Unit Rates with Fractions
Aligned to 7.RP.A.1 — Common Core State Standards for Mathematics.
What this lesson teaches
A unit rate tells how much of one quantity goes with exactly 1 of another. To find it, divide the two amounts. When the amounts are fractions, dividing means multiplying by the reciprocal.
Worked examples
Example 1
A snail crawls 1/2 mile in 1/4 hour. Unit rate = (1/2) ÷ (1/4) = (1/2) × (4/1) = 4/2 = 2 miles per hour.
Example 2
A runner covers 3/4 mile in 1/6 hour. Unit rate = (3/4) ÷ (1/6) = (3/4) × 6 = 18/4 = 4.5 miles per hour.
Example 3
Divide 'how much' by 'how long' to get a rate per unit of time. Reversing them gives hours per mile, a different (and usually less useful) number.
Practice questions
- You paint 3/4 of a wall in 1/2 hour. How much wall per hour?
- A recipe uses 2/3 cup of sugar for 1/4 of a batch. How many cups per full batch?
- A runner goes 1 1/2 km in 3/5 hour. Find the speed in km per hour.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Tasas Unitarias con Fracciones
Una tasa unitaria indica cuánto de una cantidad corresponde a exactamente 1 de otra. Para hallarla, divide las dos cantidades. Cuando son fracciones, dividir significa multiplicar por el recíproco.
Ejemplo 1: Un caracol avanza 1/2 milla en 1/4 de hora. Tasa unitaria = (1/2) ÷ (1/4) = (1/2) × (4/1) = 4/2 = 2 millas por hora.
Ejemplo 2: Un corredor recorre 3/4 de milla en 1/6 de hora. Tasa unitaria = (3/4) ÷ (1/6) = (3/4) × 6 = 18/4 = 4.5 millas por hora.
Ejemplo 3: Divide 'cuánto' entre 'cuánto tiempo' para obtener una tasa por unidad de tiempo. Al revés da horas por milla, un número distinto (y normalmente menos útil).
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