Calculator Fractions

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calculator fractions
Addition (+)Subtraction (-)Multiplication (×)Division (÷)
Fraction 1
 
Fraction 2
Answer:

Enter fractions above to see result

function getGCD(a, b){a=Math.abs(a);b=Math.abs(b);while(b){a%=b;var t=a;a=b;b=t;}return a;}function calculateFractions(){var w1=parseInt(document.getElementById('w1').value)||0;var n1=parseInt(document.getElementById('n1').value)||0;var d1=parseInt(document.getElementById('d1').value)||1;var w2=parseInt(document.getElementById('w2').value)||0;var n2=parseInt(document.getElementById('n2').value)||0;var d2=parseInt(document.getElementById('d2').value)||1;var op=document.getElementById('operation').value;if(d1===0||d2===0){alert('Denominator cannot be zero.');return;}var num1=(w1*d1)+n1;var den1=d1;var num2=(w2*d2)+n2;var den2=d2;var resNum,resDen;if(op==='add'){resNum=(num1*den2)+(num2*den1);resDen=den1*den2;}else if(op==='subtract'){resNum=(num1*den2)-(num2*den1);resDen=den1*den2;}else if(op==='multiply'){resNum=num1*num2;resDen=den1*den2;}else if(op==='divide'){if(num2===0){alert('Cannot divide by zero fraction.');return;}resNum=num1*den2;resDen=den1*num2;}var common=getGCD(resNum,resDen);resNum=resNum/common;resDen=resDen/common;if(resDen=resDen){mixedWhole=Math.floor(resNum/resDen);mixedNum=resNum%resDen;}var resultHTML=";if(resDen===1){resultHTML=resNum;}else{if(mixedWhole!==0){resultHTML=mixedWhole+' '+(Math.abs(mixedNum))+'/'+resDen+' ('+resNum+'/'+resDen+')';}else{resultHTML=resNum+'/'+resDen;}}document.getElementById('resultLabel').innerHTML='Result = '+resultHTML+'';}

Calculator Use

This calculator fractions tool is designed to help you quickly perform basic arithmetic operations with fractions. Whether you are dealing with proper fractions, improper fractions, or mixed numbers, this tool simplifies the process by handling common denominators and reducing results to their simplest form automatically.

Using this calculator is essential for students, teachers, and professionals who need to verify their math or solve complex fraction problems without the tedious manual work of finding the least common multiple (LCM).

Whole Number
The integer part of a mixed fraction. Leave blank or enter 0 if you are working with a simple proper or improper fraction.
Numerator
The top number of the fraction representing how many parts of the whole you have.
Denominator
The bottom number of the fraction representing the total number of parts the whole is divided into. This cannot be zero.

How It Works

When you use the calculator fractions, the logic follows standard mathematical rules for fraction arithmetic. Here is a breakdown of the formulas applied:

1. Mixed Number to Improper Fraction:

Numerator = (Whole × Denominator) + Numerator

2. Addition / Subtraction:

(a/b) ± (c/d) = (ad ± bc) / bd

3. Multiplication:

(a/b) × (c/d) = (ac) / (bd)

4. Division:

(a/b) ÷ (c/d) = (ad) / (bc)

  • Step 1: Convert all mixed numbers into improper fractions.
  • Step 2: Perform the operation based on the rules above.
  • Step 3: Calculate the Greatest Common Divisor (GCD) to simplify the fraction.
  • Step 4: Convert back to a mixed number if the result is improper (numerator > denominator).

Calculation Example

Example: Adding 1 1/2 and 2 1/3.

Step-by-step solution:

  1. Convert 1 1/2 to improper: (1×2)+1 = 3/2
  2. Convert 2 1/3 to improper: (2×3)+1 = 7/3
  3. Find common denominator: 2 × 3 = 6
  4. Adjust numerators: (3×3) + (7×2) = 9 + 14 = 23
  5. Initial Result: 23/6
  6. Simplify to Mixed Number: 23 ÷ 6 = 3 with remainder 5
  7. Final Result = 3 5/6

Common Questions

How do you simplify a fraction?

To simplify a fraction, find the greatest common divisor (GCD) of the numerator and the denominator. Divide both numbers by this GCD. For example, to simplify 10/20, the GCD is 10. 10÷10=1 and 20÷10=2, so the fraction simplifies to 1/2.

Can this calculator fractions tool handle negative numbers?

Yes, you can enter negative numbers in the whole number or numerator fields. The calculator will apply standard algebraic rules (e.g., subtracting a negative number is the same as adding a positive number).

What is an improper fraction?

An improper fraction is a fraction where the numerator (top) is greater than or equal to the denominator (bottom), such as 7/4. These are often converted to mixed numbers (1 3/4) for better readability in everyday contexts.

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