body {
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
line-height: 1.6;
color: #333;
margin: 0;
padding: 0;
}
.calculator-container {
max-width: 800px;
margin: 0 auto;
padding: 20px;
background: #f9f9f9;
border: 1px solid #ddd;
border-radius: 8px;
}
.calc-header {
text-align: center;
margin-bottom: 25px;
}
.calc-header h2 {
color: #2c3e50;
margin: 0 0 10px 0;
}
.calc-row {
display: flex;
flex-wrap: wrap;
gap: 20px;
margin-bottom: 20px;
}
.calc-column {
flex: 1;
min-width: 280px;
background: #fff;
padding: 20px;
border-radius: 6px;
box-shadow: 0 2px 4px rgba(0,0,0,0.05);
border: 1px solid #e0e0e0;
}
.calc-column h3 {
margin-top: 0;
color: #2980b9;
font-size: 1.2rem;
border-bottom: 2px solid #f0f0f0;
padding-bottom: 10px;
}
.form-group {
margin-bottom: 15px;
}
.form-group label {
display: block;
margin-bottom: 5px;
font-weight: 600;
font-size: 0.9rem;
}
.form-group input {
width: 100%;
padding: 10px;
border: 1px solid #ccc;
border-radius: 4px;
font-size: 1rem;
box-sizing: border-box;
}
.form-group .helper-text {
font-size: 0.8rem;
color: #666;
margin-top: 4px;
}
.calc-btn-wrapper {
text-align: center;
margin-top: 20px;
}
.calc-btn {
background-color: #27ae60;
color: white;
border: none;
padding: 15px 30px;
font-size: 1.1rem;
border-radius: 5px;
cursor: pointer;
transition: background-color 0.3s;
font-weight: bold;
}
.calc-btn:hover {
background-color: #219150;
}
#results-area {
margin-top: 30px;
display: none;
background: #fff;
padding: 20px;
border-radius: 8px;
border-left: 5px solid #27ae60;
box-shadow: 0 4px 6px rgba(0,0,0,0.1);
}
.result-row {
display: flex;
justify-content: space-between;
margin-bottom: 10px;
padding-bottom: 10px;
border-bottom: 1px solid #eee;
}
.result-highlight {
font-size: 1.2rem;
font-weight: bold;
color: #2c3e50;
}
.comparison-box {
background-color: #e8f8f5;
padding: 15px;
border-radius: 5px;
margin-top: 15px;
color: #16a085;
font-weight: bold;
text-align: center;
}
.article-content {
max-width: 800px;
margin: 40px auto;
padding: 20px;
background: #fff;
}
.article-content h2 {
color: #2c3e50;
margin-top: 30px;
}
.article-content h3 {
color: #34495e;
}
.article-content ul, .article-content ol {
margin-bottom: 20px;
padding-left: 20px;
}
.article-content li {
margin-bottom: 10px;
}
.formula-box {
background: #f8f9fa;
padding: 15px;
border-left: 4px solid #3498db;
font-family: monospace;
margin: 15px 0;
}
@media (max-width: 600px) {
.calc-row {
flex-direction: column;
}
}
function calculateUnitRates() {
// Get Input Values
var valA = parseFloat(document.getElementById('val_a').value);
var unitsA = parseFloat(document.getElementById('units_a').value);
var labelA = document.getElementById('label_a').value || "unit";
var valB = parseFloat(document.getElementById('val_b').value);
var unitsB = parseFloat(document.getElementById('units_b').value);
var labelB = document.getElementById('label_b').value || "unit";
// DOM Elements for Results
var resultsArea = document.getElementById('results-area');
var resContainerA = document.getElementById('result-a-container');
var resContainerB = document.getElementById('result-b-container');
var resRateA = document.getElementById('result-rate-a');
var resRateB = document.getElementById('result-rate-b');
var comparisonBox = document.getElementById('comparison-result');
// Validation for Option A
if (isNaN(valA) || isNaN(unitsA) || unitsA === 0) {
alert("Please enter valid numbers for Option A. The denominator cannot be zero.");
return;
}
// Show Results Area
resultsArea.style.display = "block";
