INTERPRET QUOTIENTS OF RATIONAL NUMBERS BY DESCRIBING REAL-WORLD CONTEXTS
About "Interpret quotients of rational numbers by describing real-world contexts"
Interpret quotients of rational numbers by describing real-world contexts :
In mathematics, a rational number is any number that can be expressed in the form p/q where "q" is not equal to zero.
The quotient of the rational number p/q is nothing but the result that we get when we divide "p" by "q".
The rules for the sign of quotient are summarized below.
Let p and q be rational numbers.
Interpret quotients of rational numbers by describing real-world contexts - Examples
Example 1 :
A diver needs to descend to a depth of 100 feet below sea level. She wants to do it in 5 equal descents. How far should she travel in each descent ?
Solution :
To find how far she should travel in each descent, we have to divide 100 by 5.
Step 1 :
Take the reciprocal of the divisor 5.
5 ---- reciprocal ----> 1/5
Step 2 :
Multiply 100 by 1/5
(100) x (1/5)
Step 3 : Simplify
(20) x (1/1)
Step 4 : Multiply
(20) x (1/1) = 20
Hence, she should travel 20 feet in each descent.
Example 2 :
Over 5 months, Carlos wrote 5 checks for a total of $323.75 to pay for his cable TV service. His cable bill is the same amount each month. What was the change in Carlos’s bank account each month to pay for cable?
Solution :
Step 1 :
Use a negative number to represent the withdrawal from his account each month
Step 2 :
Find -323.75 / 5
Step 3 :
Determine the sign of the quotient.
The quotient will be negative because the signs are different.
Step 4 :
Divide.
-323.75 / 5 = -64.75
Hence, Carlos withdrew $64.75 each month to pay for cable TV.
Example 3 :
Maya wants to divide a 3/4 -pound box of trail mix into small bags. Each bag will hold 1/12 pound of trail mix. How many bags of trail mix can Maya fill ?
Solution :
Step 1 :
To get answer for the above question, we have to divide 3/4 by 1/12.
That is, we have to find the value of (3/4) / (1/12).
Step 2 :
Determine the sign of the quotient.
The quotient will be positive, because the signs of both numerator (3/4) and denominator (1/12) are same.
Step 3 :
Write the complex fraction as division :
(3/4) / (1/12) = (3/4) ÷ (1/12)
Step 4 :
Rewrite the above division as multiplication by taking the reciprocal of the second fraction.
(3/4) ÷ (1/12) = (3/4) x (12/1)
Step 5 :
Simplify
(3/4) x (12/1) = (3/1) x (3/1)
(3/4) x (12/1) = 9
Hence, Maya can fill 9 bags of trail mix.
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