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Course: Algebra 1 > Unit 3
Lesson 3: Word problems with multiple unitsWorking with units: FAQ
Google ClassroomFrequently asked questions about working with units
Why is it important to be able to convert rates?
Often, we want to compare two rates that are expressed in different units. We need to convert one of the rates to match the other one in order to make a meaningful comparison.
Practice with our Rate conversion
exercise.
How do we go about choosing appropriate quantities for modeling?
It depends on the problem we're trying to solve. We'll want to choose quantities that are relevant to the problem and that we're able to measure directly or indirectly. For example, if we're trying to model the speed of a car, we might want to use distance and time as our quantities.
Practice with our Defining appropriate quantities for modeling
exercise.
How can we use formulas and units to solve problems?
By using formulas that relate different quantities to each other, we can use known values to solve for unknown values. Units are important because they remind us what the quantities represent and help us to check our work.
Practice with our Formulas and units
exercise.
What are some real-world applications of these topics?
There are countless examples! Engineers use rate conversions in order to design systems that operate at different speeds or frequencies. Scientists use formulas and units to solve problems ranging from calculating the densities of substances to measuring the rates of chemical reactions. And of course, people in all sorts of professions use these skills to make everyday calculations, such as converting measurements for a recipe or determining how long it will take to drive somewhere based on the speed limit.
Practice with our Using units to solve problems
exercise.
Want to join the conversation?
Y'all! Am I the only one who is still having trouble with this? It's making my brain hurt.(58 votes)
The world problems are the questions that trip me up. I do not understand where to put which units to cancel and get my desired results. My brain hurts.(5 votes)
- This stuff hard(22 votes)
you'll figure it out(4 votes)
This topic is hard.(15 votes)
Soon it will get easier(6 votes)
Yes, this is very important for many different careers.
•you need to know drug conversion if your going to be a doctor or paramedic.
•if you want to be a chemist you'll need to be able to convert between different chemical measurements.
• if your trading currency you have to be able to convert between currencies.
While most of these can be done via computer, it can still be a very useful skill to have. Hope this helps!(19 votes)
- Express 160 pounds (lbs) in kilograms (kg). Round your final answer 2 decimal places.
Units of Length Units of Weight Units of Capacity
1 in. = 2.54 cm 1 oz ≈ 28.35 g 1 L ≈ 1.06 qt
1 m ≈ 3.28 ft 1lb ≈454 g 1 gal ≈ 3.79 L
1 m ≈ 1.09 yd 1 kg ≈ 2.2 lb
1 mi ≈ 1. 61 km(8 votes)
The answer is 72.57(3 votes)
- How this can work in real life(4 votes)
- It could be helpful when using a recipe for cooking or following a blueprint that uses different units to measure in(9 votes)
I got a 20% on the unit test for this unit and im very confused on everything
someone please help me(2 votes)
Rate Conversion:
Key note is that you can treat units algebraically. For example, when 2 km / (1 km), the (km) cancels out, leaving you with only 2.
When you attempt to convert a rate, you would like to divide out the initial unit, then multiply with the final unit.
Let's say we have 500m and we want to convert it to km.
Since 1000m = 1km,
500m * (some km) / (some m)
Since we don't want to affect the result, the (some km) / (some m) should be equal to 1, as any number multiplied by 1 equals itself.
By 1000m = 1km, 1 = 1km / 1000m
500m * 1km / 1000m
Let's cancel out the m.
500m / 1000m * 1km
500 / 1000 * 1km
0.5 * 1km
0.5km
Let's say we have 7kmh⁻¹, and we want to convert it to meters per minute.
We do each unit separately. First, we can do km to m first.
7kmh⁻¹
7km * h⁻¹
= (7km * 1000m / 1km) * h⁻¹
= 7000mh⁻¹
Now, we'll do h⁻¹ to min⁻¹. Note h⁻¹ = 1 / h
7000mh⁻¹
7000m * (1 / h)
= 7000m * [1 / (1h * 60min / 1h)]
= 7000m * (1 / 60min)
≈ 116.7 m min⁻¹
Word Problems:
In general, word problems require you to be familiar on the topic, and it's hard to generalize a set of procedures to solve any kind of word problems.
But as always, visualizing the problem is helpful. Try to draw out something. Also, simply list out all possible equations, even if some are repeated.
However, for this unit, the objects are usually connected with each other. What does this mean? Let's look at one example on previous video.
Using units to solve problems: Toy factory
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:working-units/x2f8bb11595b61c86:word-problems-multiple-units/v/using-units-to-solve-problems-toy-factory
Let's change the problem a bit.A factory makes toys that are sold for $10 a piece. The factory has 40 workers, and they each produce 25 toys a day. The factory is open 5 days a week.*a week?*
What is the total value of toys the factory produces in
Now you can see
5 days a week -> 5 factories (Let's assume it)
1 factory -> 40 workers
1 worker -> 25 toys
1 toy -> $10 (Base)
See how all units are connected to one another? It is important to identify the base, then work your way back upward.
$10 * 25 * 40 * 5
= $50000
If you have problems that you find confusing, feel free to ask it.(8 votes)
- What happens if the quantity for modeling is not appropiate?(4 votes)
Not gonna lie this unit was extremely hard for me i feel like the videos didnt cover enough and the questions were completely different to the examples, i am usually really good in maths and stuff like this for example the unit prior i got mastered and proficient in everythig but this is all 25%-75% and its really hard(4 votes)- Im glad Im not the only one who had trouble with this. The explanation videos do not cover everything the questions ask, which makes things very confusing.(4 votes)