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:
4 3/9 - 2 7/9 = 14/9 = 1 5/9 ≅ 1.5555556
Spelled result in words is fourteen ninths (or one and five ninths).How do you solve fractions step by step?
- Conversion a mixed number 4 3/9 to a improper fraction: 4 3/9 = 4 3/9 = 4 · 9 + 3/9 = 36 + 3/9 = 39/9
To find new numerator:
a) Multiply the whole number 4 by the denominator 9. Whole number 4 equally 4 * 9/9 = 36/9
b) Add the answer from previous step 36 to the numerator 3. New numerator is 36 + 3 = 39
c) Write a previous answer (new numerator 39) over the denominator 9.
Four and three ninths is thirty-nine ninths - Conversion a mixed number 2 7/9 to a improper fraction: 2 7/9 = 2 7/9 = 2 · 9 + 7/9 = 18 + 7/9 = 25/9
To find new numerator:
a) Multiply the whole number 2 by the denominator 9. Whole number 2 equally 2 * 9/9 = 18/9
b) Add the answer from previous step 18 to the numerator 7. New numerator is 18 + 7 = 25
c) Write a previous answer (new numerator 25) over the denominator 9.
Two and seven ninths is twenty-five ninths - Subtract: 39/9 - 25/9 = 39 - 25/9 = 14/9
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(9, 9) = 9. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 9 = 81. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - thirty-nine ninths minus twenty-five ninths = fourteen ninths.
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:
- Comparing and sorting
Arrange in descending order this fractions: 2/7, 7/10 & 1/2
- Equivalent fractions
Are these two fractions equivalent -4/9 and 11/15?
- Ten fractions
Write ten fractions between 1/3 and 2/3
- Fractions
Sort fractions ? by its size. Result write as three serial numbers 1,2,3.
- Compare
Compare fractions ?. Which fraction of the lower?
- Fraction
Determine for what x fraction (10x -4)/(5x +9) equals:
- How many
How many integers are greater than 547/3 and less than 931/4?
- Dividends
The three friends divided the win by the invested money. Karlos got three-eighths, John 320 permille, and the rest got Martin. Who got the most and which the least?
- A laundry
Mr. Green washed 1/4 of his laundry. His son washed 3/7 of it. Who washed most of the laundry? How much of the laundry still needs to be washed?
- Leo hiked
Leo hiked 6/7 of a kilometer. Jericho hiked 2/3 kilometer. Who covered a longer distance? How much longer?
- Buing
Brother got to buy 240 CZK and could buy for 1/8 what he wanted. Could he pay the rest of the purchase for 200 CZK?
- Paper collecting
At the paper collecting contest gathered Franta 2/9 ton, Karel 1/4 ton, and Patrick 19/36 tons of paper. Who has gathered the most and the least?
- Math test
Brayden was solving some math problems for the math team. He answered 2 math problems. Matthew answered 3, John answered 1 reasoning. Matthew 1/2 times as many. Brayden said that 2/6. Is he correct? Why or why not? Be sure to explain your answer.
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