Calculating Unit Rates from Ratios with Fractions
Calculating unit rates from ratios with fractions is a Grade 7 ratio and proportion skill in Big Ideas Math, Course 2. A unit rate expresses a quantity per single unit of another—like miles per hour or cost per item. When the ratio contains fractions, divide the fraction in the numerator by the fraction in the denominator using the rule: multiply by the reciprocal. For example, (3/4 mile) ÷ (1/2 hour) = (3/4) × (2/1) = 6/4 = 1.5 miles per hour. Simplifying complex fractions by multiplying by the least common denominator is an alternative approach. Unit rates enable direct comparison between quantities in real-world contexts.
Key Concepts
When working with rates, you may encounter complex fractions where the numerator or denominator contains a fraction. To simplify a complex fraction in a rate, treat the main fraction bar as division. Step 1. Rewrite the complex fraction as a division problem. Step 2. Multiply by the reciprocal of the divisor. Step 3. Simplify to find the unit rate.
Common Questions
What is a unit rate?
A unit rate is a ratio with a denominator of 1, expressing how much of one quantity corresponds to a single unit of another. Examples: 60 miles per 1 hour, $3.50 per 1 pound.
How do you find a unit rate when both quantities are fractions?
Divide the numerator fraction by the denominator fraction using multiply-by-reciprocal: (a/b) ÷ (c/d) = (a/b) × (d/c). Simplify the result.
What is the unit rate for traveling 3/4 mile in 1/2 hour?
(3/4) ÷ (1/2) = (3/4) × (2/1) = 6/4 = 3/2 = 1.5 miles per hour.
How does multiplying by the LCD help with fractional unit rates?
Multiplying both the numerator and denominator of the complex fraction by the LCD clears all fractions, turning the problem into a simpler division of whole numbers.
Why are unit rates useful for comparing situations?
Unit rates reduce all quantities to a per-one basis, making it easy to compare different ratios directly—like comparing prices per ounce from different package sizes.
What is the difference between a ratio and a unit rate?
A ratio compares any two quantities (e.g., 3:4). A unit rate is a special ratio with denominator 1, showing the value of one quantity per single unit of the other.