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 calculateRatios() {
var valA = document.getElementById('inputA').value;
var valB = document.getElementById('inputB').value;
var valC = document.getElementById('inputC').value;
var valD = document.getElementById('inputD').value;
var numA = parseFloat(valA);
var numB = parseFloat(valB);
var numC = parseFloat(valC);
var numD = parseFloat(valD);
var inputs = [
{ id: 'inputA', value: numA, original: valA },
{ id: 'inputB', value: numB, original: valB },
{ id: 'inputC', value: numC, original: valC },
{ id: 'inputD', value: numD, original: valD }
];
var filledInputs = inputs.filter(function(input) {
return input.original !== " && !isNaN(input.value);
});
var emptyInputs = inputs.filter(function(input) {
return input.original === " || isNaN(input.value);
});
var resultDiv = document.getElementById('result');
resultDiv.style.color = '#333'; // Reset color for new results
if (filledInputs.length === 2 && emptyInputs.length === 2) {
// Case: Simplify Ratio (e.g., A:B, C and D are empty)
var term1 = filledInputs[0].value;
var term2 = filledInputs[1].value;
if (isNaN(term1) || isNaN(term2)) {
resultDiv.innerHTML = "Please enter valid numbers for the two terms you wish to simplify.";
resultDiv.style.color = 'red';
return;
}
if (term1 === 0 && term2 === 0) {
resultDiv.innerHTML = "The ratio 0:0 is indeterminate. Please provide at least one non-zero term.";
resultDiv.style.color = 'red';
return;
}
if (term1 === 0) {
resultDiv.innerHTML = "The simplified ratio is: 0 : 1";
return;
}
if (term2 === 0) {
resultDiv.innerHTML = "The simplified ratio is: 1 : 0";
return;
}
var commonDivisor = gcd(term1, term2);
var simplifiedTerm1 = term1 / commonDivisor;
var simplifiedTerm2 = term2 / commonDivisor;
resultDiv.innerHTML = "The simplified ratio is: " + simplifiedTerm1 + " : " + simplifiedTerm2 + "";
} else if (filledInputs.length === 3 && emptyInputs.length === 1) {
// Case: Find Unknown in Proportion (A:B = C:D)
var missingId = emptyInputs[0].id;
var unknownValue;
var error = false;
// Extract the known values based on their original IDs
var a = (inputs[0].original !== " && !isNaN(inputs[0].value)) ? inputs[0].value : null;
var b = (inputs[1].original !== " && !isNaN(inputs[1].value)) ? inputs[1].value : null;
var c = (inputs[2].original !== " && !isNaN(inputs[2].value)) ? inputs[2].value : null;
var d = (inputs[3].original !== " && !isNaN(inputs[3].value)) ? inputs[3].value : null;
if (missingId === 'inputA') {
if (d === 0) { error = true; resultDiv.innerHTML = "Cannot solve: Term 4 (D) is zero, which would lead to division by zero (A = B*C/D)."; }
else { unknownValue = (b * c) / d; a = unknownValue; }
} else if (missingId === 'inputB') {
if (c === 0) { error = true; resultDiv.innerHTML = "Cannot solve: Term 3 (C) is zero, which would lead to division by zero (B = A*D/C)."; }
else { unknownValue = (a * d) / c; b = unknownValue; }
} else if (missingId === 'inputC') {
if (b === 0) { error = true; resultDiv.innerHTML = "Cannot solve: Term 2 (B) is zero, which would lead to division by zero (C = A*D/B)."; }
else { unknownValue = (a * d) / b; c = unknownValue; }
} else if (missingId === 'inputD') {
if (a === 0) { error = true; resultDiv.innerHTML = "Cannot solve: Term 1 (A) is zero, which would lead to division by zero (D = B*C/A)."; }
else { unknownValue = (b * c) / a; d = unknownValue; }
}
if (error) {
resultDiv.style.color = 'red';
return;
}
if (isNaN(unknownValue)) {
resultDiv.innerHTML = "An error occurred during calculation. Please check your inputs.";
resultDiv.style.color = 'red';
return;
}
resultDiv.innerHTML = "The unknown value is " + unknownValue.toFixed(4) + ".The complete proportion is: " + a + " : " + b + " = " + c + " : " + d + "";
} else {
resultDiv.innerHTML = "Please enter either two values to simplify a ratio (e.g., Term 1 and Term 2) OR three values to find an unknown in a proportion (e.g., A:B = C:D).";
resultDiv.style.color = 'orange';
}
}
function clearInputs() {
document.getElementById('inputA').value = ";
document.getElementById('inputB').value = ";
document.getElementById('inputC').value = ";
document.getElementById('inputD').value = ";
document.getElementById('result').innerHTML = '';
document.getElementById('result').style.color = '#333';
}
Understanding Ratios and Proportions
Ratios are fundamental mathematical tools used to compare two or more quantities. They express how much of one quantity there is compared to another. For example, if a recipe calls for 2 cups of flour and 1 cup of sugar, the ratio of flour to sugar is 2:1.
