Fraction Multiplication Calculator
:root {
–primary-blue: #004a99;
–success-green: #28a745;
–light-background: #f8f9fa;
–input-border: #ced4da;
–text-dark: #212529;
–text-light: #6c757d;
}
body {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: var(–light-background);
color: var(–text-dark);
line-height: 1.6;
margin: 0;
padding: 20px;
}
.calculator-container {
max-width: 700px;
margin: 40px auto;
background-color: #ffffff;
padding: 30px;
border-radius: 8px;
box-shadow: 0 4px 15px rgba(0, 0, 0, 0.1);
border: 1px solid #dee2e6;
}
.calculator-container h1 {
color: var(–primary-blue);
text-align: center;
margin-bottom: 30px;
font-size: 2.2em;
}
.input-section, .result-section {
margin-bottom: 30px;
padding: 20px;
border: 1px solid var(–input-border);
border-radius: 5px;
background-color: var(–light-background);
}
.input-group {
margin-bottom: 20px;
display: flex;
flex-direction: column;
align-items: flex-start;
}
.input-group label {
font-weight: 600;
margin-bottom: 8px;
color: var(–primary-blue);
display: block;
}
.input-group input[type="number"],
.input-group input[type="text"] {
width: 100%;
padding: 12px;
border: 1px solid var(–input-border);
border-radius: 4px;
box-sizing: border-box; /* Include padding and border in the element's total width and height */
font-size: 1em;
transition: border-color 0.2s ease-in-out, box-shadow 0.2s ease-in-out;
}
.input-group input[type="number"]:focus,
.input-group input[type="text"]:focus {
border-color: var(–primary-blue);
box-shadow: 0 0 0 0.2rem rgba(0, 74, 153, 0.25);
outline: none;
}
.fraction-input {
display: flex;
align-items: center;
width: 100%;
}
.fraction-input input {
width: 45%;
text-align: center;
margin: 0 5px;
}
.fraction-bar {
font-size: 1.5em;
font-weight: bold;
color: var(–text-dark);
margin: 0 5px;
}
button {
display: block;
width: 100%;
padding: 12px 20px;
background-color: var(–primary-blue);
color: white;
border: none;
border-radius: 4px;
font-size: 1.1em;
font-weight: 600;
cursor: pointer;
transition: background-color 0.2s ease-in-out, transform 0.1s ease-in-out;
margin-top: 10px;
}
button:hover {
background-color: #003a7f;
transform: translateY(-1px);
}
button:active {
transform: translateY(0);
}
.result-section h2 {
color: var(–primary-blue);
text-align: center;
margin-bottom: 20px;
}
#result {
background-color: var(–success-green);
color: white;
padding: 25px;
text-align: center;
font-size: 2.5em;
font-weight: bold;
border-radius: 5px;
min-height: 80px; /* Ensure a minimum height */
display: flex;
align-items: center;
justify-content: center;
box-shadow: 0 2px 10px rgba(40, 167, 69, 0.3);
}
.article-section {
margin-top: 50px;
background-color: #ffffff;
padding: 30px;
border-radius: 8px;
box-shadow: 0 4px 15px rgba(0, 0, 0, 0.1);
border: 1px solid #dee2e6;
}
.article-section h2 {
color: var(–primary-blue);
border-bottom: 2px solid var(–primary-blue);
padding-bottom: 10px;
margin-bottom: 20px;
}
.article-section p, .article-section ul {
margin-bottom: 15px;
}
.article-section code {
background-color: #e9ecef;
padding: 2px 5px;
border-radius: 3px;
font-family: Consolas, Monaco, 'Andale Mono', 'Ubuntu Mono', monospace;
}
/* Responsive adjustments */
@media (max-width: 768px) {
.calculator-container {
margin: 20px auto;
padding: 20px;
}
.calculator-container h1 {
font-size: 1.8em;
}
.result-section #result {
font-size: 2em;
padding: 20px;
}
.fraction-input {
flex-direction: column;
align-items: center;
}
.fraction-input input {
width: 80%;
margin-bottom: 10px;
}
.fraction-bar {
margin: 5px 0;
}
}
@media (max-width: 480px) {
.calculator-container {
padding: 15px;
}
button {
font-size: 1em;
}
.article-section {
padding: 20px;
}
}
Fraction Multiplication Calculator
Understanding Fraction Multiplication
Multiplying fractions is a fundamental concept in arithmetic with straightforward rules. When you multiply two fractions, you essentially find a portion of a portion. The process involves multiplying the numerators together to get the new numerator, and multiplying the denominators together to get the new denominator.
