Decimal Fractions — Exercise 7(B)

Add the following:

0.243, 2.47 and 3.009

Answer

Converting the decimals into like decimals :

The like decimal numbers are 0.243, 2.470 and 3.009

$\begin{array}{r} & 0.243 \\ & 2.470 \\ + & 3.009 \\ \hline & 5.722 \end{array}$

Hence, 0.243 + 2.47 + 3.009 = 5.722

Add the following:

0.0736, 0.6095 and 0.9107

Answer

Converting the decimals into like decimals :

The like decimal numbers are 0.0736, 0.6095 and 0.9107

$\begin{array}{r} & 0.0736 \\ & 0.6095 \\ + & 0.9107 \\ \hline & 1.5938 \end{array}$

Hence, 0.0736 + 0.6095 + 0.9107 = 1.5938

Add the following:

1.01, 257 and 0.200

Answer

Converting the decimals into like decimals :

The like decimal numbers are 1.010, 257.000 and 0.200

$\begin{array}{rr} & 1.010 \\ & 257.000 \\ + & 0.200 \\ \hline & 258.210 \end{array}$

Hence, 1.01 + 257 + 0.200 = 258.21

Add the following:

18, 200.35, 11.72 and 2.3

Answer

Converting the decimals into like decimals :

The like decimal numbers are 18.00, 200.35, 11.72 and 2.30

$\begin{array}{rr} & 18.00 \\ & 200.35 \\ & 11.72 \\ + & 2.30 \\ \hline & 232.37 \end{array}$

Hence, 18 + 200.35 + 11.72 + 2.3 = 232.37

Add the following:

0.586, 0.0586 and 0.00586

Answer

Converting the decimals into like decimals :

The like decimal numbers are 0.58600, 0.05860 and 0.00586

$\begin{array}{r} & 0.58600 \\ & 0.05860 \\ + & 0.00586 \\ \hline & 0.65046 \end{array}$

Hence, 0.586 + 0.0586 + 0.00586 = 0.65046

Subtract the following:

6.8 - 2.64

Answer

Converting the decimals into like decimals :

The like decimal numbers are 6.80 and 2.64

$\begin{array}{r} & 6.80 \\ - & 2.64 \\ \hline & 4.16 \end{array}$

Hence, 6.8 - 2.64 = 4.16

Subtract the following:

2 - 1.0304

Answer

Converting the decimals into like decimals :

The like decimal numbers are 2.0000 and 1.0304

$\begin{array}{r} & 2.0000 \\ - & 1.0304 \\ \hline & 0.9696 \end{array}$

Hence, 2 - 1.0304 = 0.9696

Subtract the following:

0.1 - 0.08

Answer

Converting the decimals into like decimals :

The like decimal numbers are 0.10 and 0.08

$\begin{array}{r} & 0.10 \\ - & 0.08 \\ \hline & 0.02 \end{array}$

Hence, 0.1 - 0.08 = 0.02

Subtract the following:

0.83 - 0.342

Answer

Converting the decimals into like decimals :

The like decimal numbers are 0.830 and 0.342

$\begin{array}{r} & 0.830 \\ - & 0.342 \\ \hline & 0.488 \end{array}$

Hence, 0.83 - 0.342 = 0.488

Subtract:

0.43 from 0.97

Answer

Converting the decimals into like decimals :

The like decimal numbers are 0.97 and 0.43

$\begin{array}{r} & 0.97 \\ - &0.43 \\ \hline & 0.54 \end{array}$

Hence, 0.97 - 0.43 = 0.54

Subtract:

2.008 from 22.1058

Answer

Converting the decimals into like decimals :

The like decimal numbers are 22.1058 and 2.0080

$\begin{array}{rr} & 22.1058 \\ - & 2.0080 \\ \hline & 20.0978 \end{array}$

Hence, 22.1058 - 2.008 = 20.0978

Subtract:

0.18 from 0.6

Answer

Converting the decimals into like decimals :

The like decimal numbers are 0.60 and 0.18

$\begin{array}{r} & 0.60 \\ - & 0.18 \\ \hline & 0.42 \end{array}$

Hence, 0.6 - 0.18 = 0.42

Subtract:

1.002 from 17

Answer

Converting the decimals into like decimals :

The like decimal numbers are 17.000 and 1.002

$\begin{array}{rr} & 17.000 \\ - & 1.002 \\ \hline & 15.998 \end{array}$

Hence, 17 - 1.002 = 15.998

Subtract:

83 from 92.05

Answer

Converting the decimals into like decimals :

