Calculator adding fractions and mixed numbers
This fraction calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step information.
8/5 + 6 2/7 = 276/35 = 7 31/35 ≅ 7.8857143
The result spelled out in words is two hundred seventy-six thirty-fifths (or seven and thirty-one thirty-fifths).How do we solve fractions step by step?
- Conversion a mixed number 6 2/7 to a improper fraction: 6 2/7 = 6 2/7 = 6 · 7 + 2/7 = 42 + 2/7 = 44/7
To find a new numerator:
a) Multiply the whole number 6 by the denominator 7. Whole number 6 equally 6 * 7/7 = 42/7
b) Add the answer from the previous step 42 to the numerator 2. New numerator is 42 + 2 = 44
c) Write a previous answer (new numerator 44) over the denominator 7.
Six and two sevenths is forty-four sevenths. - Add: 8/5 + 44/7 = 8 · 7/5 · 7 + 44 · 5/7 · 5 = 56/35 + 220/35 = 56 + 220/35 = 276/35
It is suitable to adjust both fractions to a common (equal) denominator for adding fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(5, 7) = 35. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 7 = 35. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, eight fifths plus forty-four sevenths equals two hundred seventy-six thirty-fifths.
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) |
The calculator follows well-known rules for the order of operations. The most common mnemonics for remembering this order are:
- PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
- BEDMAS: Brackets, Exponents, Division, Multiplication, Addition, Subtraction.
- BODMAS: Brackets, Order (or "Of"), Division, Multiplication, Addition, Subtraction.
- GEMDAS: Grouping symbols (brackets: (){}), Exponents, Multiplication, Division, Addition, Subtraction.
- MDAS: Multiplication and Division (same precedence), Addition and Subtraction (same precedence). MDAS is a subset of PEMDAS.
1. Multiplication/Division vs. Addition/Subtraction: Always perform multiplication and division *before* addition and subtraction.
2. Left-to-Right Rule: Operators with the same precedence (e.g., + and -, or * and /) must be evaluated from left to right.
Fractions in word problems:
- There 22
There is 5/8 of a pizza in one box and 9/12 of a pizza in another box. How much do you have altogether? - Sum of fractions
What is the sum of 2/3+3/5? - A miner
A miner is working at an elevation of -64 7/9 and then ascends 22 1/3. What is the miner's new location? - Fresh chickens
In the market, one stall is selling fresh chickens worth P120 per kilo. A person bought two fresh chickens weighing 1 1/2 and 1 1/4 kilos each. What is the total weight of the two chickens? - Plus minus mixed numbers
If possible, perform the indicated operation/s and reduce your answer to the lowest term. 1. 3 1/8 + 3/5= 2. 6 3/7 + 4/9= 3. 9 6/13 + 1 3/7= 4. 10 4/5 - 2/3= 5. 13 6/7 - 3/11= - Students 82194
Out of 30 students in the class, 2 thirds of the children were on a trip, and all the others were at home. How many students stayed at home? - What is 23
What is the answer to sum 2 1/2 and 1 3/8 minus 5 1/4?
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Last Modified: June 23, 2025
