Fraction Calculator with Steps

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Fraction Calculator with Steps :root { –primary-blue: #004a99; –success-green: #28a745; –light-background: #f8f9fa; –white: #ffffff; –gray-border: #dee2e6; –text-dark: #343a40; –text-muted: #6c757d; } body { font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif; line-height: 1.6; background-color: var(–light-background); color: var(–text-dark); margin: 0; padding: 20px; } .loan-calc-container { max-width: 700px; margin: 30px auto; background-color: var(–white); padding: 30px; border-radius: 8px; box-shadow: 0 4px 15px rgba(0, 0, 0, 0.1); border: 1px solid var(–gray-border); } h1, h2, h3 { color: var(–primary-blue); text-align: center; margin-bottom: 20px; } .input-group { margin-bottom: 20px; padding: 15px; border: 1px solid var(–gray-border); border-radius: 5px; background-color: var(–white); display: flex; flex-direction: column; gap: 10px; } .input-group label { font-weight: bold; color: var(–primary-blue); margin-bottom: 5px; display: block; } .input-group input[type="number"], .input-group select { width: 100%; padding: 10px; border: 1px solid var(–gray-border); border-radius: 4px; box-sizing: border-box; /* Include padding and border in the element's total width and height */ font-size: 1rem; } button { display: inline-block; background-color: var(–primary-blue); color: var(–white); border: none; padding: 12px 25px; font-size: 1.1rem; font-weight: bold; border-radius: 5px; cursor: pointer; transition: background-color 0.3s ease, transform 0.2s ease; margin-top: 10px; width: auto; /* Adjust width to content */ box-sizing: border-box; } button:hover { background-color: #003366; transform: translateY(-2px); } #result, #steps { margin-top: 30px; padding: 20px; border-radius: 8px; text-align: center; } #result { background-color: var(–success-green); color: var(–white); font-size: 1.8rem; font-weight: bold; margin-bottom: 20px; } #steps { background-color: var(–white); border: 1px solid var(–gray-border); text-align: left; font-size: 0.95rem; color: var(–text-muted); } #steps h3 { text-align: left; color: var(–primary-blue); margin-bottom: 15px; } #steps ol { padding-left: 20px; } #steps li { margin-bottom: 10px; } .error-message { color: #dc3545; font-weight: bold; margin-top: 15px; text-align: center; } /* Responsive Adjustments */ @media (max-width: 768px) { .loan-calc-container { padding: 20px; } h1 { font-size: 1.8rem; } button { width: 100%; padding: 15px; } #result { font-size: 1.5rem; } }

Fraction Calculator with Steps

+ – × ÷

Understanding Fraction Arithmetic

Fractions are a fundamental part of mathematics, representing a part of a whole. They consist of a numerator (the top number, indicating how many parts you have) and a denominator (the bottom number, indicating the total number of equal parts the whole is divided into).

Key Concepts:

  • Numerator: The number above the fraction bar.
  • Denominator: The number below the fraction bar. It cannot be zero.
  • Proper Fraction: Numerator is smaller than the denominator (e.g., 3/4).
  • Improper Fraction: Numerator is greater than or equal to the denominator (e.g., 5/4).
  • Mixed Number: A whole number combined with a proper fraction (e.g., 1 3/4).
  • Equivalent Fractions: Fractions that represent the same value, even if they have different numerators and denominators (e.g., 1/2 is equivalent to 2/4).
  • Simplifying Fractions: Dividing both the numerator and denominator by their greatest common divisor (GCD) to express the fraction in its simplest form.

How the Calculator Works:

This calculator helps you perform basic arithmetic operations (addition, subtraction, multiplication, and division) on two fractions and provides a step-by-step explanation of the process. Below are the general rules for each operation:

1. Addition and Subtraction (a/b + c/d or a/b – c/d)

To add or subtract fractions, they must have a common denominator. The steps are:

  1. Find a Common Denominator: The least common denominator (LCD) is often preferred, which is the least common multiple (LCM) of the two denominators (b and d). If you can't find the LCM easily, you can multiply the denominators together (b × d) to get a common denominator, though this might result in a larger number.
  2. Convert Fractions: Adjust the numerators of both fractions so they match the common denominator. Multiply the numerator and denominator of the first fraction by (Common Denominator / Original Denominator 1) and do the same for the second fraction.
  3. Perform Operation: Add or subtract the numerators, keeping the common denominator the same.
  4. Simplify: Reduce the resulting fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor (GCD).

Example (Addition): 1/2 + 1/3

LCD of 2 and 3 is 6. Convert to 3/6 + 2/6. Add numerators: (3+2)/6 = 5/6. Simplified.

2. Multiplication (a/b × c/d)

Multiplying fractions is straightforward:

  1. Multiply Numerators: Multiply the top numbers together (a × c).
  2. Multiply Denominators: Multiply the bottom numbers together (b × d).
  3. Simplify: Reduce the resulting fraction (ac)/(bd) to its simplest form.

Example: 2/3 × 4/5

Multiply numerators: 2 × 4 = 8. Multiply denominators: 3 × 5 = 15. Result: 8/15. Simplified.

3. Division (a/b ÷ c/d)

Dividing by a fraction is the same as multiplying by its reciprocal:

  1. Find the Reciprocal: Invert the second fraction (c/d becomes d/c).
  2. Multiply: Multiply the first fraction (a/b) by the reciprocal of the second fraction (d/c).
  3. Simplify: Reduce the resulting fraction (ad)/(bc) to its simplest form.

