Simplify the following. 3 1 5 ÷ 2 3 5 of 1 1 2

We have to simplify 3 1 5 ÷ 2 3 5 of 1 1 2 Now, 3 1 5 ÷ 2 3 5 of 1 1 2 can be written as 3 1 5 ÷ 2 3 5 × 1 1 2 = 16 5 ÷ 13 5 × 3 2 [By converting mixed fractions to improper fractions] = 16 5 × 5 13 × 3 2 = 8 13 × 3 = 24 13 = 1 11 13 Hence, 3 1 5 ÷ 2 3 5 of 1 1 2 = 1 11 13

Simplify the following. 3 1 5 ÷ 2 3 5 of 1 1 2

We have to simplify 3 1 5 ÷ 2 3 5 of 1 1 2 Now, 3 1 5 ÷ 2 3 5 of 1 1 2 can be written as 3 1 5 ÷ 2 3 5 × 1 1 2 = 16 5 ÷ 13 5 × 3 2 [By converting mixed fractions to improper fractions] = 16 5 × 5 13 × 3 2 = 8 13 × 3 = 24 13 = 1 11 13 Hence, 3 1 5 ÷ 2 3 5 of 1 1 2 = 1 11 13

Simplify the following. 1 3 - 3 5 + 1 12 of 1 1 2 ÷ 3 4

The given expression is 1 3 - 3 5 + 1 12 of 1 1 2 ÷ 3 4 According to the BODMAS rule, if an expression contains brackets ((), {}, []) we have first to solve or simplify the bracket followed by 'order' (that means powers and roots, etc.), then division, multiplication, addition and subtraction from left to right. Now, 1 3 - 3 5 + 1 12 of 1 1 2 ÷ 3 4 = 1 3 - 3 5 + 1 12 × 3 2 ÷ 3 4 = 1 3 - 3 5 + 1 8 ÷ 3 4 = 1 3 - 3 5 + 1 8 × 4 3 = 1 3 - 3 5 + 1 2 × 1 3 = 1 3 - 3 5 + 1 6 = 10 30 - 18 30 + 5 30 = 10 - 18 + 5 30 = - 3 30 = - 1 10 Hence, 1 3 - 3 5 + 1 12 of 1 1 2 ÷ 3 4 = - 1 10 .

Simplify the following. 11 169 ÷ 121 225 ÷ 15 13

The given expression is 11 169 ÷ 121 225 ÷ 15 13 According to the BODMAS rule, if an expression contains brackets ((), {}, []) we have first to solve or simplify the bracket followed by 'order' (that means powers and roots, etc.), then division, multiplication, addition and subtraction from left to right. Now, 11 169 ÷ 121 225 ÷ 15 13 = 11 169 × 225 121 ÷ 15 13 = 1 169 × 225 11 ÷ 15 13 = 225 169 × 11 ÷ 15 13 = 225 169 × 11 × 13 15 = 15 13 × 11 = 15 143 Hence, 11 169 ÷ 121 225 ÷ 15 13 = 15 143 .

Simplify the following. 3 1 2 - 2 3 4 of 4 9 + 5 14 ÷ 2 1 7

The given expression is 3 1 2 - 2 3 4 of 4 9 + 5 14 ÷ 2 1 7 When brackets are present, we follow BODMAS rule. Apart from the operations of division, multiplication, addition and subtraction, we drop brackets one by one in the order of , and . Now, 3 1 2 - 2 3 4 of 4 9 + 5 14 ÷ 2 1 7 = 7 2 - 11 4 of 4 9 + 5 14 ÷ 15 7 = 14 4 - 11 4 of 4 9 + 5 14 ÷ 15 7 = 14 - 11 4 of 4 9 + 5 14 ÷ 15 7 = 3 4 of 4 9 + 5 14 ÷ 15 7 = 3 4 × 4 9 + 5 14 ÷ 15 7 = 1 3 + 5 14 ÷ 15 7 = 1 3 + 5 14 × 7 15 = 1 3 + 1 2 × 1 3 = 1 3 + 1 6 = 2 6 + 1 6 = 2 + 1 6 = 3 6 = 1 2 Hence, 3 1 2 - 2 3 4 of 4 9 + 5 14 ÷ 2 1 7 = 1 2 .

Simplify the following. 5 12 + 1 3 × 8 2 5 of 25 16 - 3 - 2 1 2

The given expression is 5 12 + 1 3 × 8 2 5 of 25 16 - 3 - 2 1 2 When brackets are present, we follow BODMAS rule. Apart from the operations of division, multiplication, addition and subtraction, we drop brackets one by one in the order of , and . Now, 5 12 + 1 3 × 8 2 5 of 25 16 - 3 - 2 1 2 = 5 12 + 1 3 × 8 2 5 of 25 16 - 3 - 5 2 = 5 12 + 1 3 × 8 2 5 of 25 16 - 6 - 5 2 = 5 12 + 1 3 × 8 2 5 of 25 16 - 1 2 = 5 12 + 1 3 × 8 2 5 × 25 16 - 1 2 = 5 12 + 1 3 × 8 5 8 - 1 2 = 5 12 + 1 3 × 8 5 8 - 4 8 = 5 12 + 1 3 × 8 5 - 4 8 = 5 12 + 1 3 × 8 1 8 = 5 12 + 1 3 × 1 = 5 12 + 1 3 = 5 12 + 4 12 = 9 12 = 3 4 Hence, 5 12 + 1 3 × 8 2 5 of 25 16 - 3 - 2 1 2 = 3 4 .

Simplify the following. 4 1 2 - 2 3 4 + 3 5 of 1 7 8 - 2 1 4 - 1 3 8

The given expression is 4 1 2 - 2 3 4 + 3 5 of 1 7 8 - 2 1 4 - 1 3 8 When brackets are present, we follow BODMAS rule. Apart from the operations of division, multiplication, addition and subtraction, we drop brackets one by one in the order of , and . Now, 4 1 2 - 2 3 4 + 3 5 of 1 7 8 - 2 1 4 - 1 3 8 = 9 2 - 11 4 + 3 5 of 15 8 - 9 4 - 11 8 = 9 2 - 11 4 + 3 5 of 15 8 - 18 8 - 11 8 = 9 2 - 11 4 + 3 5 of 15 8 - 18 - 11 8 = 9 2 - 11 4 + 3 5 × 15 8 - 7 8 = 9 2 - 11 4 + 9 8 - 7 8 = 9 2 - 22 8 + 9 8 - 7 8 = 9 2 - 22 + 9 - 7 8 = 9 2 - 24 8 = 9 2 - 3 = 9 - 6 2 = 3 2 = 1 1 2 Hence, 4 1 2 - 2 3 4 + 3 5 of 1 7 8 - 2 1 4 - 1 3 8 = 1 1 2 .

Evaluate the following: 10 + 3 5 7 - 5 2 21

The given expression is 10 + 3 5 7 - 5 2 21 . First, we convert the mixed fractions into improper fractions. Now, 10 + 3 5 7 - 5 2 21 = 10 + 26 7 - 107 21 = 210 21 + 78 21 - 107 21 = 210 + 78 - 107 21 = 181 21 = 8 13 21 Hence, 10 + 3 5 7 - 5 2 21 = 8 13 21 .