function gcd(a, b) {
a = Math.abs(a);
b = Math.abs(b);
while (b) {
var temp = b;
b = a % b;
a = temp;
}
return a;
}
function calculateRatio() {
var firstQuantityInput = document.getElementById("firstQuantity").value;
var secondQuantityInput = document.getElementById("secondQuantity").value;
var firstQuantity = parseFloat(firstQuantityInput);
var secondQuantity = parseFloat(secondQuantityInput);
var resultRatioSimplified = document.getElementById("resultRatioSimplified");
var resultRatioDecimal1 = document.getElementById("resultRatioDecimal1");
var resultRatioDecimal2 = document.getElementById("resultRatioDecimal2");
var resultPercentage1of2 = document.getElementById("resultPercentage1of2");
var resultPercentage2of1 = document.getElementById("resultPercentage2of1");
resultRatioSimplified.innerHTML = "";
resultRatioDecimal1.innerHTML = "";
resultRatioDecimal2.innerHTML = "";
resultPercentage1of2.innerHTML = "";
resultPercentage2of1.innerHTML = "";
if (isNaN(firstQuantity) || isNaN(secondQuantity)) {
resultRatioSimplified.innerHTML = "Please enter valid numbers for both quantities.";
return;
}
// Simplified Ratio
if (firstQuantity === 0 && secondQuantity === 0) {
resultRatioSimplified.innerHTML = "Simplified Ratio (First : Second): Undefined (0:0)";
} else if (firstQuantity === 0) {
resultRatioSimplified.innerHTML = "Simplified Ratio (First : Second): 0 : 1″;
} else if (secondQuantity === 0) {
resultRatioSimplified.innerHTML = "Simplified Ratio (First : Second): Undefined (division by zero)";
} else {
// To handle decimals in GCD, multiply by a power of 10 to make them integers
var multiplier = 1;
var firstDecimalPlaces = (firstQuantityInput.split('.')[1] || ").length;
var secondDecimalPlaces = (secondQuantityInput.split('.')[1] || ").length;
multiplier = Math.pow(10, Math.max(firstDecimalPlaces, secondDecimalPlaces));
var intFirst = Math.round(firstQuantity * multiplier);
var intSecond = Math.round(secondQuantity * multiplier);
var commonDivisor = gcd(intFirst, intSecond);
var simplifiedFirst = intFirst / commonDivisor;
var simplifiedSecond = intSecond / commonDivisor;
resultRatioSimplified.innerHTML = "Simplified Ratio (First : Second): " + simplifiedFirst + " : " + simplifiedSecond;
}
// Decimal Ratio (First / Second)
if (secondQuantity === 0) {
resultRatioDecimal1.innerHTML = "Decimal Ratio (First / Second): Undefined (division by zero)";
} else {
var decimalRatio1 = firstQuantity / secondQuantity;
resultRatioDecimal1.innerHTML = "Decimal Ratio (First / Second): " + decimalRatio1.toFixed(4);
}
// Decimal Ratio (Second / First)
if (firstQuantity === 0) {
resultRatioDecimal2.innerHTML = "Decimal Ratio (Second / First): Undefined (division by zero)";
} else {
var decimalRatio2 = secondQuantity / firstQuantity;
resultRatioDecimal2.innerHTML = "Decimal Ratio (Second / First): " + decimalRatio2.toFixed(4);
}
// First as a percentage of Second
if (secondQuantity === 0) {
resultPercentage1of2.innerHTML = "First as % of Second: Undefined (division by zero)";
} else {
var percentage1of2 = (firstQuantity / secondQuantity) * 100;
resultPercentage1of2.innerHTML = "First as % of Second: " + percentage1of2.toFixed(2) + "%";
}
// Second as a percentage of First
if (firstQuantity === 0) {
resultPercentage2of1.innerHTML = "Second as % of First: Undefined (division by zero)";
} else {
var percentage2of1 = (secondQuantity / firstQuantity) * 100;
resultPercentage2of1.innerHTML = "Second as % of First: " + percentage2of1.toFixed(2) + "%";
}
}
.calculator-container {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: #f9f9f9;
border: 1px solid #ddd;
border-radius: 8px;
padding: 20px;
max-width: 400px;
margin: 20px auto;
box-shadow: 0 4px 8px rgba(0, 0, 0, 0.05);
}
.calculator-container h2 {
text-align: center;
color: #333;
margin-bottom: 20px;
font-size: 1.8em;
}
.calculator-content .input-group {
margin-bottom: 15px;
}
.calculator-content label {
display: block;
margin-bottom: 5px;
color: #555;
font-weight: bold;
}
.calculator-content input[type="number"] {
width: calc(100% – 22px);
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 1em;
}
.calculator-content button {
width: 100%;
padding: 12px;
background-color: #007bff;
color: white;
border: none;
border-radius: 4px;
font-size: 1.1em;
cursor: pointer;
transition: background-color 0.3s ease;
margin-top: 10px;
}
.calculator-content button:hover {
background-color: #0056b3;
}
.calculator-content .result-group {
background-color: #e9ecef;
border: 1px solid #dee2e6;
border-radius: 4px;
padding: 15px;
margin-top: 20px;
}
.calculator-content .result-group h3 {
color: #333;
margin-top: 0;
margin-bottom: 10px;
font-size: 1.3em;
border-bottom: 1px solid #ced4da;
padding-bottom: 8px;
}
.calculator-content .result-group div {
margin-bottom: 8px;
color: #343a40;
line-height: 1.5;
}
.calculator-content .result-group div:last-child {
margin-bottom: 0;
}
Understanding and Calculating Ratios
Ratios are fundamental mathematical tools used to compare two or more quantities. They express how much of one quantity there is relative to another. Ratios are incredibly versatile and appear in various aspects of daily life, from cooking and finance to engineering and science.
