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:
7 1/2 + 3 1/7 = 149/14 = 10 9/14 ≅ 10.6428571
Spelled result in words is one hundred forty-nine fourteenths (or ten and nine fourteenths).How do we solve fractions step by step?
- Conversion a mixed number 7 1/2 to a improper fraction: 7 1/2 = 7 1/2 = 7 · 2 + 1/2 = 14 + 1/2 = 15/2
To find a new numerator:
a) Multiply the whole number 7 by the denominator 2. Whole number 7 equally 7 * 2/2 = 14/2
b) Add the answer from the previous step 14 to the numerator 1. New numerator is 14 + 1 = 15
c) Write a previous answer (new numerator 15) over the denominator 2.
Seven and one half is fifteen halfs. - Conversion a mixed number 3 1/7 to a improper fraction: 3 1/7 = 3 1/7 = 3 · 7 + 1/7 = 21 + 1/7 = 22/7
To find a new numerator:
a) Multiply the whole number 3 by the denominator 7. Whole number 3 equally 3 * 7/7 = 21/7
b) Add the answer from the previous step 21 to the numerator 1. New numerator is 21 + 1 = 22
c) Write a previous answer (new numerator 22) over the denominator 7.
Three and one seventh is twenty-two sevenths. - Add: 15/2 + 22/7 = 15 · 7/2 · 7 + 22 · 2/7 · 2 = 105/14 + 44/14 = 105 + 44/14 = 149/14
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(2, 7) = 14. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 7 = 14. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - fifteen halfs plus twenty-two sevenths is one hundred forty-nine fourteenths.
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 | 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) - 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 /) have the same priority and must evaluate from left to right.
Fractions in word problems:
- My whole
My whole number is 88 if you add 5 thousandths, 8 tenths, and 7 thousandths. What number will I be?
- 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?
- In one day
In one day, a baker used 2/3 of a pound of flour, 3/4 of a pound of flour, and 5/12 of a pound of flour. How much flour was used that day?
- Sum of three fractions
What is the sum of 6/7, 1/2 & 3/4?
- Mary read
Mary read 2/9 books in the morning and 5/9 in the evening. What fraction of books has she read?
- Add fractions
Add/subtract the following similar fraction. Express the answer in the lowest terms if possible. Write your answer inside the box: 5/12 + 6/12
- Add two fractions
What is the sum of 2/3 and 3/10?
- Adding mixed fractions
Add these two mixed numbers: 1 5/6 + 2 2/11=
- Work out 2
Work out the sum of 2/6 and 1/6. Give your answer in its simplest form.
- Evaluate 27
Evaluate the expression shown below and write your answer as a fraction in the simplest form. (8)/(3)+ (11)/(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?
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