The Rule:
To multiply two fractions, say a/b and c/d, the formula is:
(a / b) * (c / d) = (a * c) / (b * d)
Where:
a is the numerator of the first fraction.b is the denominator of the first fraction.c is the numerator of the second fraction.d is the denominator of the second fraction.
Steps:
- Identify Numerators and Denominators: For the first fraction (
a/b), identify a and b. For the second fraction (c/d), identify c and d.
- Multiply Numerators: Calculate the product of the numerators:
a * c.
- Multiply Denominators: Calculate the product of the denominators:
b * d.
- Form the Resulting Fraction: The new fraction is (
a * c) / (b * d).
- Simplify (Optional but Recommended): If possible, reduce the resulting fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor (GCD).
Example Calculation:
Let's multiply 1/2 by 3/4 using our calculator logic:
- First Fraction: Numerator (a) = 1, Denominator (b) = 2
- Second Fraction: Numerator (c) = 3, Denominator (d) = 4
- Multiply Numerators: 1 * 3 = 3
- Multiply Denominators: 2 * 4 = 8
- Resulting Fraction: 3 / 8
In this case, 3/8 is already in its simplest form.
Handling Edge Cases:
- Zero Denominator: A denominator cannot be zero in a fraction. The calculator will prevent or indicate an error if a zero denominator is entered.
- Zero Numerator: If either numerator is zero, the resulting product will be zero (0/something = 0), assuming valid denominators.
Use Cases:
Fraction multiplication is used in various contexts, including:
- Scaling Recipes: If a recipe calls for
3/4 cup of flour and you want to make 1/2 of the recipe, you multiply (3/4) * (1/2) to find you need 3/8 cup.
- Calculating Areas: Finding the area of a rectangular region where dimensions are given as fractions.
- Probability: Calculating the probability of sequential independent events.
- General Arithmetic and Algebra: As a building block for more complex mathematical operations.
// Function to find the Greatest Common Divisor (GCD) for simplification
function gcd(a, b) {
var absA = Math.abs(a);
var absB = Math.abs(b);
while (absB) {
var temp = absB;
absB = absA % absB;
absA = temp;
}
return absA;
}
// Function to simplify a fraction
function simplifyFraction(numerator, denominator) {
if (denominator === 0) {
return { numerator: numerator, denominator: denominator, error: "Denominator cannot be zero." };
}
if (numerator === 0) {
return { numerator: 0, denominator: 1, error: null };
}
var commonDivisor = gcd(numerator, denominator);
var simplifiedNumerator = numerator / commonDivisor;
var simplifiedDenominator = denominator / commonDivisor;
// Ensure the denominator is positive
if (simplifiedDenominator < 0) {
simplifiedNumerator = -simplifiedNumerator;
simplifiedDenominator = -simplifiedDenominator;
}
return { numerator: simplifiedNumerator, denominator: simplifiedDenominator, error: null };
}
function multiplyFractions() {
var num1 = parseInt(document.getElementById("numerator1").value);
var den1 = parseInt(document.getElementById("denominator1").value);
var num2 = parseInt(document.getElementById("numerator2").value);
var den2 = parseInt(document.getElementById("denominator2").value);
var resultDiv = document.getElementById("result");
// Input validation
if (isNaN(num1) || isNaN(den1) || isNaN(num2) || isNaN(den2)) {
resultDiv.innerHTML = "Error: Please enter valid numbers.";
return;
}
if (den1 === 0 || den2 === 0) {
resultDiv.innerHTML = "Error: Denominator cannot be zero.";
return;
}
var resultNumerator = num1 * num2;
var resultDenominator = den1 * den2;
var simplifiedResult = simplifyFraction(resultNumerator, resultDenominator);
if (simplifiedResult.error) {
resultDiv.innerHTML = "Error: " + simplifiedResult.error;
} else {
if (simplifiedResult.denominator === 1) {
resultDiv.innerHTML = simplifiedResult.numerator;
} else {
resultDiv.innerHTML = simplifiedResult.numerator + " / " + simplifiedResult.denominator;
}
}
}