Question

4. Simplify :
(i) 3.5 - 2.43 + 0.075
(ii) 7.84 +0.3 – 4.016
(iii) 2.987 - 1-25 - 0-54
(iv) 52.9 - 231.666 + 204
(v) 8.57 – 6.4432 - 1.70 + 0.683
​

Answer 1

Simplify :

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(i) $\tt\:3.5-2.43+0.075$

Converting decimal into fraction form

$\tt\implies\:\frac{35}{10}-\frac{243}{100}+\frac{75}{1000}$

LCM of 10 , 100 and 1000 = 1000

$\tt\implies\:\frac{(100 \times 35)-(10 \times 243) +(1 \times 75)}{1000}$

Proceeding with simple calculation

$\tt\implies\:\frac{3500-2430+75}{1000}$

$\tt\implies\:\frac{1070+75}{1000}$

$\tt\implies\:\frac{1145}{1000}$

Converting fraction into decimal

$\small{\underline{\boxed{\mathrm\pink{\implies\:1.145}}}}$ ⛥

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(ii) $\tt\:7.84 +0.3 -4.016$

Converting decimal into fraction form

$\tt\implies\:\frac{784}{100}+\frac{3}{10}-\frac{4016}{1000}$

LCM of 100 , 10 and 1000 = 1000

$\tt\implies\:\frac{(10 \times 784) + (100 \times 3) - (1 \times 4016)}{1000}$

Proceeding with simple calculation

$\tt\implies\:\frac{7840+ 300 - 4016}{1000}$

$\tt\implies\:\frac{8140 - 4016}{1000}$

$\tt\implies\:\frac{4124}{1000}$

Converting fraction into decimal

$\small{\underline{\boxed{\mathrm\pink{\implies\:4.124}}}}$ ⛥

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(iii) $\tt\:2.987 - 1.25 - 0.54$

Converting decimal into fraction form

$\tt\implies\:\frac{2987}{1000}-\frac{125}{100}-\frac{54}{100}$

LCM of 1000 , 100 and 100 = 1000

$\tt\implies\:\frac{(1 \times 2987)-(10 \times 125) - (10 \times 54)}{1000}$

Proceeding with simple calculation

$\tt\implies\:\frac{2987-1250-540}{1000}$

$\tt\implies\:\frac{1737-540}{1000}$

$\tt\implies\:\frac{1197}{1000}$

Converting fraction into decimal

$\small{\underline{\boxed{\mathrm\pink{\implies\:1.197}}}}$ ⛥

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(iv) $\tt\:52.9 - 231.666 + 204$

Converting decimal into fraction form

$\tt\implies\:\frac{529}{10}-\frac{231666}{1000}+204$

LCM of 10 , 1000 and 1 = 1000

$\tt\implies\:\frac{(100 \times 529) - (1 \times 231666)+(1000 \times 204)}{1000}$

Proceeding with simple calculation

$\tt\implies\:\frac{52900-231666+204000}{1000}$

$\tt\implies\:\frac{-178766+204000}{1000}$

$\tt\implies\:\frac{-178766+204000}{1000}$

$\tt\implies\:\frac{25243}{1000}$

Converting fraction into decimal

$\small{\underline{\boxed{\mathrm\pink{\implies\:25.243}}}}$ ⛥

════════════════════ ‎

(v) $\tt\:8.57 - 6.4432 - 1.70 + 0.683$

Converting decimal into fraction form

$\tt\implies\:\frac{857}{100}-\frac{64432}{10000}-\frac{170}{100}+\frac{683}{1000}$

LCM of 100 , 10000 , 100 and 1000 = 100000

$\tt\implies\:\frac{(1000 \times 857) - (10 \times 64432) - (1000 \times 170) + (100 \times 683)}{100000}$

Proceeding with simple calculation

$\tt\implies\:\frac{857000 - 644320 - 170000 +68300}{10000}$

$\tt\implies\:\frac{212680- 170000 +68300}{100000}$

$\tt\implies\:\frac{42680 +68300}{100000}$

$\tt\implies\:\frac{110980}{100000}$

Reducing the fraction

$\tt\implies\:\frac{11098\cancel{0}}{10000\cancel{0}}$

$\tt\implies\:\frac{11098}{10000}$

Converting fraction into decimal

$\small{\underline{\boxed{\mathrm\pink{\implies\:1.1098}}}}$ ⛥

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‎Final anSwerS :

(i) 3.5 - 2.43 + 0.075 = $\bf\color{black}{1.145}$ $\sf\color{cyan}{⋆}$

(ii) 7.84 +0.3 – 4.016 = $\bf\color{black}{4.124}$ $\sf\color{cyan}{⋆}$

(iii) 2.987 - 1-25 - 0-54 = $\bf\color{black}{1.197}$ $\sf\color{cyan}{⋆}$

(iv) 52.9 - 231.666 + 204 = $\bf\color{black}{25.243}$ $\sf\color{cyan}{⋆}$

(v) 8.57 – 6.4432 - 1.70 + 0.683 = $\bf\color{black}{1.1098}$ $\sf\color{cyan}{⋆}$

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