#### Solved Examples and Worksheet for Application of Rational Numbers involving 4 Operations

Q1Willa cooked 112 pounds of chicken for 4 people. How much chicken did each serving contain, if all 4 servings contained the same amount of chicken?

A. 18
B. 38
C. 6
D. 83

Step: 1
The problem asks us to find out how much chicken each serving contained. So, we need to divide the pounds of chicken cooked by the number of servings.
Step: 2
112 ÷ 4
[Original expression.]
Step: 3
= 32 ÷ 4
[Convert the mixed number into an improper fraction.]
Step: 4
= 32 × 14
[Multiply by 14, the reciprocal of 4.]
Step: 5
= 3 × 12 × 4
[Multiply the numerators and the denominators.]
Step: 6
= 38

Step: 7
So, each serving contained 38 of a pound of chicken.
Q213 of the students in a class got an A in a test and 14 of the students got a B. What fraction of the students got grade A or grade B?
A. 412
B. 112
C. 17
D. 712

Step: 1
The fraction of the students with grade A or grade B = 13 + 14.
Step: 2
= 1×43×4 + 1×34×3
[Use LCD 12 to write the equivalent fractions.]
Step: 3
= 412 + 312
[Simplify.]
Step: 4
= 4+312 = 712
Step: 5
Q3Henry has 14 acre of land. He plans to grow strawberries in 120 acre of land and tomatoes in 116 acre. Find what fraction of land Henry is left with after growing both strawberries and tomatoes.
A. 18 acres
B. 320 acres
C. 1180 acres
D. 1380 acres

Step: 1
The acres of land required to grow both strawberries and tomatoes = 120 + 116.
Step: 2
= [(1x4)(20x4)] + [(1x5)(16x5)]
[Use LCD 80 to write the equivalent fractions.]
Step: 3
= 480 + 580
[Simplify.]
Step: 4
= (4+5)80 = 980
Step: 5
Remaining acres of land = 14 - 980.
Step: 6
= [(1x20)(4x20)] - [(9x1)(80x1)]
[Use LCD 80 to write the equivalent fractions.]
Step: 7
= 2080 - 980
[Simplify.]
Step: 8
= (20-9)80 = 1180
[Subtract the numerators.]
Step: 9
Henry is left with 1180 acres of land after growing both strawberries and tomatoes.
Correct Answer is :   1180 acres
Q4Jeff has a rope that measures 513 in. He wants to cut it into pieces each measuring 113 in. long. How many pieces would he get?

A. 3
B. 4
C. 5
D. 6

Step: 1
513 ÷ 113
[Original expression.]
Step: 2
= 163 ÷ 43
[Rewrite the mixed numbers as improper fractions.]
Step: 3
= 163 × 34
[Multiply 163 by the reciprocal of 43.]
Step: 4
= 41 × 11
[Cancel 3 with 3 and 16 with 4.]
Step: 5
= 4
[Simplify.]
Step: 6
Jeff gets 4 pieces.
Q5Chris buys an 27 lb can of Mighty Dog food. His dogs eat 214 lbs each day. How many days will the can last?

A. 14
B. 11
C. 12
D. 13

Step: 1
214 = 94
[Rewrite the mixed number 214 as improper fraction 94.]
Step: 2
27 = 271
[Rewrite the whole number 27 as a fraction, with the denominator 1.]
Step: 3
271 ÷ 94
[Divide 27 by 94.]
Step: 4
271 ÷ 94 = 271 × 49
[Multiply 271 with the reciprocal of 94.]
Step: 5
= 27 × 41 × 9
[Multiply the numerators and the denominators.]
Step: 6
= 1089 = 12
[Simplify.]
Step: 7
The can would last for 12 days.
Q6Jeff had $48.15. He bought two shirts that cost$11.23 and $15.96. How much does he have after he pays for the shirts? A.$48
B. $27.19 C.$20.96
D. $48.15 Step: 1 Amount Jeff has after paying for two shirts = Amount Jeff had - Cost of two shirts Step: 2 Cost of two shirts = 11.23 + 15.96 =$27.19
Step: 3
Amount Jeff has after paying for two shirts = $48.15 -$27.19
= $20.96 [Subtract.] Correct Answer is :$20.96
Q7Ethan had $188.37. He gave$35.31 to Paul but borrowed another $106.71 from Paul. How much does Ethan have now? A.$35.31
B. $153.06 C.$259.77
D. $209.77 Step: 1 Amount Ethan had after he gave$35.31 to Paul = 188.37 - 35.31
= $153.06 Step: 2 Amount Ethan has after he borrowed$106.71 from Paul
= 153.06 + 106.71

Step: 3
= $259.77 Correct Answer is :$259.77
Q8How long will Sunny take to drive a distance of 499.38 mi, if he drives at a speed of 40.6 mi/hr?

