Fraction calculator
This fraction calculator performs basic and advanced fraction operations, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps in finding value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.
The result:
6 1/2 - 2 3/4 = 15/4 = 3 3/4 = 3.75
Spelled result in words is fifteen quarters (or three and three quarters).How do we solve fractions step by step?
- Conversion a mixed number 6 1/2 to a improper fraction: 6 1/2 = 6 1/2 = 6 · 2 + 1/2 = 12 + 1/2 = 13/2
To find a new numerator:
a) Multiply the whole number 6 by the denominator 2. Whole number 6 equally 6 * 2/2 = 12/2
b) Add the answer from the previous step 12 to the numerator 1. New numerator is 12 + 1 = 13
c) Write a previous answer (new numerator 13) over the denominator 2.
Six and one half is thirteen halfs. - Conversion a mixed number 2 3/4 to a improper fraction: 2 3/4 = 2 3/4 = 2 · 4 + 3/4 = 8 + 3/4 = 11/4
To find a new numerator:
a) Multiply the whole number 2 by the denominator 4. Whole number 2 equally 2 * 4/4 = 8/4
b) Add the answer from the previous step 8 to the numerator 3. New numerator is 8 + 3 = 11
c) Write a previous answer (new numerator 11) over the denominator 4.
Two and three quarters is eleven quarters. - Subtract: 13/2 - 11/4 = 13 · 2/2 · 2 - 11/4 = 26/4 - 11/4 = 26 - 11/4 = 15/4
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(2, 4) = 4. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 4 = 8. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - thirteen halfs minus eleven quarters is fifteen quarters.
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:
- Peter's calculation
Peter wrote the following: 7 1/4 - 3 3/4 = 4 2/4 = 4 1/2 . Is Peter's calculation correct? Using words (math vocabulary) and numbers to explain why he is correct or incorrect.
- 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?
- The cat
The cat starts with 4/6 of a cup in his bowl. She eats 1/4 of a cup of food. How much food is left?
- You have 2
You have 6/13 of a pie. If you share 9/10, how much will you have left?
- Cherries 2
If a farmer reaped 636 cherries and he sold one-third to a shopkeeper, how many did he retain?
- King
King had four sons. First inherit 1/2, second 1/4, third 1/5 of property. What part of the property was left to the last of the brothers?
- You have 4
You have eaten ⅔ of a pizza. Your friend eats what is left. How much of the original pizza is left?
- Subtract 19
Subtract as indicated. 11/10 - (- 2/5)
- Mr Peter
Mr Peter bought a pizza. He ate 2/5. His son ate 1/5, and the rest his wife ate. What amount of pizza did his wife eat?
- Fraction subtraction
Find the difference. Reduce the answer to the simplest form: 1.) ¾ - 1/8 = 2.) ½ - 1/8 = 3.) ½ - 1/6 = 4.) 7/8 - ¾ = 5.) 1/5 - 1/10
- Marbles 82374
How many marbles do I have if I am missing a fifth of 15 marbles?
- Sundar
Sundar has 50 chocolates. He gave 2/5 of these chocolates to Ram and ate 1/5 of them. How many chocolates are left with Sundar?
- From a
From a 1-meter ribbon, Ericka cut 2/4 meters for her hat and another 1/4 meters for her bag. How long was the remaining piece?
- Difference of two fractions
What is the difference between 1/2 and 1/6? (Write the answer as a fraction in the lowest terms. )
- The recipe
The recipe they are following requires 7/8 cups of milk. Tom already put 3/8 cups of milk. How much milk should Lea add to follow the recipe?
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