Fraction calculator
The calculator performs basic and advanced operations with fractions, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. Solve problems with two, three, or more fractions and numbers in one expression.
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 you 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 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 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 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 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
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 the both denominators - LCM(3, 7) = 21. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 7 = 21. In the next intermediate step the fraction result cannot be further simplified by canceling.
In words - twenty-nine thirds minus twenty sevenths = one hundred forty-three twenty-firsts.
Rules for expressions with fractions:
Fractions - use the slash “/” between the numerator and denominator, i.e., for five-hundredths, enter 5/100. If you are using mixed numbers, be sure to leave a single space between the whole and fraction part.The slash separates the numerator (number above a fraction line) and denominator (number below).
Mixed numerals (mixed fractions or mixed numbers) write as non-zero integer separated by one space and fraction i.e., 1 2/3 (having the same sign). An example of a negative mixed fraction: -5 1/2.
Because slash is both signs for fraction line and division, we recommended use colon (:) as the operator of division fractions i.e., 1/2 : 3.
Decimals (decimal numbers) enter with a decimal point . and they are automatically converted to fractions - i.e. 1.45.
The colon : and slash / is the symbol of division. Can be used to divide mixed numbers 1 2/3 : 4 3/8 or can be used for write complex fractions i.e. 1/2 : 1/3.
An asterisk * or × is the symbol for multiplication.
Plus + is addition, minus sign - is subtraction and ()[] is mathematical parentheses.
The exponentiation/power symbol is ^ - for example: (7/8-4/5)^2 = (7/8-4/5)2
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 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.
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:
- Length subtracting
Express in mm: 5 3/10 cm - 2/5 mm
- Add sub fractions
What is 4 1/2+2/7-213/14?
- Pizza fractions
Ann ate a third of a pizza and then another quater. Total part of pizza eaten by Ann and how much pizza is left?
- School
There are 150 pupils in grade 5 . 2/3 of it are female. By what fractions are the males?
- Difference mixed fractions
What is the difference between 4 2/3 and 3 1/6?
- Cake fractions
Thomas ate 1/3 of cake, Bohouš of the rest of the cake ate 2/5. What fraction of cake left over for others?
- Pounds
3 pounds subtract 1/3 of a pound.
- Employees
Of all 360 employees, there are 11/12 women. How many men work in a company?
- Package
The package was 23 meters of textile. The first day sold 12.3 meters. How many meters of textile remained in the package?
- Find the 24
Find the difference between 2/7 and 1/21
- Akpan
Akpan spent 3/8 of his time in school during the week. What fraction of his time does he spend at home during the week?
- Pupils 7
There are 40 pupils in a certain class. 3/5 of the class are boys. How many are girls?
- Michael
Michael had a bar if chocolate. He ate 1/2 of it and gave away 1/3. What fraction had he left?
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