SIMPLIFICATION: NUMERICAL EXPRESSIONS WITHOUT BRACKETS (DMAS)
DMAS RULE
DMAS rule is followed when multiple arithmetic operations like addition, subtraction,
multiplication, and division are present in a given mathematical expression. In ‘DMAS’, D
stands for division, M for multiplication, A for addition, and S for subtraction. DMAS
represents the order of operations. When a mathematical expression involving all four
operations is given, we solve these operations in the order:
1. Division 2. Multiplication 3. Addition 4. Subtraction
For example, consider the following cases.
Example: Simplify: 5 + 4 × 3 – 9 ÷ 3
Sol. In this example, all the four operations are there, so we have to use DMAS rule.
5+ 4 × 3 – 9 ÷ 3= 5 + 4 × 3 – 3 (Division: 9 ÷ 3 = 3)
= 5 + 12 – 3 (Multiplication: 4 × 3 = 12)
= 17 – 3 (Addition: 5 + 12 = 17)
= 14 (Subtraction: 17 – 3 = 14)
Example : Simplify using DMAS rule 5 x 3 +8 ÷ 4
Solution. 5 x 3 +8 ÷ 4= 5 x 3 +8 ÷ 4
= 5 x 3 +2
=15+2
=17
DMAS SUMS FOR CLASS 5 (solved examples)
Simplify the following numerical expressions:
(i) 28-3 x 5 +4
Sol. 28-3 x 5 +4=28-15+4
=32-15
=17
(ii) 15-3 x 4 ÷2+2
, Sol. 15-3 x 4 ÷2+2= 15-3 x 2+2
=15-6+2
=17-6
=11
(iii) 39-18÷3+2 x 3
Sol. 39-18÷3+2 x 3 =39-6+2 x 3
=39-6+6
=45-6
=39
(iv) 5 x 8-6 ÷2
Sol. 5 x 8 -6 ÷2=5 x 8-3
=40-3
=37
(v) 15÷5 x 4 ÷ 2
Sol. 15÷5 x 4 ÷ 2=3 x 2
=6
(vi)10+8÷4-2 x 6
Sol. 10+8÷4-2 x 6=10+2-2 x 6
=10+2-12
=12-12
=0
(vii)42-18 ÷2 x 3
Sol. 42-18 ÷2 x 3=42-9 x 3
=42-27
=15
(viii) 5 ÷ 5 +6 x 6
DMAS RULE
DMAS rule is followed when multiple arithmetic operations like addition, subtraction,
multiplication, and division are present in a given mathematical expression. In ‘DMAS’, D
stands for division, M for multiplication, A for addition, and S for subtraction. DMAS
represents the order of operations. When a mathematical expression involving all four
operations is given, we solve these operations in the order:
1. Division 2. Multiplication 3. Addition 4. Subtraction
For example, consider the following cases.
Example: Simplify: 5 + 4 × 3 – 9 ÷ 3
Sol. In this example, all the four operations are there, so we have to use DMAS rule.
5+ 4 × 3 – 9 ÷ 3= 5 + 4 × 3 – 3 (Division: 9 ÷ 3 = 3)
= 5 + 12 – 3 (Multiplication: 4 × 3 = 12)
= 17 – 3 (Addition: 5 + 12 = 17)
= 14 (Subtraction: 17 – 3 = 14)
Example : Simplify using DMAS rule 5 x 3 +8 ÷ 4
Solution. 5 x 3 +8 ÷ 4= 5 x 3 +8 ÷ 4
= 5 x 3 +2
=15+2
=17
DMAS SUMS FOR CLASS 5 (solved examples)
Simplify the following numerical expressions:
(i) 28-3 x 5 +4
Sol. 28-3 x 5 +4=28-15+4
=32-15
=17
(ii) 15-3 x 4 ÷2+2
, Sol. 15-3 x 4 ÷2+2= 15-3 x 2+2
=15-6+2
=17-6
=11
(iii) 39-18÷3+2 x 3
Sol. 39-18÷3+2 x 3 =39-6+2 x 3
=39-6+6
=45-6
=39
(iv) 5 x 8-6 ÷2
Sol. 5 x 8 -6 ÷2=5 x 8-3
=40-3
=37
(v) 15÷5 x 4 ÷ 2
Sol. 15÷5 x 4 ÷ 2=3 x 2
=6
(vi)10+8÷4-2 x 6
Sol. 10+8÷4-2 x 6=10+2-2 x 6
=10+2-12
=12-12
=0
(vii)42-18 ÷2 x 3
Sol. 42-18 ÷2 x 3=42-9 x 3
=42-27
=15
(viii) 5 ÷ 5 +6 x 6
