L4 · Rates and unit rates

Learning goal

“I can tell a rate from a ratio, and find a unit rate by scaling the second quantity down to 1 - then use unit rates to compare two rates fairly.”

Rate — a ratio comparing two quantities measured in DIFFERENT units, like 150 km in 3 hours.

Unit rate — a rate whose second quantity is 1, like 50 km per 1 hour (50 km/h).

Per — the word that means 'for each one' in a unit rate: $3 per notebook = $3 for each 1 notebook.

Worked example

A car travels 240 km in 4 hours, at a steady speed. Step 1: This is a rate: two different units, kilometres and hours. Write it as a ratio table: km 240, hours 4. Step 2: A unit rate has 1 as the second quantity. Scale both terms down by 4 (4 -> 1): 240 / 4 = 60. Step 3: The unit rate is 60 km per hour (60 km/h). On the double number line, hours 0, 1, 2, 3, 4 align with km 0, 60, 120, 180, 240 - the unit rate is the mark above 1 hour. Finding a unit rate is just scaling a ratio down until the second term is 1 - the same skill as L2, with units attached.

Check yourself — explain it

A unit rate always has which number as its second quantity?

Paired problem — example still visible

A cyclist rides 100 km in 2 hours. Find the unit rate -> 50 km per hour

Faded completion — last step is yours

"$12 for 4 kg of rice is $___ per kg" -> $3

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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