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:
3 3/4 * 2 2/5 = 9/1 = 9
Spelled result in words is nine.How do we solve fractions step by step?
- Conversion a mixed number 3 3/4 to a improper fraction: 3 3/4 = 3 3/4 = 3 · 4 + 3/4 = 12 + 3/4 = 15/4
To find a new numerator:
a) Multiply the whole number 3 by the denominator 4. Whole number 3 equally 3 * 4/4 = 12/4
b) Add the answer from the previous step 12 to the numerator 3. New numerator is 12 + 3 = 15
c) Write a previous answer (new numerator 15) over the denominator 4.
Three and three quarters is fifteen quarters. - Conversion a mixed number 2 2/5 to a improper fraction: 2 2/5 = 2 2/5 = 2 · 5 + 2/5 = 10 + 2/5 = 12/5
To find a new numerator:
a) Multiply the whole number 2 by the denominator 5. Whole number 2 equally 2 * 5/5 = 10/5
b) Add the answer from the previous step 10 to the numerator 2. New numerator is 10 + 2 = 12
c) Write a previous answer (new numerator 12) over the denominator 5.
Two and two fifths is twelve fifths. - Multiple: 15/4 * 12/5 = 15 · 12/4 · 5 = 180/20 = 9 · 20/1 · 20 = 9
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(180, 20) = 20. In the following intermediate step, cancel by a common factor of 20 gives 9/1.
In other words - fifteen quarters multiplied by twelve fifths is nine.
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 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) : 4/22 - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction
• 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:
- Samantha
Samantha took 72 pictures on her beach vacation. 3/4 of those pictures are on the beach. How many pictures from her vacation are on the beach? - Someone
Someone ate 1/10 of a cake, leaving only 9/10. If you eat 2/3 of the cake left, how much of a whole cake will you have eaten? - Multiplying fractions
What is 1/3 of 5? - In dividing
In dividing fractions, get the reciprocal of the divisor and change the division symbol to the multiplication symbol. 2/3 : 5/6
- Paper clips
Mrs. Bright is organizing her office supplies. There are five open boxes of paper clips in her desk drawer. Each box has 1/2 of the paper clips remaining. How many boxes of paper clips are left? - Ms. Sheppard
Ms. Sheppard cuts ½ of a piece of construction paper. She uses ⅙ of the piece to make a flower. What fraction of the sheet of paper does she use to make the flower? - On Tuesday 3
On Tuesday, the ABC store sold 2/3 of its stock of mugs. If there are 363 mugs stocked, to begin with, how many mugs were sold on Tuesday? TYPE THE NUMBER ONLY! - A store
A store received a shipment of 240 skateboards. In three weeks, it sold 1/3 of those skateboards. How many skateboards did the store sell? - 7918/45510 60641
From 7918/45510, calculate 4/10 and 6/10
- 19 boy
Nineteen boys in section 1 and 23 boys in section 2. If 2/6 of them are boy Scouts, how many boy scouts are them? - Beth wants
Beth wants to give 1/4 pizza to each of her 6 friends. Which choice does not show the number of pizzas Beth needs? - Shoes
Jim and Dora are collecting shoes for a yard sale. Dora collected 1/2 as many shoes as Jim did. Jim collected 3/7 of a bag of shoes. How many bags of shoes did Dora collect? - A newspaper's
A newspaper's cover page is 3/8 text, and photographs fill the rest. If 2/5 of the text is an article about endangered species, what fraction of the whole cover page is the article about endangered species? - Slices of pizza
Maria ate 1/4 of a pizza. If there were 20 slices of pizza, how many slices did Maria eat?
more math problems »