What this lesson covers
- Writing every given number with its unit attached, as a fraction
- Letting the shared unit cancel so the surviving unit is the answer's unit
- Why the flipped division fails a check you can do in your head
- Rates that stack twice, and how you know when you are done
- A practice problem where the rate has to be split, not multiplied
Chapters
- 0:00Most people multiply
- 0:04Two rates, one function
- 0:17The setup: bottles, crates and minutes
- 0:36Cancel to the answer's unit
- 1:21The flipped snap, killed by its own unit
- 1:56Your turn
- 2:38Three ways this goes wrong
- 3:00Attach the units
Lesson transcript
The narration of the video, word for word, under its chapter headings.
0:17The setup: bottles, crates and minutes
A machine fills twelve bottles a minute. A crate holds forty eight bottles. Which function counts crates after m minutes? Two rates, one function, and every wrong answer comes from snapping them together the wrong way.
0:36Cancel to the answer's unit
Write each number with its unit attached. Twelve bottles per minute. Forty eight bottles per crate. The function wants crates per minute, so bottles has to cancel. Divide. Twelve bottles per minute, divided by forty eight bottles per crate. The word bottles appears on top and on bottom. It cancels. Twelve forty eighths of a crate per minute. One quarter. So c of m equals m over four. Check it with real time. Eight minutes. Ninety six bottles. Exactly two crates. And eight over four is two. The units built the slope for you.
1:21The flipped snap, killed by its own unit
Flip the division and you get choice B. Forty eight over twelve is four, so four m. But look at its unit. Four m says thirty two crates in eight minutes. That machine would need over fifteen hundred bottles. Rates can stack twice. Six dollars per person per hour, four hours. Six times four is twenty four dollars per person. Two multiplications, one slope. The unit tags tell you when you are done, when only the answer's unit is left.
1:56Your turn
A go kart track costs fifty four dollars an hour, split equally by three friends. Which function gives one person's cost for h hours? Fifty four dollars per hour, divided by three people. Eighteen dollars per person, per hour. So f of h equals eighteen h. Not fifty four h, that bill went to one person. Not one hundred sixty two h, that charged the group three times. The answer is B.
2:38Three ways this goes wrong
Three ways this goes wrong. Dividing the wrong way, four m instead of m over four, the units catch it. Answering in the wrong unit, twelve m counts bottles, the question asked for crates. And subtracting rates. Forty eight minus twelve is thirty six of nothing. Units never subtract.
3:00Attach the units
Attach the units. Cancel to the answer's unit. That number is your slope.
Read the written version: the Linear functions strategy guide, then try 25 hard Linear functions questions with full explanations. Both are free, no account needed.