Fraction calculator
This fractions calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step information.
The result:
14 5/10 - 12 9/10 = 8/5 = 1 3/5 = 1.6
The spelled result in words is eight fifths (or one and three fifths).How do we solve fractions step by step?
- Conversion a mixed number 14 5/10 to a improper fraction: 14 5/10 = 14 5/10 = 14 · 10 + 5/10 = 140 + 5/10 = 145/10
To find a new numerator:
a) Multiply the whole number 14 by the denominator 10. Whole number 14 equally 14 * 10/10 = 140/10
b) Add the answer from the previous step 140 to the numerator 5. New numerator is 140 + 5 = 145
c) Write a previous answer (new numerator 145) over the denominator 10.
Fourteen and five tenths is one hundred forty-five tenths. - Conversion a mixed number 12 9/10 to a improper fraction: 12 9/10 = 12 9/10 = 12 · 10 + 9/10 = 120 + 9/10 = 129/10
To find a new numerator:
a) Multiply the whole number 12 by the denominator 10. Whole number 12 equally 12 * 10/10 = 120/10
b) Add the answer from the previous step 120 to the numerator 9. New numerator is 120 + 9 = 129
c) Write a previous answer (new numerator 129) over the denominator 10.
Twelve and nine tenths is one hundred twenty-nine tenths. - Subtract: 145/10 - 129/10 = 145 - 129/10 = 16/10 = 2 · 8/2 · 5 = 8/5
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(10, 10) = 10. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 10 = 100. In the following intermediate step, cancel by a common factor of 2 gives 8/5.
In other words - one hundred forty-five tenths minus one hundred twenty-nine tenths is eight fifths.
Rules for expressions with fractions:
Fractions - write a forward slash to separate the numerator and 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 whole part and fraction and use a forward slash to input fraction i.e., 1 2/3 . A negative mixed fraction write for example as -5 1/2.
A slash is both a sign for fraction line and division, use a colon (:) for division fractions i.e., 1/2 : 1/3.
Decimals (decimal numbers) enter with a decimal dot . 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
• square root of a fraction: sqrt(1/16)
• 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:
- Subtract 27
Subtract these mixed fractions: 7 2/3 and 3 1/9.
- Closer to one
Here are two sums: A=1/2 + 1/3 and B=1/5 + 1/3. Which of the two sums is closer in value to 1? You must show your work and state clearly whether the answer is A or B.
- Shopping 7
I went into a shop with 210.00 and spent 1/7 of it on eggs and 1/2 of it on fruits. How much did I have left?
- Dive Attempt
Dive Attempt ; Fraction of the distance to the pool bottom Dive 1; 1/4 Dive 2; 2/3 Dive 3; 5/6 Tony's second dive was deeper than his first dive by what fraction of the pool?
- Negative fractions
I am a number that is equal to -3/4 subtracted from the sum of 3/5 and -1/3. What number am I?
- Ahsan
Ahsan has a large pizza. He gives 1/3 to his sister and 1/4 to his mother. What fraction of the pizza does Ahsan have left?
- Chocolates left
What is the equation for Mark? He had 84 boxes of candy to sell, half of which were dark chocolate and the other half white chocolate. He sold 75% of dark chocolate and 40% white. How many did you have left over?
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Last Modified: February 7, 2025