To evaluate the numerical expressions with fractions, we need to be aware the concepts given below.
Note :
Calculate :
Problem 1 :
3 3/7 + 1 4/5
Solution :
= 3 3/7 + 1 4/5
Converting the mixed fraction to improper fraction, we get
= 24/7 + 9/5
Least common multiple of 7 and 5 is 35.
= [24(5) + 9(7)]/35
= (120 + 63)/35
= 183/35
Converting the improper fraction to mixed fraction, we get
= 5 8/35
Problem 2 :
(3/4)^{4}
Solution :
= (3/4)^{4}
= 3^{4}/4^{4}
= (3 × 3 × 3 × 3)/(4 × 4 × 4 × 4)
= (81)/256
Problem 3 :
7 - [6 × (3/4)]
Solution :
= 7 – [6 × (3/4)]
= 7 – (18/4)
Least common multiple of 1 and 4 is 4.
= [7(4) – 18(1)]/4
= (28 – 18)/4
= 10/4
Converting the improper fraction to mixed fraction, we get
= 2 1/2
Problem 4 :
4/5 × (1 1/2 ÷ 3)
Solution :
= 4/5 × (1 1/2 ÷ 3)
Converting the mixed fraction to improper fraction, we get
= 4/5 × 3/2 ÷ 3
Since we change the division sign to multiplication sign. We have to write the reciprocal of 3.
= 4/5 × 3/2 × 1/3
Least common multiple of 5, 2 and 3 is 30.
= [(4/5 × 6/6) × (3/2 × 15/15) × (1/3 × 10/10)
= [(24/30) × (45/30) ×(10/30)]
= (24 × 45 × 10)/27000
= 10800/27000
= 2/5
Problem 5 :
(8 × 3 × 1/3)/(2/3)
Solution :
= (8 × 3 × 1/3)/(2/3)
= 8/(2/3)
Since we change the division sign to multiplication sign .We have to write the reciprocal of 2/3.
= 8 × 3/2
= 24/3
= 12
Problem 6 :
1 ÷ (1/4 + 2/3)
Solution :
= 1 ÷ (1/4 + 2/3)
Least common multiple of 4 and 3 is 12.
= 1 ÷ (1/4 × 3/3 + 2/3 × 4/4)
= 1 ÷ (3/12 + 8/12)
= 1 ÷ 11/12
Since we change the division sign to multiplication sign .We have to write the reciprocal of 11/12.
= 12/11
Converting the improper fraction to mixed fraction, we get
= 1 1/11
Problem 7 :
(1 ÷ 1/4) + 2/3
Solution :
= (1 ÷ 1/4) + 2/3
= 4 + 2/3
Least common multiple of 1 and 3 is 3.
= [4(3) + 2(1)]/3
= (12 + 2)/3
= 14/3
Converting the improper fraction to mixed fraction, we get
= 4 2/3
Problem 8 :
(3 - 1/2)/(3 × 5/3)
Solution :
= (3 - 1/2)/(3 × 5/3)
Using cross multiplication we get,
= [(6 – 1)/2]/(15/3)
= (5/2)/(15/3)
Since we change the division sign to multiplication sign .We have to write the reciprocal of 15/3.
= 5/2 × 3/15
= 1/2
Problem 9 :
2/3 + (1/3 × 1 1/2)
Solution :
= 2/3 + (1/3 × 1 1/2)
Converting the mixed fraction to improper fraction, we get
= 2/3 + (1/3 × 3/2)
= 2/3 + 3/6
Least common multiple of 3 and 6 is 6.
= [(2(2) + 3(1)]/6.
= (4 + 3)/6
= 7/6
Converting the improper fraction to mixed fraction, we get
= 1 1/6
Problem 10 :
(5/6 × 4/5) – 1/15
Solution :
= (5/6 × 4/5) – 1/15
= 2/3 – 1/15
Least common multiple of 3 and 15 is15.
= [2(5) – 1(1)]/15
= (10 -1)/15
= 9/15
= 3/5
Problem 11 :
1/3 + (1/3 ÷ 1/5) + 3/5
Solution :
= 1/3 + (1/3 ÷ 1/5) + 3/5
= 1/3 + 5/3 + 3/5
Least common multiple of 3, 3 and 5 is15.
= [1(5) + 5(5) + 3(3])/15
= (5 + 25 + 9)/15
= 39/15
= 13/5
Converting the improper fraction to mixed fraction, we get
= 2 3/5
Problem 12 :
1 1/2 – (2 1/3 ÷ 1 2/3)
Solution :
= 1 1/2 – (2 1/3 ÷ 1 2/3)
Converting the mixed fraction to improper fraction, we get
= 3/2 – (7/3 ÷ 5/3)
Since we change the division sign to multiplication sign .We have to write the reciprocal of 5/3.
= 3/2 – (7/3 × 3/5)
= 3/2 – 7/5
Least common multiple of 2 and 5 is10.
= [3(5) – 7(2)]/10
= (15 – 14)/10
= 1/10
Problem 13 :
12 – (2/7 × 3 1/2)
Solution :
= 12 – 2/7 × 3 1/2
Converting the mixed fraction to improper fraction, we get
= 12 – (2/7 × 7/2)
= 12 – 1
= 11
Problem 14 :
(1 1/3 + 5/6) – 11/12
Solution :
= (1 1/3 + 5/6) – 11/12
Converting the mixed fraction to improper fraction, we get
= (4/3 + 5/6) – 11/12
Least common multiple of 3 and 6 is 6.
= [4(2) + 5(1)]/6 – 11/12
= (8 + 5)/6 – 11/12
= 13/6 – 11/12
Least common multiple of 6 and 12 is 12.
= [13(2) – 11(1)]/12
= (26 – 11)/12
= 25/12
Converting the improper fraction to mixed fraction, we get
= 1 1/4
Problem 15 :
(6 2/5 – 1/4) × (1 1/3 ÷ 1/6)
Solution :
= (6 2/5 – 1/4) × (1 1/3 ÷ 1/6)
Converting the mixed fraction to improper fraction, we get
= (32/5 – 1/4) × (4/3 ÷ 1/6)
Since we change the division sign to multiplication sign .We have to write the reciprocal of 1/6.
= 32/5 – (1/4 × 4/3 × 6)
= (32/5 – 24/12)
Least common multiple of 5 and 12 is 60.
= [(32(12) – 24(5)]/60
= (384 – 120)/60
= 264/60
= 22/5
Converting the improper fraction to mixed fraction, we get
= 4 2/5
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM