Fractions - ACT Math

LCM = least common multiple = 2 x 2 x 3 x 5 = 60

GCF = greatest common factor = 3

Prime factor each number

3 = 3 x 1

12 = 3 x 4 = 3 x 2 x 2

30 = 5 x 6 = 5 x 2 x 3

LCM – GCF = 60 – 3 = 57

All of the denominators must be able to divide into the same number. First, see if the three smaller numbers (3, 4, 12) divide into the largest number (15)—NO. Then check the multiples of the largest number to see if the lower numbers divide into it:

15 * 2 = 30 (NO)

15 * 3 = 45 (NO)

15 * 4 = 60 (YES!)

People who prefer horror films = 1000 people x 7.5% = 1000 x 0.075 = 75 people

There are 20 total students in the class. 35% of 20 is 7. There are 7 boys in the class.

girls in the class.

To represent a percentage as a fraction, keep the percentage in the numerator and put in the denominator.

Therefore:

To convert an integer percentage into an improper fraction, set the percentage as a fraction over and simplify as far as you can. At that point, simply convert the improper fraction into a mixed fraction.

To convert a decimal percentage into a fraction, first convert it to a decimal:

Now, set ths as a fraction with as the denominator (expanding to as many significant digits as you need to line the fraction up):

Now just reduce your fraction!

To convert a percentage to a fraction, divide the percentage by 100, then simplify. The presence of a variable does not significantly affect this process.

To convert a fraction into a percentage, simply simplify the fraction into a decimal and multiply by 100.

The question asks to find what percent the last fundraiser makes up of the total funds raised. The information that's given is how much that last fundraiser made and what fraction the other fundraisers made.

This problem may be solved without the amount of money the last fundraiser raised. The reason is that we know that only 5 fundraisers were done. We're given what the fraction of the other fundraisers were.

If we were to add all the fractions together, including the last fundraiser, the sum of all would equal 1.

Fractions are another version of decimals but also another version of percentages. Percentages are essentially a prettier way of showing parts (or fractions) of a whole, which would be 100%. In the case of fractions, this is the same logic, which is why when all the fractions are summed, they equal 1. This 1 represents 100%.
Upon using lowest common denominators, adding the fractions together, and solving for x, x is calculated to be

We've almost obtained the final answer. Now it's just a matter of converting this fraction into a percent. As mentioned previously, fractions are another version of decimals. Think of decimals as being the middle conversion between fractions and percents. All that needs to be done to a decimal to turn it in to a percent is to multiply it by 100. For instance, .50 becomes 50%. Conversely, .50 is the same as in fraction form. Therefore, one half is 50%.
In order to solve for x in percent, the same conversion must be done.

To find of 80, . Next, subtract , for as the final answer.

0.825 in fraction form is . Simplifying the fraction equals .

If we were to divide 1 by the decimal value we get:

From this we can determine that 1 is our numerator and 9 is our denominator, giving us:

Convert all of the fractions to decimals. Thus, x is contained within the range of 0.33 < x < 0.76. The answers choices become 1/4 = 0.25, 4/12 = 0.33, 2/5 = 0.4, and 5/16 = 0.3125, respectively. Therefore, the only answer which is within the desired range is 2/5.

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:

To get the decimal from a fraction, divide the numerator by the denominator

When 5 is divided by 11, the decimal is 0.45 repeating, with a 5 in the hundreths place. The key here is to recognize that 100 is an even number, and the 5 in 0.45 is two places to the right of the decimal point (2 also being an even number).

1. Convert the fractions to decimals by division:

2. Add the corresponding whole numbers to the decimals:

3. Add the two decimals:

.45 is equivalent to 45 out of 100, or .

Divide both the numerator and denominator by 5 to simplify the fraction:

We need to convert into a fraction.

To do this, write down

Now, because the decimal goes to the hundreth place, multiply the numerator and denominator of the fraction by 100.

Now, simplify the fraction.