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:
5 1/4 - 2 5/7 = 71/28 = 2 15/28 ≅ 2.5357143
Spelled result in words is seventy-one twenty-eighths (or two and fifteen twenty-eighths).How do you solve fractions step by step?
- Conversion a mixed number 5 1/4 to a improper fraction: 5 1/4 = 5 1/4 = 5 · 4 + 1/4 = 20 + 1/4 = 21/4
To find new numerator:
a) Multiply the whole number 5 by the denominator 4. Whole number 5 equally 5 * 4/4 = 20/4
b) Add the answer from previous step 20 to the numerator 1. New numerator is 20 + 1 = 21
c) Write a previous answer (new numerator 21) over the denominator 4.
Five and one quarter is twenty-one quarters - Conversion a mixed number 2 5/7 to a improper fraction: 2 5/7 = 2 5/7 = 2 · 7 + 5/7 = 14 + 5/7 = 19/7
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 5. New numerator is 14 + 5 = 19
c) Write a previous answer (new numerator 19) over the denominator 7.
Two and five sevenths is nineteen sevenths - Subtract: 21/4 - 19/7 = 21 · 7/4 · 7 - 19 · 4/7 · 4 = 147/28 - 76/28 = 147 - 76/28 = 71/28
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(4, 7) = 28. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 7 = 28. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - twenty-one quarters minus nineteen sevenths = seventy-one twenty-eighths.
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?
- School
There are 150 pupils in grade 5 . 2/3 of them are female. By what fractions are the males?
- Fractions mul add sum
To three-eighths of one third, we add five quarters of one half and multiply the sum by four. How much will we get?
- 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?
- 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?
- Difference mixed fractions
What is the difference between 4 2/3 and 3 1/6?
- Mixed numbers
Rewrite mixed numbers, so the fractions have the same denominator: 5 1/5 - 2 2/3
- Pounds
3 pounds subtract 1/3 of a pound.
- Michael
Michael had a bar if chocolate. He ate 1/2 of it and gave away 1/3. What fraction had he left?
- Find the 24
Find the difference between 2/7 and 1/21
- From a
From a 1 meter ribbon, Ericka cut 2/4 meter for her hat and another 1/4 meter for her bag. How long was the remaining piece?
- 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?
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