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:
9 1/8 - 3 5/6 = 127/24 = 5 7/24 ≅ 5.2916667
Spelled result in words is one hundred twenty-seven twenty-fourths (or five and seven twenty-fourths).How do we solve fractions step by step?
- Conversion a mixed number 9 1/8 to a improper fraction: 9 1/8 = 9 1/8 = 9 · 8 + 1/8 = 72 + 1/8 = 73/8
To find a new numerator:
a) Multiply the whole number 9 by the denominator 8. Whole number 9 equally 9 * 8/8 = 72/8
b) Add the answer from the previous step 72 to the numerator 1. New numerator is 72 + 1 = 73
c) Write a previous answer (new numerator 73) over the denominator 8.
Nine and one eighth is seventy-three eighths. - Conversion a mixed number 3 5/6 to a improper fraction: 3 5/6 = 3 5/6 = 3 · 6 + 5/6 = 18 + 5/6 = 23/6
To find a new numerator:
a) Multiply the whole number 3 by the denominator 6. Whole number 3 equally 3 * 6/6 = 18/6
b) Add the answer from the previous step 18 to the numerator 5. New numerator is 18 + 5 = 23
c) Write a previous answer (new numerator 23) over the denominator 6.
Three and five sixths is twenty-three sixths. - Subtract: 73/8 - 23/6 = 73 · 3/8 · 3 - 23 · 4/6 · 4 = 219/24 - 92/24 = 219 - 92/24 = 127/24
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(8, 6) = 24. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 6 = 48. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - seventy-three eighths minus twenty-three sixths is one hundred twenty-seven twenty-fourths.
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:
- 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?
- 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.
- Paul ate
Paul ate 2/8 of a cake and his brother 3/8. What fraction of the cake is left for the parents?
- You have 2
You have 6/13 of a pie. If you share 9/10, how much will you have left?
- Sarah 5
Sarah had ten cookies and ate one-half of a cookie. How much would she have left?
- Difference between fractions
What is the difference when you take away 1/6 from 2/8?
- 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?
- A less than B
What is 3/5 less than 11/12? (Answer should be in proper or improper only: Example 1/2, -1/2, 3/2, and -3/2)
- Flags 2
1/4 are white and another 1/4 are yellow. What fraction of the flags are either white or yellow?
- Terrell
Terrell goes apple-picking. He uses 3/10 of his apples. Then he uses 5/10. What fraction of his apples does he have 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?
- Mr. Vandar
Mr. Vandar washed 1/4 of his laundry. His son washed 2/7 of it. Who washed most of the laundry? How much of the laundry still needs to be washed?
- Students 4252
Out of 35 pupils in class 15, they went on a trip. What part of the students went on a journey, and what remained at school?
- 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
more math problems »