Chase works in the stockroom of a grocery store. It takes him 20 minutes to stock 3 shelves. He has 9 more shelves to stock. His shift ends in 1 hour. Can Chase finish stocking the shelves before his shift ends?
In this concept, you will learn how to use mental math to solve proportions.
Using Mental Math to Solve Proportions
You can find equal ratios without having to write the multiplication or division on paper. Mental math is the calculation that goes on inside your head and can be used to find the unknown quantity in an equation.
First, look at the relationship between the numerators, 25 campers to 75 campers. Think, “What can I multiply 25 by to get 75. 25 times 3 equals 75.” Remember, a proportion is two equal ratios. You multiply both the numerator and the denominator by the same number to get an equivalent ratio.
Next, multiply the given number of tents by 3 to find the equivalent number of tents needed for 75 campers. Think, “1 times 3 equals 3.”
You need 3 tents for 75 campers.
Here is another proportion with a missing quantity. Solve the proportion using mental math.
Earlier, you were given a problem about Chase at the grocery store.
First, write a proportion using the known values with minutes in the numerator and shelves in the denominator.
Next, look at the relationship of the denominators. Think, “What number multiplied by 3 equals 9? 3 times 3 equals 9.”
Then, multiply the known numerator by 3 to find the unknown quantity. Think, “20 times 3 equals 60. It will take 60 minutes.”
It will take Chase 60 minutes, or 1 hour, to stock 9 shelves. Chase will finish before his shift is over.
First, look at the relationship between the denominators. Think, “What can I multiply 3 by to get 33? 3 times 11 equals 33.”
Next, multiply the given numerator by 11 to find the unknown quantity. Think “2 times 11 equals 22.”
First, look at the relationship between the denominators. Think, “What can I multiply 9 by to get 18? 9 times 2 equals 18.”
Then, multiply the given numerator to find the unknown quantity. Think, “3 times 2 equals 6.”
Solve the following proportions using mental math.