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 2/3 - 2 6/7 = 143/21 = 6 17/21 ≅ 6.8095238
Spelled result in words is one hundred forty-three twenty-firsts (or six and seventeen twenty-firsts).How do we solve fractions step by step?
- Conversion a mixed number 9 2/3 to a improper fraction: 9 2/3 = 9 2/3 = 9 · 3 + 2/3 = 27 + 2/3 = 29/3
To find a new numerator:
a) Multiply the whole number 9 by the denominator 3. Whole number 9 equally 9 * 3/3 = 27/3
b) Add the answer from the previous step 27 to the numerator 2. New numerator is 27 + 2 = 29
c) Write a previous answer (new numerator 29) over the denominator 3.
Nine and two thirds is twenty-nine thirds. - Conversion a mixed number 2 6/7 to a improper fraction: 2 6/7 = 2 6/7 = 2 · 7 + 6/7 = 14 + 6/7 = 20/7
To find a new numerator:
a) Multiply the whole number 2 by the denominator 7. Whole number 2 equally 2 * 7/7 = 14/7
b) Add the answer from the previous step 14 to the numerator 6. New numerator is 14 + 6 = 20
c) Write a previous answer (new numerator 20) over the denominator 7.
Two and six sevenths is twenty sevenths. - Subtract: 29/3 - 20/7 = 29 · 7/3 · 7 - 20 · 3/7 · 3 = 203/21 - 60/21 = 203 - 60/21 = 143/21
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(3, 7) = 21. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 7 = 21. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - twenty-nine thirds minus twenty sevenths is one hundred forty-three twenty-firsts.
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 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? - 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. - The bread 2
Sandra and Tylar baked two loaves of bread. On Monday, they ate 1/2 of one loaf. On Tuesday, they ate 1/3 of one loaf of bread. How much bread is left?
- Fraction expression
Which expression is equivalent to : Minus 9 minus left parenthesis minus 4 start fraction 1 divided by 3 end fraction right parenthesis - 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? - Evaluate 38
Evaluate the expression shown below and write your answer as a fraction in simplest form. (5)/(6) - (3)/(8) Transcription: start fraction, 5, divided by, 6, end fraction, minus, start fraction, 3, divided by, 8, end fraction - Flags 2
1/4 are white and another 1/4 are yellow. What fraction of the flags are either white or yellow? - Unload truck
Andy has just moved and is beginning to unload his boxes. The truck is currently 11/12 of the way full. He unloads 1/4 more of it. How much more does he have to unload?
- 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) - 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? - Cherries 2
If a farmer reaped 636 cherries and he sold one-third to a shopkeeper, how many did he retain? - Difference of two fractions
What is the difference between 1/2 and 1/6? (Write the answer as a fraction in the lowest terms. ) - A cake
A cake has 46 slices. Harry ate 16 slices, and Jack ate 26 slices, Dave ate 0 & Mary ate 1 slice. What fraction of the cake is remaining?
more math problems »