Fraction calculator
This fractions calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step information.
The result:
3 1/3 + 4 5/7 = 169/21 = 8 1/21 ≅ 8.047619
The spelled result in words is one hundred sixty-nine twenty-firsts (or eight and one twenty-first).How do we solve fractions step by step?
- Conversion a mixed number 3 1/3 to a improper fraction: 3 1/3 = 3 1/3 = 3 · 3 + 1/3 = 9 + 1/3 = 10/3
To find a new numerator:
a) Multiply the whole number 3 by the denominator 3. Whole number 3 equally 3 * 3/3 = 9/3
b) Add the answer from the previous step 9 to the numerator 1. New numerator is 9 + 1 = 10
c) Write a previous answer (new numerator 10) over the denominator 3.
Three and one third is ten thirds. - Conversion a mixed number 4 5/7 to a improper fraction: 4 5/7 = 4 5/7 = 4 · 7 + 5/7 = 28 + 5/7 = 33/7
To find a new numerator:
a) Multiply the whole number 4 by the denominator 7. Whole number 4 equally 4 * 7/7 = 28/7
b) Add the answer from the previous step 28 to the numerator 5. New numerator is 28 + 5 = 33
c) Write a previous answer (new numerator 33) over the denominator 7.
Four and five sevenths is thirty-three sevenths. - Add: 10/3 + 33/7 = 10 · 7/3 · 7 + 33 · 3/7 · 3 = 70/21 + 99/21 = 70 + 99/21 = 169/21
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(3, 7) = 21. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 7 = 21. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - ten thirds plus thirty-three sevenths is one hundred sixty-nine twenty-firsts.
Rules for expressions with fractions:
Fractions - write a forward slash to separate the numerator and 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 whole part and fraction and use a forward slash to input fraction i.e., 1 2/3 . A negative mixed fraction write for example as -5 1/2.
A slash is both a sign for fraction line and division, use a colon (:) for division fractions i.e., 1/2 : 1/3.
Decimals (decimal numbers) enter with a decimal dot . 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
• square root of a fraction: sqrt(1/16)
• 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 be evaluated from left to right.
Fractions in word problems:
- Benson
Benson spends ⅓ of his pocket money on transport and ⅔ on food I. What fraction of his pocket money did he spend on transport and food? ii. What fraction is left?
- The bucket
Anna and Joey share an 18-ounce bucket of clay. By the end of the week, Anna has used 1/3 of the bucket, and Joey has used 2/3 of the bucket of clay. How many ounces are left in the bucket?
- Matthew
Matthew is saving up for a car. Last year he saved 3/5 of the total amount. In addition to what he saved last year, he saved 3/10 of the total amount in the summer. If the car costs 15 000$, how much has he saved so far?
- Ahsan
Ahsan has a large pizza. He gives 1/3 to his sister and 1/4 to his mother. What fraction of the pizza does Ahsan have left?
- Ayden
Ayden is 140 cm tall, and his friend Alex is 1/5 taller than him. How tall is Alex?
- The numerator
The numerator of the fraction is 5 more than its denominator. If 4 is added to the numerator and denominator, the fraction obtained is 6/5. What is that fraction?
- Cupcakes
In a bowl were some cupcakes. Janka ate one-third, and Danka ate one-quarter of the cupcakes. a) How many cookies ate together? b) How many cookies remain in a bowl? Write the results as a decimal number and notepad as a fraction.
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Last Modified: February 7, 2025