function gcd(a, b) {
while (b) {
var temp = b;
b = a % b;
a = temp;
}
return a;
}
function calculateFractionMultiplication() {
var numeratorInput = document.getElementById("fractionNumerator").value;
var denominatorInput = document.getElementById("fractionDenominator").value;
var wholeNumberInput = document.getElementById("wholeNumber").value;
var numerator = parseFloat(numeratorInput);
var denominator = parseFloat(denominatorInput);
var wholeNumber = parseFloat(wholeNumberInput);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
if (isNaN(numerator) || isNaN(denominator) || isNaN(wholeNumber)) {
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (denominator === 0) {
resultDiv.innerHTML = "The fraction denominator cannot be zero.";
return;
}
if (wholeNumber < 0) {
resultDiv.innerHTML = "Please enter a non-negative whole number.";
return;
}
// Original problem display
var originalProblem = "
(" + numerator + " / " + denominator + ") × " + wholeNumber + "";
// Step 1: Multiply the numerator by the whole number
var newNumerator = numerator * wholeNumber;
var newDenominator = denominator;
var step1 = "
";
step1 += "" + numerator + " × " + wholeNumber + " = " + newNumerator + "";
step1 += "This gives us the unsimplified fraction: " + newNumerator + " / " + newDenominator + "";
// Step 2: Simplify the resulting fraction
var commonDivisor = gcd(Math.abs(newNumerator), Math.abs(newDenominator));
var simplifiedNumerator = newNumerator / commonDivisor;
var simplifiedDenominator = newDenominator / commonDivisor;
var simplifiedResult = "
";
simplifiedResult += "The Greatest Common Divisor (GCD) of " + newNumerator + " and " + newDenominator + " is " + commonDivisor + ".";
simplifiedResult += "Dividing both numerator and denominator by " + commonDivisor + ":";
simplifiedResult += "" + newNumerator + " ÷ " + commonDivisor + " = " + simplifiedNumerator + "";
simplifiedResult += "" + newDenominator + " ÷ " + commonDivisor + " = " + simplifiedDenominator + "";
var finalFractionDisplay = "";
if (simplifiedDenominator === 1) {
finalFractionDisplay = "
" + simplifiedNumerator + "";
} else {
finalFractionDisplay = "
" + simplifiedNumerator + " / " + simplifiedDenominator + "";
}
// Convert to mixed number if it's an improper fraction
var mixedNumberDisplay = "";
if (simplifiedNumerator > simplifiedDenominator && simplifiedDenominator !== 0) {
var wholePart = Math.floor(simplifiedNumerator / simplifiedDenominator);
var remainder = simplifiedNumerator % simplifiedDenominator;
if (remainder === 0) {
// If remainder is 0, it's a whole number, already handled above
} else {
mixedNumberDisplay = "
" + wholePart + " " + remainder + " / " + simplifiedDenominator + "";
}
}
resultDiv.innerHTML = originalProblem + step1 + simplifiedResult + finalFractionDisplay + mixedNumberDisplay;
}
Understanding Fraction Multiplication with Whole Numbers
Multiplying a fraction by a whole number is a fundamental concept in mathematics that helps us understand how to scale parts of a whole. It's a common operation used in various real-world scenarios, from cooking and construction to finance and science.
What Does It Mean?
When you multiply a fraction by a whole number, you are essentially finding a certain "number of times" that fraction. For example, if you have 1/4 of a pizza and you want to know how much pizza you'd have if you had that amount 3 times, you would multiply 1/4 by 3.
The Simple Steps
The process of multiplying a fraction by a whole number is straightforward:
- Convert the Whole Number to a Fraction: Any whole number can be written as a fraction by placing it over 1. For example, 5 can be written as 5/1.
- Multiply the Numerators: Multiply the numerator of the original fraction by the whole number (which is now the numerator of its fractional form).
- Multiply the Denominators: Multiply the denominator of the original fraction by the denominator of the whole number's fractional form (which is always 1). This means the original denominator usually remains unchanged.
- Simplify the Result: If the resulting fraction is improper (numerator is greater than or equal to the denominator) or can be reduced, simplify it to its lowest terms or convert it to a mixed number.
Formula
Given a fraction a/b and a whole number c:
(a / b) × c = (a × c) / b
Example Calculation
Let's say you want to calculate (3/5) × 7.
- Original Problem: (3 / 5) × 7
- Step 1: Multiply the numerator by the whole number.
Numerator (3) × Whole Number (7) = 21
The denominator remains 5.
This gives us the unsimplified fraction: 21 / 5
- Step 2: Simplify the fraction.
The Greatest Common Divisor (GCD) of 21 and 5 is 1, meaning the fraction 21/5 is already in its simplest form.
- Step 3: Convert to a mixed number (if applicable).
Since 21 is greater than 5, it's an improper fraction. Divide 21 by 5:
21 ÷ 5 = 4 with a remainder of 1.
So, 21/5 as a mixed number is 4 and 1/5.
Therefore, (3/5) × 7 = 21/5 or 4 1/5.
This calculator simplifies the process, allowing you to quickly find the product of any fraction and whole number, and presents the result in both simplified fractional and mixed number forms.