Simplify:

1. 6 + {4/3 + (3/4 – 1/3)}

2. 8 – {3/2 + (3/5 – 1/2)}

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Solution

(i) It is given that

6 + {4/3 + (3/4 – 1/3)}

We can write it as

= 6 + {4/3 + 3/4 – 1/3}

By further calculation

= 6/1 + 4/3 + 3/4 – 1/3

Here the LCM of 3 and 4 is 12

= (72 + 16 + 9 – 4)/ 12

So we get

= (97 – 4)/ 12

= 93/12

= 31/4

= 7 ¾

(ii) It is given that

8 – {3/2 + (3/5 – 1/2)}

We can write it as

= 8 – {3/2 + 3/5 – 1/2}

By further calculation

= 8/1 – 3/2 – 3/5 + 1/2

Here the LCM of 2 and 5 is 10

= (80 – 15 – 6 + 5)/ 10

So we get

= (85 – 21)/ 10

= 64/10

Dividing by 2

= 32/5

= 6 2/5

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(5) $- 15 + (- 4) - (+ 3)$

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Evaluate :

$(i) (3^{- 1} \times 9^{- 1}) \div 3^{- 2} (i i) (3^{- 1} \times 4^{- 1}) \div 6^{- 1} (i i i) (2^{- 1} + 3^{- 1})^{3} (i v) (3^{- 1} \div 4^{- 1})^{2} (v) (2^{2} + 3^{2}) \times {(\frac{1}{2})}^{2} (v i) (5^{2} - 3^{2}) \times {(\frac{2}{3})}^{- 3} (v i i) [{(\frac{1}{4})}^{- 3} - {(\frac{1}{3})}^{- 3}] \div {(\frac{1}{6})}^{- 3} (v i i i) {[{(- \frac{3}{4})}^{- 2}]}^{2} (i x) {{(\frac{3}{5})}^{- 2}}^{- 2} (x) (5^{- 1} \times 3^{- 1}) \div 6^{- 1}$

Q. Simplify:

{[{(\frac{2}{3})}^{2}]}^{3} \times {(\frac{2}{3})}^{- 4} \times 3^{- 1} \times \frac{1}{6}

Q. Simplify :

(\frac{3}{2} \times \frac{1}{6}) + (\frac{5}{3} \times \frac{7}{2}) - (\frac{13}{8} \times \frac{4}{3})

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Simplify: 1. 6 + {4/3 + (3/4 – 1/3)} 2. 8 – {3/2 + (3/5 – 1/2)}

Simplify:

1. 6 + {4/3 + (3/4 – 1/3)}

2. 8 – {3/2 + (3/5 – 1/2)}