QuestionSean mixes coconut oil with several other ingredients to make homemade toothpaste for his dog Rocky. He uses cup of coconut oil to make cup of toothpaste.
How much coconut oil does Sean use per cup of toothpaste?
? cup(s) coconut oil per cup toothpaste
Studdy Solution
STEP 1
What is this asking? How much coconut oil is needed for one cup of toothpaste? Watch out! Don't mix up the coconut oil and toothpaste amounts!
STEP 2
1. Set up a ratio
2. Calculate the unit rate
STEP 3
Alright, so Sean uses cup of coconut oil for every cup of toothpaste.
We can write this as a **ratio**: coconut oil per toothpaste.
This is our **starting ratio**.
STEP 4
We want to know how much coconut oil is used *per cup* of toothpaste.
That means we want the denominator of our ratio to be **one**!
To get there, we'll **divide** both the numerator and the denominator of our **starting ratio** by .
Remember, dividing both parts of the ratio by the same number keeps the ratio *equivalent*!
It's like multiplying by one, but for ratios!
STEP 5
Let's do the math!
Dividing by a fraction is the same as multiplying by its reciprocal.
So, we'll multiply the numerator by the reciprocal of , which is .
This gives us:
So, the numerator of our new ratio is .
STEP 6
Now for the denominator: divided by itself is, of course, **one**: Our denominator is now **one**, just what we wanted!
STEP 7
Our new ratio is , which means Sean uses cup of coconut oil per cup of toothpaste.
Awesome!
STEP 8
Sean uses cup of coconut oil per cup of toothpaste.
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