 1/4, 1/5, 1/6 . . . .
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