Fraction calculator
This calculator adds two fractions. First, all fractions are converted to a common denominator when fractions have different denominators. Find the Least Common Denominator (LCD) or multiply all denominators to find a common denominator. When all denominators are the same, subtract the numerators and place the result over the common denominator. Then, simplify the result to the lowest terms or a mixed number.
The result:
11/15 + 12/19 = 389/285 = 1 104/285 ≅ 1.3649123
The spelled result in words is three hundred eighty-nine two-hundred eighty-fifths (or one and one hundred four two-hundred eighty-fifths).How do we solve fractions step by step?
- Add: 11/15 + 12/19 = 11 · 19/15 · 19 + 12 · 15/19 · 15 = 209/285 + 180/285 = 209 + 180/285 = 389/285
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(15, 19) = 285. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 15 × 19 = 285. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - eleven fifteenths plus twelve nineteenths is three hundred eighty-nine two-hundred eighty-fifths.
Rules for expressions with fractions:
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
fraction and use a forward slash to input fractions i.e., 1 2/3 . An example of a negative mixed fraction: -5 1/2.
Because slash is both sign for fraction line and division, use a colon (:) as the operator of division fractions i.e., 1/2 : 1/3.
Decimals (decimal numbers) enter with a decimal point . and they are automatically converted to fractions - i.e. 1.45.
Math Symbols
| Symbol | Symbol name | Symbol Meaning | Example |
|---|---|---|---|
| + | plus sign | addition | 1/2 + 1/3 |
| - | minus sign | subtraction | 1 1/2 - 2/3 |
| * | asterisk | multiplication | 2/3 * 3/4 |
| × | times sign | multiplication | 2/3 × 5/6 |
| : | division sign | division | 1/2 : 3 |
| / | division slash | division | 1/3 / 5 |
| : | colon | complex fraction | 1/2 : 1/3 |
| ^ | caret | exponentiation / power | 1/4^3 |
| () | parentheses | calculate expression inside first | -3/5 - (-1/4) |
Examples:
• adding fractions: 2/4 + 3/4• subtracting fractions: 2/3 - 1/2
• multiplying fractions: 7/8 * 3/9
• dividing Fractions: 1/2 : 3/4
• reciprocal of a fraction: 1 : 3/4
• square of a fraction: 2/3^2
• cube of a fraction: 2/3^3
• exponentiation of a fraction: 1/2^4
• fractional exponents: 16 ^ 1/2
• adding fractions and mixed numbers: 8/5 + 6 2/7
• dividing integer and fraction: 5 ÷ 1/2
• complex fractions: 5/8 : 2 2/3
• decimal to fraction: 0.625
• Fraction to Decimal: 1/4
• Fraction to Percent: 1/8 %
• comparing fractions: 1/4 2/3
• multiplying a fraction by a whole number: 6 * 3/4
• square root of a fraction: sqrt(1/16)
• reducing or simplifying the fraction (simplification) : 4/22 - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction
• expression with brackets: 1/3 * (1/2 - 3 3/8)
• compound fraction: 3/4 of 5/7
• fractions multiple: 2/3 of 3/5
• divide to find the quotient: 3/5 ÷ 2/3
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 /) have the same priority and must be evaluated from left to right.
Fractions in word problems:
- My whole
My whole number is 88 if you add 5 thousandths, 8 tenths, and 7 thousandths. What number will I be? - A man 9
A man earns $2400 in his monthly salary. He spends 3/5 of his salary on food and rent. This month he decided to buy his family presents. What fraction of his money does he spend on presents? - Integer add to fraction
Seven is added to the sum of 4/5 and 6/7 - Adding denominators
Max is working out 2/3+7/9. He says the answer is 9/12. What mistake has Max made?
- Work out 2
Work out the sum of 2/6 and 1/6. Give your answer in its simplest form. - Katelyn
Katelyn ate ⅓ of an apple pie, and Chad ate ⅜ of the same pie. What fraction of the pie was eaten? - Sum three fractions Work out the sum of 1/4, 1/5, and 3/10.
- Evaluate 39
Evaluate the expression shown below and write your answer as a fraction in simplest form. (5)/(12) + (1)/(9) start fraction, 5, divided by, 12, end fraction, plus, one nine. - Add two fractions
What is 1/4 + 10/16?
- A cake 2 Karen sliced a cake into 10 slices. She ate 2/10 of it and after some time she ate another 4/10 of it. How much of the cake did Karen eat?
- Evaluate 27
Evaluate the expression shown below and write your answer as a fraction in the simplest form. (8)/(3)+ (11)/(12) - Sum of three fractions
What is the sum of 6/7, 1/2 & 3/4? - Add fractions Add/subtract the following similar fraction. Express the answer in the lowest terms if possible. Write your answer inside the box: 5/12 + 6/12
- Party pizza
At a party, there were some pizzas of the same size. Amelia ate 1/3 of a pizza. Chris ate 1/3 of a pizza. Miguel ate 5/12 of a pizza. How many pizzas did the three children eat?
What is the sum of 2/3 and 3/10?more math problems »