Fractions - ACT Math

Set up an equation where you add the same unknown number (x) to both the numerator and the denominator of the original fraction, and set the equation equal to .

Cross-multiply the fractions to simplify.

Now, solve for x.

To solve this, subtract 1 1/2 from both sides. Convert to common denominators.

4 1/3 – 1 1/2 = 4 2/6 – 1 3/6.

In order to subtract, you'll want to "borrow" from the 4 2/6. Rewrite 4 2/6 as 3 8/6 and then subtract 1 3/6 from this. Your solution is 2 5/6. Most calculators will also do these calculations for you.

To solve this equation, you must first make sure that both fractions have a common denominator.

In this case the common denominator will be 12:

Then you perform your operation:

To find this answer, first you need to set up your equation:

And you need to get rid of the decimal in the numerator. We can do this by multiplying each fraction by 2/2.

Then solve for your answer:

Begin by isolating your variable:

Next, you need to find the common denominator. For the left side of your equation, it is . For the right, it is . This means that you need to rewrite as follows:

Now, simplify and combine terms:

You can further simplify the left side:

Next, multiply both sides by . This gives you:

First, you must convert your fractions to the common denominator of :

Next, do your subtraction:

Next, you must be very careful. Notice how you must handle your subtractions in order to maintain the correct distribution of signs:

Now, carefully distribute for each group:

Next, simplify:

Factor out the common in the numerator:

There is still a common , but that does not help you get your fraction into the form found in the answers.

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.

To know the minumum number of baskets required for each size, simply divide the number of fruits required by the basket capacity for each fruit:

(we must round up to nearest whole number for practical purposes)

Since we need to bring both the large and small fruits to the event, we need to add these two values: baskets total.

When working with fractions or percents, it is often really helpful to write out an equation showing what you need to find. In this case, we know that three-fifths of Felicia's weekly pay (our variable—let's call it ) over six weeks results in , so our equation looks like this:

So, we want to simplify and rearrange this equation. Start by multiplying the with the :

Then, multiply both sides by , the reciprocal of :

So, , and we now know Felicia's weekly pay!

To answer this question, we need to set up a proportion for how many pounds of apples it takes to make a certain number of containers, knowing that 45 pounds of apples makes 30 containers of apple juice. We want to figure out how many pounds of apples it would take to make 20 containers of apple juice.

To set up a proportion, we must put the amounts that correspond to each other in the same fraction and equate it to a similar fraction. In this case, we will set up fractions that show containers of apple juice over pounds of apples. So for this data:

Note that we put both of the values for containers of apple juice in the numerator of the fractions and pounds of apples in the denominator. Here, is the value we are looking for.

We then cross-multiply by taking the denominator of each fraction and multiplying each side of the equation by it so that we can create an equation that is solved easier.

Therefore, it takes pounds of apples to make containers of apple juice.

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.

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:

A pie is made up of crust, apples, sugar, and the rest is jelly. What is the ratio of crust to jelly?

To compute this ratio, you must first ascertain how much of the pie is jelly. This is:

Begin by using the common denominator :

So, the ratio of crust to jelly is:

This can be written as the fraction:

, or

This problem is really an easy fraction division. You should first divide the lemon juice amount by the water amount:

Remember, to divide fractions, you multiply by the reciprocal:

This is the same as saying:

To find a ratio like this, you simply need to make the fraction that represents the division of the two values by each other. Therefore, we have:

Recall that division of fractions requires you to multiply by the reciprocal:

,

which is the same as:

This is the same as the ratio:

To average, we have to add the values and divide by two. To do this we need to find a common denomenator of 6. We then add and divide by 2, yielding 4.5/6. This reduces to 3/4.