Solved Examples and Worksheet for Application of Rational Numbers involving 4 Operations
A.
B.
C. 6
D.
Step: 1
The problem asks us to find out how much chicken each divide
Step: 2
[Original expression.]
Step: 3
= 3 2
[Convert the mixed number into an improper fraction.]
Step: 4
= 3 2 1 4
[Multiply by 1 4
Step: 5
= 3 × 1 2 × 4
[Multiply the numerators and the denominators.]
Step: 6
= 3 8
Step: 7
So, each serving contained 3 8
Correct Answer is : 3 8
A.
B.
C.
D.
Step: 1
The fraction of the students with grade A or grade B = 1 3 1 4
Step: 2
= 1×4 3×4 1×3 4×3
[Use LCD 12 to write the equivalent fractions.]
Step: 3
= 4 12 3 12
[Simplify.]
Step: 4
= 4+3 12 7 12
[Add the numerators.]
Step: 5
Correct Answer is : 7 12
A.
B.
C.
D.
Step: 1
The acres of land required to grow both strawberries and tomatoes = 1 20 1 16
Step: 2
= [(1x4) (20x4) (1x5) (16x5)
[Use LCD 80 to write the equivalent fractions.]
Step: 3
= 4 80 5 80
[Simplify.]
Step: 4
= (4+5) 80 9 80
[Add the numerators.]
Step: 5
Remaining acres of land = 1 4 9 80
Step: 6
= [(1x20) (4x20) (9x1) (80x1)
[Use LCD 80 to write the equivalent fractions.]
Step: 7
= 20 80 9 80
[Simplify.]
Step: 8
= (20-9) 80 11 80
[Subtract the numerators.]
Step: 9
Henry is left with 11 80
Correct Answer is : 11 80
A. 3
B. 4
C. 5
D. 6
Step: 1
[Original expression.]
Step: 2
= 16 3 4 3
[Rewrite the mixed numbers as improper fractions.]
Step: 3
= 16 3 3 4
[Multiply 16 3 4 3
Step: 4
= 4 1 1 1
[Cancel 3 with 3 and 16 with 4.]
Step: 5
= 4
[Simplify.]
Step: 6
Jeff gets 4 pieces.
Correct Answer is : 4
A. 14
B. 11
C. 12
D. 13
Step: 1
[Rewrite the mixed number 2 1 4 9 4
Step: 2
27 = 27 1
[Rewrite the whole number 27 as a fraction, with the denominator 1.]
Step: 3
[Divide 27 by 9 4
Step: 4
[Multiply 27 1 9 4
Step: 5
= 2 7 × 4 1 × 9
[Multiply the numerators and the denominators.]
Step: 6
= 108 9
[Simplify.]
Step: 7
The can would last for 12 days.
Correct Answer is : 12
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
[Add.]
Step: 3
Amount Jeff has after paying for two shirts = $48.15 - $27.19
= $20.96
[Subtract.]
Correct Answer is : $20.96
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
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
A. 5
B.
C.
D.
Step: 1
The cost of the fabric per meter = the cost of the fabric for 18 3 5 4 1 5 18 3 5 4 1 5
Step: 2
= 93 5 21 5
[Rewrite the mixed fraction as an improper fraction.]
Step: 3
= 93 5 5 21
[a b c d a b d c
Step: 4
= (93)(5) (5)(21)
[a b c d ac bd
Step: 5
= 31 7
[Divide the numerator and the denominator by their GCF.]
Step: 6
= 4 3 7
[Rewrite the fraction as an improper fraction.]
Step: 7
The cost of the fabric per meter is $ 4 3 7
Correct Answer is : 4 3 7
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
[Original equation.]
Step: 3
[Divide each side by 4.]
Step: 4
[Simplify.]
Step: 5
Each of them should pay $206.80 for the apartment.
Correct Answer is : $206.80
A. $1160.06
B. $1159.06
C. $1157.06
D. $1158.06
Step: 1
Let x
Step: 2
16x
[Write an equation.]
Step: 3
[Divide each side by 16.]
Step: 4
[Simplify.]
Step: 5
[Round to nearest cent.]
Step: 6
So, the rent paid by each company is $1159.06.
Correct Answer is : $1159.06
A.
B.
C.
D.
Step: 1
[Divide 6 1 3 2 1 3
Step: 2
= 19 3 7 3
[Convert the mixed numbers into improper fractions.]
Step: 3
= 19 3 3 7
[Multiply by 3 7 7 3
Step: 4
= 19 1 1 7
[Cancel 3 with 3.]
Step: 5
= 19×1 7×1 19 7
[Multiply numerators and denominators separately.]
Step: 6
= 2 5 7
[Represent 19 7
Step: 7
Valerie sold 2 5 7
Correct Answer is : 2 5 7
A. 9
B. 10
C. 12
D. 11
Step: 1
Let n
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
[Substitute.]
Step: 4
= (6.22 x n
[Subtract 30.42 from both sides.]
Step: 5
= (6.22 x n
Step: 6
= n 24.88 6.22
[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
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
Correct Answer is : $1.40
A.
B.
C. 30
D.
Step: 1
[Write the expression.]
Step: 2
= 4 6 20 1
[Write the whole number as a fraction.]
Step: 3
= 4 6 1 20
[Multiply by the reciprocal of 20 1 1 20
Step: 4
= 1 6 1 5
[Cancel 20 with 4.]
Step: 5
= 1 × 1 6 × 5
[Multiply numerators and denominators separately.]
Step: 6
= 1 30
[Simplify.]
Step: 7
So, each student gets 1 30
Correct Answer is : 1 30
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