What is a Ratio?
A ratio is a way to show the relationship between two numbers. It can be written in several ways:
Using a colon: A : B
As a fraction: A/B
Using the word "to": A to B
Ratios are often simplified to their lowest terms, much like fractions. For instance, the ratio 10:15 can be simplified by dividing both numbers by their greatest common divisor (GCD), which is 5. So, 10:15 simplifies to 2:3.
What is a Proportion?
A proportion is an equation that states that two ratios are equal. It's typically written as A:B = C:D or A/B = C/D. Proportions are incredibly useful for solving problems where you know three parts of a relationship and need to find the fourth.
The key principle behind proportions is cross-multiplication: if A/B = C/D, then A × D = B × C. This allows us to find an unknown value.
How to Use the Ratios Calculator
This calculator can perform two main functions:
Simplify a Ratio: Enter two numbers into any two of the "Term" fields (e.g., Term 1 and Term 2) and leave the other two blank. Click "Calculate" to see the ratio in its simplest form.
Find an Unknown in a Proportion: Enter three known values into any three of the "Term" fields (A, B, C, or D) and leave one field blank for the unknown. Click "Calculate" to find the missing value that completes the proportion.
Examples:
Example 1: Simplifying a Ratio
You have 12 red marbles and 18 blue marbles. What is the ratio of red to blue marbles in its simplest form?
Enter '12' into Term 1 (A)
Enter '18' into Term 2 (B)
Leave Term 3 (C) and Term 4 (D) blank.
Click "Calculate".
The calculator will output: "The simplified ratio is: 2 : 3". (Because GCD of 12 and 18 is 6, so 12/6 = 2 and 18/6 = 3).
Example 2: Finding an Unknown in a Proportion
If 3 apples cost $2, how much would 9 apples cost? (This can be set up as 3:2 = 9:X)
Enter '3' into Term 1 (A)
Enter '2' into Term 2 (B)
Enter '9' into Term 3 (C)
Leave Term 4 (D) blank (this is your unknown 'X').
Click "Calculate".
The calculator will output: "The unknown value is 6.0000. The complete proportion is: 3 : 2 = 9 : 6". (Since 3 × X = 2 × 9, then 3X = 18, so X = 6).
Example 3: Another Proportion Example
A map has a scale where 1 inch represents 50 miles. If two cities are 3.5 inches apart on the map, how many miles apart are they in reality? (1:50 = 3.5:X)
Enter '1' into Term 1 (A)
Enter '50' into Term 2 (B)
Enter '3.5' into Term 3 (C)
Leave Term 4 (D) blank.
Click "Calculate".
The calculator will output: "The unknown value is 175.0000. The complete proportion is: 1 : 50 = 3.5 : 175". (Since 1 × X = 50 × 3.5, then X = 175).