What is 2/3 of 3/4 as a fraction

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For example, in order to get a decimal fraction, 3/4 is expanded to 75/100 by multiplying the numerator by 25 and denominator by 25:

Other method is to do long division of 3 divided by 4.

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See also

Use this fraction calculator for adding, subtracting, multiplying and dividing fractions. Answers are fractions in lowest terms or mixed numbers in reduced form.

Input proper or improper fractions, select the math sign and click Calculate. This is a fraction calculator with steps shown in the solution.

If you have negative fractions insert a minus sign before the numerator. So if one of your fractions is -6/7, insert -6 in the numerator and 7 in the denominator.

Sometimes math problems include the word "of," as in What is 1/3 of 3/8? Of means you should multiply so you need to solve 1/3 × 3/8.

To do math with mixed numbers (whole numbers and fractions) use the Mixed Numbers Calculator.

Math on Fractions with Unlike Denominators

There are 2 cases where you need to know if your fractions have different denominators:

• if you are adding fractions
• if you are subtracting fractions

How to Add or Subtract Fractions

1. Find the least common denominator
2. You can use the LCD Calculator to find the least common denominator for a set of fractions
3. For your first fraction, find what number you need to multiply the denominator by to result in the least common denominator
4. Multiply the numerator and denominator of your first fraction by that number
5. Repeat Steps 3 and 4 for each fraction
6. For addition equations, add the fraction numerators
7. For subtraction equations, subtract the fraction numerators
8. Convert improper fractions to mixed numbers
9. Reduce the fraction to lowest terms

How to Multiply Fractions

1. Multiply all numerators together
2. Multiply all denominators together
3. Reduce the result to lowest terms

How to Divide Fractions

1. Rewrite the equation as in "Keep, Change, Flip"
2. Keep the first fraction
3. Change the division sign to multiplication
4. Flip the second fraction by switching the top and bottom numbers
5. Multiply all numerators together
6. Multiply all denominators together
7. Reduce the result to lowest terms

Fraction Formulas

There is a way to add or subtract fractions without finding the least common denominator (LCD). This method involves cross multiplication of the fractions. See the formulas below.

You may find that it is easier to use these formulas than to do the math to find the least common denominator.

The formulas for multiplying and dividing fractions follow the same process as described above.

Adding Fractions

The formula for adding fractions is:

\( \dfrac{a}{b} + \dfrac{c}{d} = \dfrac{ad + bc}{bd} \)

Example steps:

\( \dfrac{2}{6} + \dfrac{1}{4} = \dfrac{(2\times4) + (6\times1)}{6\times4} \)

\( = \dfrac{14}{24} = \dfrac {7}{12} \)

The formula for subtracting fractions is:

\( \dfrac{a}{b} - \dfrac{c}{d} = \dfrac{ad - bc}{bd} \)

Example steps:

\( \dfrac{2}{6} - \dfrac{1}{4} = \dfrac{(2\times4) - (6\times1)}{6\times4} \)

\( = \dfrac{2}{24} = \dfrac {1}{12} \)

Multiplying Fractions

The formula for multiplying fractions is:

\( \dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{ac}{bd} \)

Example steps:

\( \dfrac{2}{6} \times \dfrac{1}{4} = \dfrac{2\times1}{6\times4} \)

\( = \dfrac{2}{24} = \dfrac {1}{12} \)

Dividing Fractions

The formula for dividing fractions is:

\( \dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{ad}{bc} \)

Example steps:

\( \dfrac{2}{6} \div \dfrac{1}{4} = \dfrac{2\times4}{6\times1} \)

\( = \dfrac{8}{6} = \dfrac {4}{3} = 1 \dfrac{1}{3} \)

Related Calculators

To perform math operations on mixed number fractions use our Mixed Numbers Calculator. This calculator can also simplify improper fractions into mixed numbers and shows the work involved.

If you want to simplify an individual fraction into lowest terms use our Simplify Fractions Calculator.

For an explanation of how to factor numbers to find the greatest common factor (GCF) see the Greatest Common Factor Calculator.

If you are simplifying large fractions by hand you can use the Long Division with Remainders Calculator to find whole number and remainder values.

Notes

The fraction calculator will add, subtract, multiply and divide fractions with like or unlike denominators. It will also enable us to simplify fractions, convert fractions to decimals and decimals to fractions.

