# EVALUATING NUMERICAL EXPRESSIONS WITH FRACTIONS

To evaluate the numerical expressions with fractions, we need to be aware the concepts given below.

Note :

• If the given is mixed fractions, convert them to improper fractions.

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

= 34/44

= (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

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