APPLYING RATIONAL NUMBER OPERATIONS
About "Applying rational number operations"
Applying rational number operations :
In this section, we are going to learn how rational number operations (addition, subtraction, multiplication and division) can be applied to solve real world problems.
Applying rational number operations - Examples
Example 1 :
Malachi hikes for 2.5 miles and stops for lunch. Then he hikes for 1.5 more miles. How many miles did he hike altogether?
Solution :
Step 1 :
Use positive numbers to represent the distance Malachi hiked.
Step 2 :
Find 2.5 + 1.5.
Let us use the real number line to add 2.5 and 1.5.
Step 3 :
Start at 2.5.
Step 4 :
Move 1.5 units to the right because the second addend is positive.
The result is 4.
Malachi hiked 4 miles.
Example 2 :
The temperature on an outdoor thermometer on Monday was 5.5 °C. The temperature on Thursday was 7.25 degrees less than the temperature on Monday. What was the temperature on Thursday ?
Answer :
Step 1 :
Find 5.5 - 7.25.
Step 2 :
Start at 5.5.
Step 3 :
Move |7.25| = 7.25 units to the left, because we are subtracting a positive numbe
The result is -1.75.
The temperature on Thursday was -1.75 °C.
Example 3 :
The science teacher is filling her new fish aquarium. The aquarium holds 40 gallons. If she fills the aquarium 4/5 of the way full, how many gallons will she need?
Solution :
If 4/5 of the aquarium is filled, then 1/5 th of the aquarium to be filled to make it full. Because 5 - 4 = 1.
To find number of gallons, we have to multiply 40 by 1/5.
Step 1 : Multiply 40 by 1/5
40 x 1/5
Step 2 : Simplify
8 x 1/1
Step 3 : Multiply
8 x 1/1 = 8
Hence, the science teacher needs 8 gallons to make the aquarium full.
Example 4 :
Cooper's bird feeder holds 9/10 of a cup of birdseed. Cooper is filling the bird feeder with a scoop that holds 3/10 of a cup. How many scoops of birdseed will Cooper put into the feeder?
Solution :
Step 1 :
To get answer for the above question, divide the total amount of birdseed by the size of each scoop.
That is, we have to find the value of (9/10) / (3/10).
Step 2 :
Determine the sign of the quotient.
The quotient will be positive, because the signs of both numerator (9/10) and denominator (3/10) are same.
Step 3 :
Write the complex fraction as division :
(9/10) / (3/10) = (9/10) ÷ (3/10)
Step 4 :
Rewrite the above division as multiplication by taking the reciprocal of the second fraction.
(9/10) ÷ (3/10) = (9/10) x (10/3)
Step 5 :
Simplify
(9/10) x (10/3) = (3/1) x (1/1)
(9/10) x (10/3) = 3
Hence, Cooper will put 3 scoops of birdseed into the feeder
After having gone through the stuff given above, we hope that the students would have understood "Applying rational number operations".
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WORD PROBLEMS
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