A. 123 hrs
B. 12.3 hrs
C. 1.23 hrs
D. 2.81 hrs

Step: 1
Time taken by Sunny to travel a distance of 499.38 mi = total distance ÷ the speed at which he travels
= 499.38 ÷ 40.6
[Substitute the values.]
Step: 2 Step: 3
Time taken by Sunny to travel to 499.38 mi is 12.3 hrs.
Correct Answer is :   12.3 hrs
Q9The cost of 415 meters of a fabric is $1835. Find the cost of the fabric per meter. A. 5 B. 31013 C. 437 D. 41219 Step: 1 The cost of the fabric per meter = the cost of the fabric for 1835 meters ÷ 415 = 1835 ÷ 415. Step: 2 = 935 ÷ 215 [Rewrite the mixed fraction as an improper fraction.] Step: 3 = 935 × 521 [ab ÷ cd = ab × dc.] Step: 4 = (93)(5)(5)(21) [ab × cd = acbd.] Step: 5 = 317 [Divide the numerator and the denominator by their GCF.] Step: 6 = 437 [Rewrite the fraction as an improper fraction.] Step: 7 The cost of the fabric per meter is$ 437.
Q10Sam, Jake, Arthur and Matt plan to share an apartment in Dugway. How much should each of them pay every month, if the rent of the apartment is $827.20 per month? A.$204.80
B. $206.80 C.$208.80
D. $210.30 Step: 1 Let the share of each individual be x. Step: 2 4x = 827.20 [Original equation.] Step: 3 x = 827.204 [Divide each side by 4.] Step: 4 x = 206.80 [Simplify.] Step: 5 Each of them should pay$206.80 for the apartment.
Correct Answer is :   $206.80 Q11A 16-storied building was rented to 16 different software companies for$18545 as a whole, per month. Find the rent paid by each company, if each company pays the same rent.
A. $1160.06 B.$1159.06
C. $1157.06 D.$1158.06

Step: 1
Let x be the rent paid by each company.
Step: 2
16x = 18545
[Write an equation.]
Step: 3
x = 1854516
[Divide each side by 16.]
Step: 4
x = 1159.0625
[Simplify.]
Step: 5
x 1159.06
[Round to nearest cent.]
Step: 6
So, the rent paid by each company is $1159.06. Correct Answer is :$1159.06
Q12Valerie sells 613 lbs of fruits in 213 days. How many lbs of fruits does she sell in one day?

A. 215
B. 238
C. 257
D. 212

Step: 1
613 ÷ 213
[Divide 613 by 213.]
Step: 2
= 193 ÷ 73
[Convert the mixed numbers into improper fractions.]
Step: 3
= 193 × 37
[Multiply by 37, the reciprocal of 73.]
Step: 4
= 191 × 17
[Cancel 3 with 3.]
Step: 5
= 19×17×1= 197
[Multiply numerators and denominators separately.]
Step: 6
= 257
[Represent 197 as a mixed number.]
Step: 7
Valerie sold 257 lbs of fruits in one day.
Q13Tim wanted to rent a car. He had to pay $30.42 for the first 6 hours and$6.22 for each extra hour. If he paid a total of $55.30, find the total number of hours he rented the car. A. 9 B. 10 C. 12 D. 11 Step: 1 Let n be the number of extra hours. Step: 2 Total amount = Amount taken for 6 hours + (amount taken for each extra hour x number of extra hours). Step: 3 = 30.42 + (6.22 x n) = 55.30 [Substitute.] Step: 4 = (6.22 x n) = 55.30 - 30.42 [Subtract 30.42 from both sides.] Step: 5 = (6.22 x n) = 24.88 Step: 6 = n = 24.886.22 = 4 [Divide both sides with 6.22.] Step: 7 Total number of hours Tim took the car for rent = 6 + 4 = 10. Correct Answer is : 10 Q14Edward bought 3 pencils of equal price for$4.20. Find the price of each pencil.

A. $1.20 B.$12.60
C. $1.40 D.$14.0

Step: 1
The price of three pencils = $4.20. Step: 2 Price of each pencil = Price of 3 pencils ÷ Number of pencils = 4.20 ÷ 3 [Substitute the values.] Step: 3 Step: 4 The price of each pencil =$1.40
Q15Mike distributes 46 of a cake to 20 students in his class on his birthday. What fraction of cake does each student get?

A. 130
B. 120
C. 30
D. 530

Step: 1
46 ÷ 20
[Write the expression.]
Step: 2
= 46 ÷ 201
[Write the whole number as a fraction.]
Step: 3
= 46 × 120
[Multiply by the reciprocal of 201, which is 120.]
Step: 4
= 16 × 15
[Cancel 20 with 4.]
Step: 5
= 1 × 16 × 5
[Multiply numerators and denominators separately.]
Step: 6
= 130
[Simplify.]
Step: 7
So, each student gets 130 of the cake.