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. 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 .

Evaluate the following: 1 3 4 + 2 5 7 - 1 3 14

The given expression is 1 3 4 + 2 5 7 - 1 3 14 . First, we convert the mixed fractions into improper fractions. Now, 1 3 4 + 2 5 7 - 1 3 14 = 7 4 + 19 7 - 17 14 = 49 28 + 76 28 - 34 28 [L.C.M. of 4 , 7 , 14 is 28 ] = 49 + 76 - 34 28 = 91 28 = 13 4 = 3 1 4 Hence, 1 3 4 + 2 5 7 - 1 3 14 = 3 1 4 .

Evaluate the following: 8 - 3 1 2 - 2 1 5

The given expression is 8 - 3 1 2 - 2 1 5 . First, we convert the mixed fractions into improper fractions. Now, 8 - 3 1 2 - 2 1 5 = 8 - 7 2 - 11 5 = 80 10 - 35 10 - 22 10 [L.C.M. of 2 , 5 is 10 ] = 80 - 35 - 22 10 = 23 10 = 2 3 10 Hence, 8 - 3 1 2 - 2 1 5 = 2 3 10 .

Evaluate the following: 2 3 10 + 1 4 5 - 1 1 4 - 9 20

The given expression is 2 3 10 + 1 4 5 - 1 1 4 - 9 20 . First, we convert the mixed fractions into improper fractions. Now, 2 3 10 + 1 4 5 - 1 1 4 - 9 20 = 23 10 + 9 5 - 5 4 - 9 20 = 46 20 + 36 20 - 25 20 - 9 20 [L.C.M. of 4 , 5 , 10 , 20 is 20 ] = 46 + 36 - 25 - 9 20 = 48 20 = 12 5 = 2 2 5 Hence, 2 3 10 + 1 4 5 - 1 1 4 - 9 20 = 2 2 5 .