The like decimal numbers are 92.05 and 83.00

$\begin{array}{rr} & 92.05 \\ -& 83.00 \\ \hline & 9.05 \end{array}$

Hence, 92.05 - 83 = 9.05

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

(i) The like decimal numbers are 3.500, 2.430 and 0.075

First, adding the positive numbers 3.500 and 0.075

$\begin{array}{r} & 3.500 \\ + & 0.075 \\ \hline & 3.575 \end{array}$

Now, subtracting 2.430 from 3.575

$\begin{array}{r} & 3.575 \\ - & 2.430 \\ \hline & 1.145 \end{array}$

Hence, 3.5 - 2.43 + 0.075 = 1.145

(ii) The like decimal numbers are 7.840, 0.300 and 4.016

First, adding the positive numbers 7.840 and 0.300

$\begin{array}{r} & 7.840 \\ + & 0.300 \\ \hline & 8.140 \end{array}$

Now, subtracting 4.016 from 8.140

$\begin{array}{r} & 8.140 \\ - & 4.016 \\ \hline & 4.124 \end{array}$

Hence, 7.84 + 0.3 - 4.016 = 4.124

(iii) The like decimal numbers are 2.987, 1.250 and 0.540

First, adding the numbers to be subtracted 1.250 and 0.540

$\begin{array}{r} & 1.250 \\ + &0.540 \\ \hline & 1.790 \end{array}$

Now, subtracting 1.790 from 2.987

$\begin{array}{r} & 2.987 \\ - & 1.790 \\ \hline & 1.197 \end{array}$

Hence, 2.987 - 1.25 - 0.54 = 1.197

(iv) The like decimal numbers are 52.900, 231.666 and 204.000

First, adding the positive numbers 52.900 and 204.000

$\begin{array}{rr} & 52.900 \\ + &204.000 \\ \hline & 256.900 \end{array}$

Now, subtracting 231.666 from 256.900

$\begin{array}{r} & 256.900 \\ - & 231.666 \\ \hline & 25.234 \end{array}$

Hence, 52.9 - 231.666 + 204 = 25.234

(v) The like decimal numbers are 8.5700, 6.4432, 1.7000 and 0.6830

First, adding the positive numbers 8.5700 and 0.6830

$\begin{array}{r} & 8.5700 \\ + & 0.6830 \\ \hline & 9.2530 \end{array}$

Adding the numbers to be subtracted 6.4432 and 1.7000

$\begin{array}{r} & 6.4432 \\ + &1.7000 \\ \hline & 8.1432 \end{array}$

Now, subtracting 8.1432 from 9.2530

$\begin{array}{r} & 9.2530 \\ - & 8.1432 \\ \hline & 1.1098 \end{array}$

Hence, 8.57 - 6.4432 - 1.70 + 0.683 = 1.1098

From the sum of 75.75 and 4.9, subtract 28.465.

Answer

The like decimal numbers are 75.750, 4.900 and 28.465

First, adding 75.750 and 4.900

$\begin{array}{rr} & 75.750 \\ + & 4.900 \\ \hline & 80.650 \end{array}$

Now, subtracting 28.465 from 80.650

$\begin{array}{r} & 80.650 \\ - & 28.465 \\ \hline & 52.185 \end{array}$

Hence, the required answer = 52.185

Subtract the sum of 8.14 and 12.9 from 32.7.

Answer

The like decimal numbers are 8.14, 12.90 and 32.70

First, adding 8.14 and 12.90

$\begin{array}{rr} & 8.14 \\ + & 12.90 \\ \hline & 21.04 \end{array}$

Now, subtracting 21.04 from 32.70

$\begin{array}{r} & 32.70 \\ - & 21.04 \\ \hline & 11.66 \end{array}$

Hence, the required answer = 11.66

Subtract the sum of 34.27 and 159.8 from the sum of 20.937 and 200.6.

Answer

The like decimal numbers are 34.270, 159.800, 20.937 and 200.600

First, adding 34.270 and 159.800

$\begin{array}{rr} & 34.270 \\ + & 159.800 \\ \hline & 194.070 \end{array}$

Adding 20.937 and 200.600

$\begin{array}{rr} & 20.937 \\ + & 200.600 \\ \hline & 221.537 \end{array}$

Now, subtracting 194.070 from 221.537

$\begin{array}{rr} & 221.537 \\ - & 194.070 \\ \hline & 27.467 \end{array}$

Hence, the required answer = 27.467

From the sum of 2.43 and 4.349, subtract the sum of 0.8 and 3.15.

Answer

The like decimal numbers are 2.430, 4.349, 0.800 and 3.150

First, adding 2.430 and 4.349

$\begin{array}{r} &2.430 \\ + & 4.349 \\ \hline & 6.779 \end{array}$

Adding 0.800 and 3.150

$\begin{array}{r} & 0.800 \\ + & 3.150 \\ \hline & 3.950 \end{array}$

Now, subtracting 3.950 from 6.779

$\begin{array}{r} & 6.779 \\ - & 3.950 \\ \hline & 2.829 \end{array}$

Hence, the required answer = 2.829

By how much does the sum of 18.0495 and 34.9644 exceed the sum of 7.6752 and 24.876?

Answer

The like decimal numbers are 18.0495, 34.9644, 7.6752 and 24.8760

First, adding 18.0495 and 34.9644

$\begin{array}{r} & 18.0495 \\ + & 34.9644 \\ \hline & 53.0139 \end{array}$

Adding 7.6752 and 24.8760

$\begin{array}{rr} & 7.6752 \\ + & 24.8760 \\ \hline & 32.5512 \end{array}$

Now, subtracting 32.5512 from 53.0139

$\begin{array}{r} & 53.0139 \\ - & 32.5512 \\ \hline & 20.4627 \end{array}$

Hence, the first sum exceeds the second sum by 20.4627

What least number must be added to 89.376 to get 1000?

Answer

Required least number = 1000 - 89.376

$\begin{array}{rr} & 1000.000 \\ - & 89.376 \\ \hline & 910.624 \end{array}$

Hence, 910.624 must be added to 89.376 to get 1000.