Calculator expression with brackets



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.

1/3 * (1/2 - 3 3/8) = -23/24 ≅ -0.9583333

Spelled result in words is minus twenty-three twenty-fourths.

How do you solve fractions step by step?

  1. Conversion a mixed number 3 3/8 to a improper fraction: 3 3/8 = 3 3/8 = 3 · 8 + 3/8 = 24 + 3/8 = 27/8

    To find new numerator:
    a) Multiply the whole number 3 by the denominator 8. Whole number 3 equally 3 * 8/8 = 24/8
    b) Add the answer from previous step 24 to the numerator 3. New numerator is 24 + 3 = 27
    c) Write a previous answer (new numerator 27) over the denominator 8.

    Three and three eighths is twenty-seven eighths
  2. Subtract: 1/2 - 27/8 = 1 · 4/2 · 4 - 27/8 = 4/8 - 27/8 = 4 - 27/8 = -23/8
    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 the both denominators - LCM(2, 8) = 8. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 8 = 16. In the next intermediate step the fraction result cannot be further simplified by canceling.
    In words - one half minus twenty-seven eighths = minus twenty-three eighths.
  3. Multiple: 1/3 * the result of step No. 2 = 1/3 * (-23/8) = 1 · (-23)/3 · 8 = -23/24
    Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(-23, 24) = 1. In the next intermediate step the fraction result cannot be further simplified by canceling.
    In words - one third multiplied by minus twenty-three eighths = minus twenty-three twenty-fourths.

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

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:

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  • Fractions 3
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  • Write 3
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  • Milimeters
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  • Pie
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  • Seeds
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  • Classroom 4
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  • Women
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  • Employees
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  • Mixed with percentages
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