comparisonBox.style.display = "none";
resContainerB.style.display = "none";
// Calculate Rate A
var rateA = valA / unitsA;
resRateA.innerHTML = rateA.toFixed(4) + " per " + labelA;
// Check if Option B is being used
if (!isNaN(valB) && !isNaN(unitsB) && unitsB !== 0) {
// Calculate Rate B
var rateB = valB / unitsB;
resContainerB.style.display = "flex";
resRateB.innerHTML = rateB.toFixed(4) + " per " + labelB;
comparisonBox.style.display = "block";
// Compare
if (rateA < rateB) {
comparisonBox.innerHTML = "Option A is lower by " + (rateB – rateA).toFixed(4) + " per unit.If calculating cost, Option A is the better buy.";
comparisonBox.style.color = "#27ae60";
comparisonBox.style.backgroundColor = "#e8f8f5";
} else if (rateB < rateA) {
comparisonBox.innerHTML = "Option B is lower by " + (rateA – rateB).toFixed(4) + " per unit.If calculating cost, Option B is the better buy.";
comparisonBox.style.color = "#27ae60";
comparisonBox.style.backgroundColor = "#e8f8f5";
} else {
comparisonBox.innerHTML = "Both options have the exact same unit rate.";
comparisonBox.style.color = "#2980b9";
comparisonBox.style.backgroundColor = "#eaf2f8";
}
}
}
Mastering Unit Rate Word Problems
Unit rates are a fundamental concept in mathematics and everyday life. Whether you are grocery shopping and trying to find the best deal, calculating the speed of a vehicle, or determining hourly wages, you are using unit rates. This calculator is designed to help you solve these word problems instantly by breaking down the "Total Quantity" (Numerator) and the "Total Units" (Denominator).
What is a Unit Rate?
A rate is a ratio that compares two quantities of different units (like dollars and ounces, or miles and hours). A unit rate is a rate where the denominator (the bottom number) is 1.
Formula: Unit Rate = Total Quantity ÷ Total Count
For example, if you drive 120 miles in 2 hours, your rate is 120 miles/2 hours. To turn this into a unit rate, you divide 120 by 2 to get 60. The unit rate is 60 miles per hour.
How to Use This Calculator
- Identify the Numerator: This is usually the primary value you want to break down, such as Total Cost ($), Total Distance (miles), or Total Output (words written). Enter this in the "Numerator" field.
- Identify the Denominator: This is the unit you want to measure 'per' one of, such as Weight (ounces), Time (hours), or Items (count). Enter this in the "Denominator" field.
- Compare (Optional): If you are solving a "Better Buy" word problem, fill in the fields for Option B. The calculator will determine which option has the lower rate.
Common Types of Word Problems
1. The "Better Buy" Problem
Example: A 12-ounce box of cereal costs $4.50, while an 18-ounce box costs $6.00. Which is the better deal?
To solve this, you calculate the price per ounce for both:
- Option A: $4.50 ÷ 12 = $0.375 per oz
- Option B: $6.00 ÷ 18 = $0.333 per oz
Since $0.33 is less than $0.37, the 18-ounce box is the better buy.
2. Speed and Velocity
Example: A train travels 300 miles in 5 hours. What is its average speed?
Here, the numerator is distance (300) and the denominator is time (5).
300 ÷ 5 = 60 miles per hour.
3. Wages and Income
Example: Sarah earned $150 for working 6 hours. What is her hourly wage?
Divide the total money earned by the total hours worked.
$150 ÷ 6 = $25 per hour.
Why is the denominator never zero?
In mathematics, division by zero is undefined. In real-world word problems, you cannot have a rate "per zero units." If you enter 0 as the denominator, the calculator will ask for a valid number.