First, simply input the values a,b,c,d for the fractions \(\frac{a}{b}\) and \(\frac{c}{d}\), then the mathematical operation you wish to perform (+, -, x, /). The calculator will instantly and accurately perform the operation and give the answer in the simplest form. You can also use the calculator to check your work that you’ve done manually.

Adding and Subtracting Fractions

Like (Common) Denominators

Add or subtract the numerators and keep the denominators the same.

Ex: \(\frac{3}{5} + \frac{4}{5}\)

Since the denominator is 5 in both fractions, add 3 and 4 to get 7. The denominator remains 5, so the answer is 7/5.

Since the denominator is 6 in both fractions, subtract 5 from 7 to get 2. The fraction is then \(\frac{2}{6}\).

But now we can simplify \(\frac{2}{6}\).  To simplify, look for a common factor. Notice that 2 divides evenly into both 2 and 6. Therefore, divide both numerator and denominator by 2 to get \(\frac{1}{3}\). The fraction is now simplified.

Unlike Denominators

To add and subtract unlike denominators, first calculate the common denominator. The easiest way to do that is to multiply the two denominators. This wont always give the lowest common denominator, but you can simplify after adding and subtracting.

Ex: \(\frac{2}{5} + \frac{4}{7}\)

A common denominator is 5(7) = 35.  Since the denominator in the first fraction is multiplied by 7, the numerator must also be multiplied by 7 to get \(\frac{14}{35}\). Since the denominator in the second fraction is multiplied by 5, the numerator must be as well to get \(\frac{20}{35}\).

Now add \(\frac{14}{35}+\frac{20}{35}=\frac{34}{35}\)

Subtraction is done the same way, just subtract the two fractions after rewriting the fractions with their common denominators. If you must simplify, remember to divide by the greatest common factor.

Multiplying and Dividing Fractions

When multiplying fractions, simply multiply across the numerators and across the denominators. Then simplify. You can also simplify first before multiplying.

Ex: \(\frac{2}{9}\times\frac{4}{7}\)

Multiply  2 and 4 to get 8. Then multiply 9 and 7 to get 63. The result is \(\frac{8}{63}\). There is no simplification needed since the greatest common factor is 1.

Now suppose we wish to divide \(\frac{2}{9} \div \frac{4}{7}\).

When dividing fractions, take the first fraction and multiply by the reciprocal of the second. The reciprocal is just interchanging the numerator and denominator. The division problem turns into a multiplication problem.

2 × 7 = 14 and 9 × 4 = 36. So the answer is \(\frac{14}{36}\). But notice this isn’t in simplest form. The greatest common factor is 2, so dividing both by 2 gives the simplified answer of \(\frac{7}{18}\).

Converting Fractions to Decimals

The convert fraction to decimal calculator will take any fraction and change it to a decimal.

The method to change a fraction to a decimal is quite simple. Just divide the numerator by the denominator.

Change \(\frac{14}{25}\) to a decimal.

Divide 14 by 25 to get 0.56.  You can do this on a calculator or manually using long division. Some fractions are not as easy to work by hand, particularly those that are non-terminating. Those are much easier to work on this calculator.

But if you choose to solve manually, the calculator makes a great tool to instantly check your work.

Converting Decimals to Fractions

Changing decimals to fractions is the inverse of changing fractions to decimals. The calculator will perform this rapidly with accurate results by simply entering the decimal value.

To convert manually, take the decimal and convert to a whole number, then divide by 10 raised to the number of decimal places moved to the right to convert the number. From there you can simplify the fraction if needed.

Ex:

Convert 0.68 to a fraction. To change 0.68 to a whole number, move the decimal point 2 places ot the right to get 68. Since we moved 2 decimal places, divide 68 by 10 raised to the second power, which is 100.

That gives us \(\frac{68}{100}\). Now we can simplify the fraction by looking for a common factor. If you don’t know the greatest common factor you can start by dividing by any common factor. Notice 68 and 100 are both divisible by 2. This reduces the fraction to 34/50. From here, notice that both 34 and 50 are divisible by 2. This reduces to \(\frac{17}{25}\), which is the simplified answer.

You can check your manual calculations using this calculator or simply input the information for your particular problem for nearly instant, accurate results!