Example: 3/4 ÷ 1/2

Reciprocal of 1/2 is 2/1. Multiply: 3/4 × 2/1. Multiply numerators: 3 × 2 = 6. Multiply denominators: 4 × 1 = 4. Result: 6/4. Simplify by dividing by GCD (2): 3/2.

This calculator is a useful tool for students, educators, and anyone needing to perform fraction arithmetic accurately and understand the underlying mathematical processes.

function gcd(a, b) { a = Math.abs(a); b = Math.abs(b); while (b) { var t = b; b = a % b; a = t; } return a; } function simplifyFraction(num, den) { if (den === 0) return { num: NaN, den: NaN, message: "Denominator cannot be zero." }; if (num === 0) return { num: 0, den: 1, message: "Fraction is zero." }; var commonDivisor = gcd(num, den); num /= commonDivisor; den /= commonDivisor; if (den < 0) { num = -num; den = -den; } return { num: num, den: den, message: "" }; } function findLCM(a, b) { if (a === 0 || b === 0) return 0; return Math.abs(a * b) / gcd(a, b); } function calculateFraction() { var num1 = parseFloat(document.getElementById("numerator1").value); var den1 = parseFloat(document.getElementById("denominator1").value); var num2 = parseFloat(document.getElementById("numerator2").value); var den2 = parseFloat(document.getElementById("denominator2").value); var operation = document.getElementById("operation").value; var resultDiv = document.getElementById("result"); var stepsDiv = document.getElementById("steps"); var errorMessageDiv = document.getElementById("errorMessage"); errorMessageDiv.innerHTML = ""; resultDiv.innerHTML = ""; stepsDiv.innerHTML = ""; if (isNaN(num1) || isNaN(den1) || isNaN(num2) || isNaN(den2)) { errorMessageDiv.innerHTML = "Please enter valid numbers for all inputs."; return; } if (den1 === 0 || den2 === 0) { errorMessageDiv.innerHTML = "Denominators cannot be zero."; return; } var resultNum, resultDen; var steps = "
    "; var fraction1Str = num1 + "/" + den1; var fraction2Str = num2 + "/" + den2; if (operation === "add" || operation === "subtract") { steps += "
  1. " + (operation === "add" ? "Adding" : "Subtracting") + " " + fraction1Str + " and " + fraction2Str + ".
    2. "; steps += "
  2. Find a common denominator for " + den1 + " and " + den2 + ". The least common multiple (LCM) is " + findLCM(den1, den2) + ".
    3. "; var commonDenominator = findLCM(den1, den2); if (commonDenominator === 0) { // Handle cases where one denominator is 0, though already checked errorMessageDiv.innerHTML = "Invalid denominators."; return; } var newNum1 = num1 * (commonDenominator / den1); var newNum2 = num2 * (commonDenominator / den2); var convertedFraction1 = newNum1 + "/" + commonDenominator; var convertedFraction2 = newNum2 + "/" + commonDenominator; steps += "
  3. Convert fractions to have the common denominator: " + fraction1Str + " becomes " + convertedFraction1 + ", and " + fraction2Str + " becomes " + convertedFraction2 + ".
    4. "; if (operation === "add") { resultNum = newNum1 + newNum2; steps += "
  4. Add the numerators: " + newNum1 + " + " + newNum2 + " = " + resultNum + ".
    5. "; } else { // subtract resultNum = newNum1 – newNum2; steps += "
  5. Subtract the numerators: " + newNum1 + " – " + newNum2 + " = " + resultNum + ".
    6. "; } resultDen = commonDenominator; steps += "
  6. The result before simplification is " + resultNum + "/" + resultDen + ".
    7. "; } else if (operation === "multiply") { steps += "
  7. Multiplying " + fraction1Str + " by " + fraction2Str + ".
    8. "; resultNum = num1 * num2; resultDen = den1 * den2; steps += "
  8. Multiply the numerators: " + num1 + " × " + num2 + " = " + resultNum + ".
    9. "; steps += "
  9. Multiply the denominators: " + den1 + " × " + den2 + " = " + resultDen + ".
    10. "; steps += "
  10. The result before simplification is " + resultNum + "/" + resultDen + ".
    11. "; } else if (operation === "divide") { steps += "
  11. Dividing " + fraction1Str + " by " + fraction2Str + ".
    12. "; steps += "
  12. To divide, multiply the first fraction by the reciprocal of the second fraction. The reciprocal of " + fraction2Str + " is " + den2 + "/" + num2 + ".
    13. "; if (num2 === 0) { errorMessageDiv.innerHTML = "Cannot divide by zero."; return; } resultNum = num1 * den2; resultDen = den1 * num2; steps += "
  13. Multiply the numerator of the first fraction by the denominator of the second: " + num1 + " × " + den2 + " = " + resultNum + ".
    14. "; steps += "
  14. Multiply the denominator of the first fraction by the numerator of the second: " + den1 + " × " + num2 + " = " + resultDen + ".
    15. "; steps += "
  15. The result before simplification is " + resultNum + "/" + resultDen + ".
    16. "; } var simplified = simplifyFraction(resultNum, resultDen); if (isNaN(simplified.num)) { errorMessageDiv.innerHTML = simplified.message; return; } steps += "
  16. Simplify the fraction " + resultNum + "/" + resultDen + " by dividing by the greatest common divisor (" + gcd(resultNum, resultDen) + ").
    17. "; steps += "
  17. The simplified result is " + simplified.num + "/" + simplified.den + ".
    18. "; steps += "
"; stepsDiv.innerHTML = "

Calculation Steps:

" + steps; resultDiv.innerHTML = "Result: " + simplified.num + "/" + simplified.den; }

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