What is a Ratio?
A ratio is a way to show the relationship between two numbers. For example, if you have 3 apples and 2 oranges, the ratio of apples to oranges is 3 to 2, often written as 3:2. This means for every 3 apples, there are 2 oranges.
Ratios can be expressed in several ways:
Using a colon: A : B (e.g., 3:2)
Using the word "to": A to B (e.g., 3 to 2)
As a fraction: A/B (e.g., 3/2)
It's important to note that the order of the numbers in a ratio matters. A ratio of 3:2 is different from 2:3.
Why are Ratios Important?
Ratios help us understand proportions and scale. Here are a few examples:
Recipes: A recipe might call for a ratio of 2 parts flour to 1 part sugar. This ensures the correct consistency and taste, regardless of the batch size.
Maps and Models: A map scale of 1:10,000 means that 1 unit on the map represents 10,000 units in real life.
Finance: Debt-to-equity ratios help assess a company's financial health.
Science: Chemical reactions often involve specific ratios of reactants.
Sports Statistics: Win-loss ratios provide insight into a team's performance.
Simplifying Ratios
Just like fractions, ratios can often be simplified to their lowest terms. To simplify a ratio, you find the greatest common divisor (GCD) of the two numbers and divide both numbers by it. For instance, a ratio of 10:25 can be simplified:
The GCD of 10 and 25 is 5.
Divide both numbers by 5: 10 ÷ 5 = 2, and 25 ÷ 5 = 5.
The simplified ratio is 2:5.
This means that for every 2 units of the first quantity, there are 5 units of the second quantity.
Ratios as Decimals and Percentages
Ratios can also be expressed as decimals or percentages, which can be useful for comparison or understanding proportions in a different light:
Decimal Ratio: To get a decimal ratio of A to B, simply divide A by B (A/B). For 2:5, the decimal ratio is 2/5 = 0.4.
Percentage: To express A as a percentage of B, calculate (A/B) * 100%. For 2:5, (2/5) * 100% = 0.4 * 100% = 40%. This means the first quantity is 40% of the second quantity.
How to Use the Ratio Calculator
Our Ratio Calculator simplifies the process of understanding the relationship between two numbers. Here's how to use it:
First Quantity: Enter the first number you want to compare.
Second Quantity: Enter the second number you want to compare.
Calculate Ratio: Click the button to see the results.
The calculator will provide you with:
Simplified Ratio (First : Second): The ratio in its simplest integer form.
Decimal Ratio (First / Second): The first quantity divided by the second, expressed as a decimal.
Decimal Ratio (Second / First): The second quantity divided by the first, expressed as a decimal.
First as % of Second: The first quantity expressed as a percentage of the second quantity.
Second as % of First: The second quantity expressed as a percentage of the first quantity.
Example Usage:
Let's say you have 15 red marbles and 45 blue marbles.
First Quantity: 15
Second Quantity: 45
The calculator would show:
Simplified Ratio (First : Second): 1 : 3 (since GCD of 15 and 45 is 15)
Decimal Ratio (First / Second): 0.3333 (15 / 45)
Decimal Ratio (Second / First): 3.0000 (45 / 15)
First as % of Second: 33.33% (15 is one-third of 45)
Second as % of First: 300.00% (45 is three times 15)
This calculator is a handy tool for anyone needing to quickly analyze and understand proportional relationships between two values.