Fraction calculator
This 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 fraction value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.
Result:
2 1/7 + 1 2/5 = 124/35 = 3 19/35 ≅ 3.5428571
Spelled result in words is one hundred twenty-four thirty-fifths (or three and nineteen thirty-fifths).How do you solve fractions step by step?
- Conversion a mixed number 2 1/7 to a improper fraction: 2 1/7 = 2 1/7 = 2 · 7 + 1/7 = 14 + 1/7 = 15/7
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 previous step 14 to the numerator 1. New numerator is 14 + 1 = 15
c) Write a previous answer (new numerator 15) over the denominator 7.
Two and one seventh is fifteen sevenths - Conversion a mixed number 1 2/5 to a improper fraction: 1 2/5 = 1 2/5 = 1 · 5 + 2/5 = 5 + 2/5 = 7/5
To find a new numerator:
a) Multiply the whole number 1 by the denominator 5. Whole number 1 equally 1 * 5/5 = 5/5
b) Add the answer from previous step 5 to the numerator 2. New numerator is 5 + 2 = 7
c) Write a previous answer (new numerator 7) over the denominator 5.
One and two fifths is seven fifths - Add: 15/7 + 7/5 = 15 · 5/7 · 5 + 7 · 7/5 · 7 = 75/35 + 49/35 = 75 + 49/35 = 124/35
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(7, 5) = 35. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 5 = 35. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - fifteen sevenths plus seven fifths = one hundred twenty-four thirty-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 are using mixed numbers, leave a space between the whole and fraction part.Mixed numerals (mixed fractions or mixed numbers) 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 signs for fraction line and division, use 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
• exponentiation of fraction: 3/5^3
• 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) - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction: 4/22
• 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 /) has the same priority and then must evaluate from left to right.
Fractions in word problems:
- Sum three fractions
Work out the sum of 1/4, 1/5 and 3/10.
- Adding mixed fractions
Add this two mixed numbers: 1 5/6 + 2 2/11=
- Integer add to fraction
7 is added to the sum of 4/5 and 6/7
- Add fractions
Add/subtract the following similar fraction. Express answer in lowest terms if possible. Write your answer inside the box: 5/12 + 6/12
- One evening
One evening, a restaurant served a total of 1/2 of a loaf of wheat bread and 7/8 of a loaf of white bread. How many loaves were served in all?
- Samuel
Samuel has 1/3 of a bag of rice and Isabella has a 1/2 bag of rice. What fraction of are bag of rice do they have altogether?
- Add two fractions
What is 1/4 + 10/16?
- Add two fractions
What is the sum of 2/3 and 3/10?
- Sum of three fractions
What is the sum of 6/7, 1/2 & 3/4?
- Adding denominators
Max is working out 2/3+7/9. He says the answer is 9/12. What mistake have Max made?
- Team run
The first team member in a 926-person relay race must run 2 1/4 laps, the second team member must run 1 1/2 laps, and the third team member must run 3 1/4 laps. How many laps in all must each team run?
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