What is 2/3 + 1/4 as a fraction

2/3 + 1/4 is 11/12.

Steps for adding fractions

1. Find the least common denominator or LCM of the two denominators:
   LCM of 3 and 4 is 12

   Next, find the equivalent fraction of both fractional numbers with denominator 12

2. For the 1st fraction, since 3 × 4 = 12,
   2/3 = 2 × 4/3 × 4 = 8/12
3. Likewise, for the 2nd fraction, since 4 × 3 = 12,
   1/4 = 1 × 3/4 × 3 = 3/12
4. Add the two like fractions:
   8/12 + 3/12 = 8 + 3/12 = 11/12
5. So, 2/3 + 1/4 = 11/12

MathStep (Works offline)

Related: 4/3+1/4 2/3+2/4 2/6+1/4 2/3+1/8 6/3+1/4 2/3+3/4 2/9+1/4 2/3+1/12 10/3+1/4 2/3+5/4 2/15+1/4 2/3+1/20 14/3+1/4 2/3+7/4 2/21+1/4 2/3+1/28

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

To find out, we try dividing it by 2...

Nope! So now we try the next greatest prime number, 3...

Nope! So now we try the next greatest prime number, 5...

Nope! So now we try the next greatest prime number, 7...

No good. 7 is larger than 5. So we're done reducing.

Page 2

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

When adding or subtracting fractions, we must always start by putting the fractions over the same denominator, that is the number on the bottom half of the fraction. To do this, we need to find a number which we can divide by both the current denominators 3 and 4, i.e. we need to find the lowest common denominator of 3 and 4. In this case, the lowest common denominator is 12. So we need to change both fractions so that their denominator is 12. We will start by changing 2/3 to ?/12. To do this , we need to multiply the first denominator (3) by 4 to get 12, and so we also need to multiply the numerator by 4. So, we get 2x4=8 and the fraction becomes 8/12. We must always multiply the numerator by the same number as we multiply the denominator by. For the second fraction, 1/4, we need to multiply the first denominator (4) by 3 to get the second denominator (12), so we also need to multiply the numerator by 3, giving 1x3=3 and the fraction becomes 3/12. Now we have 8/12 + 3/12 = ? To add fractions which are already in the same denominator, as these fractions are, all we need to do is add the numerators together (8+3=11) and put it over the denominator which both fractions are already in (12) and so our final answer is 11/12. 

This calculator adds two fractions. When fractions have different denominators, firstly convert all fractions to common denominator. Find Least Common Denominator (LCD) or simple multiply all denominators to find common denominator. When all denominators are same, simply add the numerators and place the result over the common denominator. Then simplify the result to the lowest terms or a mixed number.

Spelled result in words is eleven twelfths.

How do we solve fractions step by step?

1. Add: 2/3 + 1/4 = 2 · 4/3 · 4 + 1 · 3/4 · 3 = 8/12 + 3/12 = 8 + 3/12 = 11/12
   For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(3, 4) = 12. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 4 = 12. In the following intermediate step, it cannot further simplify the fraction result by canceling.
   In other words - two thirds plus one quarter is eleven twelfths.

Fractions - use a forward slash to divide the numerator by the denominator, i.e., for five-hundredths, enter 5/100. If you use mixed numbers, leave a space between the whole and fraction parts.

Mixed numerals (mixed numbers or fractions) keep one space between the integer and

The calculator follows well-known rules for the order of operations. The most common mnemonics for remembering this order of operations are:
PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction
BODMAS - Brackets, Of or Order, Division, Multiplication, Addition, Subtraction.
GEMDAS - Grouping Symbols - brackets (){}, Exponents, Multiplication, Division, Addition, Subtraction.
MDAS - Multiplication and Division have the same precedence over Addition and Subtraction. The MDAS rule is the order of operations part of the PEMDAS rule.
Be careful; always do multiplication and division before addition and subtraction. Some operators (+ and -) and (* and /) has the same priority and then must evaluate from left to right.