**Order of operations and the Use of Brackets – Maharashtra Board Class 6 Solutions for Mathematics (English Medium)**

MathematicsGeneral ScienceMaharashtra Board Solutions

### Exercise-10

**Solution 1(1):**

12 × 14 ÷ 7

= 168 ÷ 7 | Multiplication first.

= 24 | Then, division.

**Solution 1(2):**

160 × 10 ÷ 5 × 4

= 1600 ÷ 5 × 4 | Multiplication from left.

= 320 × 4 | Division

= 1280 | Multiplication

**Solution 1(3):**

160 × 10 ÷ (5 × 4)

=160 × 10 ÷ 20 | Multiplication in the brackets.

= 1600 ÷ 20 | Multiplication

= 80 | Division

**Solution 1(4):**

(160 × 10) ÷ (5 × 4)

= 1600 ÷ 20 | Multiplication in both brackets.

= 80 | Division

**Solution 1(5):**

94 – 61 – 23

= 33 – 23 | Subtraction on left.

= 10 | Subtraction

**Solution 1(6):**

94 – (61 – 23)

= 94 – 38 |Subtraction in the brackets.

= 56 | Subtraction

**Solution 1(7):**

237 – 87 + 30

= 150 + 30 | Subtraction

= 180 | Addition

**Solution 1(8):**

237 – (87 + 30)

= 237 – 117 | Adding in the brackets.

= 120 | Subtraction

**Solution 1(9):**

450 ÷ 10 ÷ 5

= 45 ÷ 5 | Division on the left.

= 9 | Division

**Solution 1(10):**

450 ÷ (10 ÷ 5)

= 450 ÷ 2 | Division in the brackets.

= 225 | Division

**Solution 1(11):**

103 + 91 × 2 + 8

= 103 + 182 + 8 | Multiplication

= 285 + 8 | Addition on the left.

= 293 | Addition

**Solution 1(12):**

(103 + 91) × (2 + 8)

= 194 × 10 | Addition in the brackets.

= 1940 | Multiplication

**Solution 1(13):**

216 ÷ (24 – 6) + 2 × (53 – 14 – 6)

= 216 ÷ 18 + 2 × (39 – 6) | Subtraction in brackets.

= 12 + 2 × 33 | Subtraction in brackets.

= 12 + 66 | Multiplication

= 78 | Addition

**Solution 1(14):**

[18 + 5(7 – 3)] + 64 ÷ [20 – (8 × 2)]

= (18 + 5 × 4) + 64 ÷ (20 – 16) |Operations in inner brackets of square brackets.

= (18 + 20) + 64 ÷ 4 | Multiplication and subtraction in the brackets.

= 38 + 16 | Addition and division.

= 54 | Addition

**Solution 1(15):**

210 ÷ {125 – [5 + 3 (14 – 9)]}

= 210 ÷ {125 – (5 + 3 × 5)} | Operation in the innermost brackets.

= 210 ÷ {125 – (5 + 15)} | Multiplication

= 210 ÷ (125 – 20 ) | Addition

= 210 ÷ 105 | Subtraction

= 2 | Division

**Solution 2(1):**

18 ÷ 6 + 3 (value 2)

If the brackets are inserted as 18 ÷ (6 + 3),

we get the value 18 ÷ 6 + 3 = 18 ÷ 9 = 2

∴ 18 ÷ (6 + 3) is the required expression.

**Solution 2(2):**

4 × 13 + 2 + 40

If the brackets are inserted as 4 × (13 + 2) + 40,

we get the value 4 × (13 + 2) + 40 = 4 × 15 + 40 = 60 + 40 = 100

∴ 4 × (13 + 2) + 40 is the required expression.

**Solution 2(3):**

If the brackets are inserted as (100 + 20) ÷ 5,

we get the value (100 + 20) ÷ 5 = 120 ÷ 5 = 24

∴ (100 + 20) ÷ 5 is the required expression.

**Solution 2(4):**

If the brackets are inserted as 100 ÷ (20 ÷ 5),

we get the value 100 ÷ (20 ÷ 5) = 100 ÷ 4 = 25

∴ 100 ÷ (20 ÷ 5) is the required expression.

**Solution 2(5):**

If the brackets are inserted as 13 – (9 + 2),

we get the value 13 – (9 + 2) = 13 – 11 = 2.

∴ 13 – (9 + 2) is the required expression.