Manipulation of Fractions - Basic Math

To find the reciprocal of a fraction, we simply need to switch the numerator and the denominator: for example, the reciprocal of a fraction is .

With integers, it helps to remember that all integers are really fractions with a denominator of :

, , and

The reciprocals of these numbers are and respectively.

Therefore, to solve the problem, we first need to find the reciprocals of and . If we keep in mind that , we can determine that the reciprocals are and , respectively. The product of these two numbers is:

is our final answer.

To find the reciprocal of a fraction, flip the numerator and the denominator.

Thus, the reciprocal of is .

Then we need to find the sum of 4 and 7, which is 11.

We will need to rewrite this in order to eliminate the negative exponent in the problem.

Because the denominator has a negative exponent, that is the same as having a positive exponent in the numerator. Therefore we can rewrite the problem as follows and then multiply.

To divide a term by a fraction, take the reciprocal of the fraction.

Then mutiply both terms.

To rewrite the mixed fractions as improper fractions we multiply the whole number by the denominator and add the numerator to get our new numerator. Our denominator stays the same. With this in mind we get the following:

and

.

Adding them gives us

.

The correct answer is .

The mixed number can be broken down as follows: 3 is the whole number, 1 is the numerator, and 4 is the denominator.

In order to convert the mixed number to an improper fraction, you must first multiply the denominator with the whole number and then add the numerator to it.

This answer is the numerator of the improper fraction:

.

The denominator of the fraction remains the same and the final answer is .

To add mixed numbers, you need to first change both of them into improper fractions.

Then, add the two improper fractions like you would any other fraction.

We need both fractions to have the same denominator before we can add them. Since 27 is a multiple of 3, we only need to change 1 fraction.

Now, we can add these fractions.

Finally, change the improper fraction back into a mixed number.

This question is asking you to change an improper fraction into a mixed number. To do that we will need to divide 75 by 6.

Now, we place the remainder as the numerator of a fraction with a denominator that is 6 because we just divided by six.

So then, 12 remainder 3 becomes .

Simplify this mixed fraction.

The correct answer is

is greater than half so you can eliminate and right away.

You should memorize common fractions:

To easily express a fraction as a decimal, we need to convert the denominator into a power of . We can do this by dividing both the top and the bottom of the given fraction by to express it in tenths.

, or six tenths, can be expressed as .

The best way to answer this question is to find the smallest fraction among the answer choices.

Comparing fractions can be done easily when they are converted to decimals.

Of these options, only , or 0.60, is less than .

So we first multiply the numerators:

We then multiply the denominators

Our resulting fraction is:

We reduce by dividing by 2 from the numerator and denominator.

For the numerator:

For the denominator:

The resulting fraction is:

We first multiply the numerators:

Then we multiply the denominators:

The resulting fraction is:

We divide the numerator and denominator by 12.

The numerator is:

The denominator results in:

Our resulting fraction is:

First, multiply the terms in the numerators:

Then multiply the terms in the denominators:

This results in the fraction .

Notice that both the numerator and denominator have a common factor of 6. Dividing both the numerator and denominator by 6 results in the simplest form fraction .

First, multiply the numerators of the terms:

Then, multiply the denominators of the terms:

The resulting fraction is . Note that the numerator and denominator both have a common factor of 6. Dividing both parts of the fraction by 6, we get the simplest form fraction .

First, multiply the numerators of each term:

Then, multiply the denominators:

This results in a fraction of . Since the numerator and denominator both have a common factor of 4, reduce both the numerator and denominator by dividing by 4 to get the simplest form fraction .

The correct answer is

is greater than half so you can eliminate and right away.

You should memorize common fractions:

To easily express a fraction as a decimal, we need to convert the denominator into a power of . We can do this by dividing both the top and the bottom of the given fraction by to express it in tenths.

, or six tenths, can be expressed as .

The best way to answer this question is to find the smallest fraction among the answer choices.

Comparing fractions can be done easily when they are converted to decimals.

Of these options, only , or 0.60, is less than .