(Simplified)';
}
return resultHtml;
}
function calculateFraction(operation) {
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 resultDisplay = document.getElementById('resultDisplay');
if (isNaN(num1) || isNaN(den1) || isNaN(num2) || isNaN(den2)) {
resultDisplay.innerHTML = 'Please enter valid numbers for all fields.';
return;
}
if (den1 === 0 || den2 === 0) {
resultDisplay.innerHTML = 'Denominator cannot be zero.';
return;
}
var resultNum, resultDen;
switch (operation) {
case 'add':
resultNum = (num1 * den2) + (num2 * den1);
resultDen = den1 * den2;
break;
case 'subtract':
resultNum = (num1 * den2) – (num2 * den1);
resultDen = den1 * den2;
break;
case 'multiply':
resultNum = num1 * num2;
resultDen = den1 * den2;
break;
case 'divide':
if (num2 === 0) {
resultDisplay.innerHTML = 'Cannot divide by zero.';
return;
}
resultNum = num1 * den2;
resultDen = den1 * num2;
break;
default:
resultDisplay.innerHTML = 'Invalid operation.';
return;
}
resultDisplay.innerHTML = displayFraction(resultNum, resultDen);
}
function simplifyFraction() {
var num = parseFloat(document.getElementById('simplifyNumerator').value);
var den = parseFloat(document.getElementById('simplifyDenominator').value);
var resultDisplay = document.getElementById('resultDisplay');
if (isNaN(num) || isNaN(den)) {
resultDisplay.innerHTML = 'Please enter valid numbers for numerator and denominator.';
return;
}
if (den === 0) {
resultDisplay.innerHTML = 'Denominator cannot be zero.';
return;
}
var simplified = simplify(num, den);
resultDisplay.innerHTML = 'Original: ' + displayFraction(num, den) + 'Simplified: ' + displayFraction(simplified.numerator, simplified.denominator);
}
Understanding Fractions: Your Essential Guide
Fractions are a fundamental concept in mathematics, representing a part of a whole. They are written as a ratio of two numbers, a numerator (the top number) and a denominator (the bottom number). The denominator indicates how many equal parts the whole is divided into, and the numerator indicates how many of those parts are being considered.
What is a Fraction?
A fraction like 3⁄4 means that a whole has been divided into 4 equal parts, and we are looking at 3 of those parts. Fractions are everywhere, from recipes (1⁄2 cup of flour) to telling time (a quarter past the hour, or 1⁄4 of an hour).
Types of Fractions
Proper Fractions: The numerator is less than the denominator (e.g., 1⁄2, 3⁄4). These fractions are always less than 1.
Improper Fractions: The numerator is greater than or equal to the denominator (e.g., 5⁄4, 7⁄3). These fractions are equal to or greater than 1.
Mixed Numbers: A combination of a whole number and a proper fraction (e.g., 1 1⁄2, which is equivalent to 3⁄2).
Operations with Fractions
Adding and Subtracting Fractions
To add or subtract fractions, they must have a common denominator. If they don't, you need to find the least common multiple (LCM) of the denominators and convert the fractions to equivalent fractions with that common denominator. Once the denominators are the same, you simply add or subtract the numerators and keep the denominator the same.
Example: Add 1⁄2 and 1⁄4.
Find a common denominator: The LCM of 2 and 4 is 4.
Convert 1⁄2 to 2⁄4.
Add the numerators: 2⁄4 + 1⁄4 = (2+1)⁄4 = 3⁄4.
Using the calculator: Enter Numerator 1: 1, Denominator 1: 2, Numerator 2: 1, Denominator 2: 4. Click "Add Fractions" to get 3⁄4.
Multiplying Fractions
Multiplying fractions is straightforward: multiply the numerators together and multiply the denominators together. Then, simplify the resulting fraction if possible.
Example: Multiply 2⁄3 by 1⁄2.
Multiply numerators: 2 × 1 = 2.
Multiply denominators: 3 × 2 = 6.
The result is 2⁄6.
Simplify: 2⁄6 simplifies to 1⁄3 (divide both by 2).
Using the calculator: Enter Numerator 1: 2, Denominator 1: 3, Numerator 2: 1, Denominator 2: 2. Click "Multiply Fractions" to get 2⁄6, simplified to 1⁄3.
Dividing Fractions
To divide fractions, you "flip" the second fraction (find its reciprocal) and then multiply it by the first fraction.
Example: Divide 3⁄4 by 1⁄2.
Flip the second fraction (1⁄2 becomes 2⁄1).
Multiply the first fraction by the flipped second fraction: 3⁄4 × 2⁄1 = (3×2)⁄(4×1) = 6⁄4.
Simplify: 6⁄4 simplifies to 3⁄2 (divide both by 2), or 1 1⁄2 as a mixed number.
Using the calculator: Enter Numerator 1: 3, Denominator 1: 4, Numerator 2: 1, Denominator 2: 2. Click "Divide Fractions" to get 6⁄4, simplified to 3⁄2.
Simplifying Fractions
Simplifying a fraction means reducing it to its lowest terms. This is done by dividing both the numerator and the denominator by their greatest common divisor (GCD). A fraction is in its simplest form when the only common factor between the numerator and denominator is 1.
Example: Simplify 10⁄15.
Find the GCD of 10 and 15. The factors of 10 are 1, 2, 5, 10. The factors of 15 are 1, 3, 5, 15. The greatest common divisor is 5.
Divide both the numerator and denominator by 5: 10 ÷ 5⁄15 ÷ 5 = 2⁄3.
Using the calculator: Enter Numerator: 10, Denominator: 15. Click "Simplify Fraction" to get 2⁄3.
Why are Fractions Important?
Fractions are crucial for developing a strong foundation in mathematics. They are used in everyday life for measurements, cooking, finance, and understanding proportions. Mastering fraction operations is essential for algebra, geometry, and higher-level math concepts.