Decimal Fractions — Exercise 5(D)

Add:

(i) 27.5, 8.93, 0.759, 9.6

(ii) 0.83, 8.07, 17.9, 294.678

(iii) 0.53, 7.07, 77.7, 0.835

(iv) 9.38, 3.895, 109.5, 72.87, 0.005

(v) 9.008, 27.689, 247.96, 39.8

(vi) 325.7, 98.079, 0.87, 236.68

Answer

(i) Converting the given decimals into like decimals, each having 3 places of decimal, we get :

27.500, 8.930, 0.759, 9.600

Writing these decimals in column form and adding, we get:

$\begin{array}{r} \phantom{+}27.500 \\ 8.930 \\ 0.759 \\ +\space 9.600 \\ \hline 46.789 \end{array}$

Therefore, the sum is 46.789.

(ii) Converting the given decimals into like decimals, each having 3 places of decimal, we get :

0.830, 8.070, 17.900, 294.678

Writing these decimals in column form and adding, we get:

$\begin{array}{r} \phantom{+}0.830 \\ 8.070 \\ 17.900 \\ +\space 294.678 \\ \hline 321.478 \end{array}$

Therefore, the sum is 321.478.

(iii) Converting the given decimals into like decimals, each having 3 places of decimal, we get :

0.530, 7.070, 77.700, 0.835

Writing these decimals in column form and adding, we get:

$\begin{array}{r} \phantom{+}0.530 \\ 7.070 \\ 77.700 \\ +\space 0.835 \\ \hline 86.135 \end{array}$

Therefore, the sum is 86.135.

(iv) Converting the given decimals into like decimals, each having 3 places of decimal, we get :

9.380, 3.895, 109.500, 72.870, 0.005

Writing these decimals in column form and adding, we get:

$\begin{array}{r} \phantom{+}9.380 \\ 3.895 \\ 109.500 \\ 72.870 \\ +\space 0.005 \\ \hline 195.650 \end{array}$

Therefore, the sum is 195.65.

(v) Converting the given decimals into like decimals, each having 3 places of decimal, we get :

9.008, 27.689, 247.960, 39.800

Writing these decimals in column form and adding, we get:

$\begin{array}{r} \phantom{+}9.008 \\ 27.689 \\ 247.960 \\ +\space 39.800 \\ \hline 324.457 \end{array}$

Therefore, the sum is 324.457.

(vi) Converting the given decimals into like decimals, each having 3 places of decimal, we get :

325.700, 98.079, 0.870, 236.680

Writing these decimals in column form and adding, we get:

$\begin{array}{r} \phantom{+}325.700 \\ 98.079 \\ 0.870 \\ +\space 236.680 \\ \hline 661.329 \end{array}$

Therefore, the sum is 661.329.

Find the difference:

(i) 17.05 - 9.78

(ii) 30.23 - 17.495

(iii) 107.5 - 58.69

(iv) 60 - 18.35

(v) 48.3 - 29.571

(vi) 100 - 72.745

(vii) 215.4 - 69.845

(viii) 1.5 - 0.703

(ix) 42 - 0.764

Answer

(i) Writing the decimals in column form and subtracting, we get :

$\begin{array}{r} \phantom{+}17.05 \\ -\space 9.78 \\ \hline 7.27 \end{array}$

Therefore, the difference is 7.27.

(ii) Converting the given decimals into like decimals, each having 3 places of decimal, we get 30.230 and 17.495.

Writing the decimals in column form and subtracting, we get :

$\begin{array}{r} \phantom{+}30.230 \\ -\space 17.495 \\ \hline 12.735 \end{array}$

Therefore, the difference is 12.735.

(iii) Converting the given decimals into like decimals, each having 2 places of decimal, we get 107.50 and 58.69.

Writing the decimals in column form and subtracting, we get :

$\begin{array}{r} \phantom{+}107.50 \\ -\space 58.69 \\ \hline 48.81 \end{array}$

Therefore, the difference is 48.81 .

(iv) Converting the given decimals into like decimals, each having 2 places of decimal, we get 60.00 and 18.35.

Writing the decimals in column form and subtracting, we get :

$\begin{array}{r} \phantom{+}60.00 \\ - \space 18.35 \\ \hline 41.65 \end{array}$

Therefore, the difference is 41.65 .

(v) Converting the given decimals into like decimals, each having 3 places of decimal, we get 48.300 and 29.571.

Writing the decimals in column form and subtracting, we get :

$\begin{array}{r} \phantom{+}48.300 \\ -\space 29.571 \\ \hline 18.729 \end{array}$

Therefore, the difference is 18.729

(vi) Converting the given decimals into like decimals, each having 3 places of decimal, we get 100.000 and 72.745.

Writing the decimals in column form and subtracting, we get :

$\begin{array}{r} \phantom{+}100.000 \\ -\space 72.745 \\ \hline 27.255 \end{array}$

Therefore, the difference is 27.255.

(vii) Converting the given decimals into like decimals, each having 3 places of decimal, we get 215.400 and 69.845.

Writing the decimals in column form and subtracting, we get :

$\begin{array}{r} \phantom{+}215.400 \\ -\space 69.845 \\ \hline 145.555 \end{array}$

Therefore, the difference is 145.555.

(viii) Converting the given decimals into like decimals, each having 3 places of decimal, we get 1.500 and 0.703.

Writing the decimals in column form and subtracting, we get :

$\begin{array}{r} \phantom{+}1.500 \\ -\space 0.703 \\ \hline 0.797 \end{array}$

Therefore, the difference is 0.797.

(ix) Converting the given decimals into like decimals, each having 3 places of decimal, we get 42.000 and 0.764.

Writing the decimals in column form and subtracting, we get :

$\begin{array}{r} \phantom{+}42.000 \\ -\space 0.764 \\ \hline 41.236 \end{array}$

Therefore, the difference is 41.236.

Simplify:

(i) 74.8 + 68.79 - 47.609 - 7.08

(ii) 68.3 - 102.735 + 217.96 - 37.7

(iii) 203.5 - 43.76 - 9.89 - 13.086

(iv) 77.7 - 7.555 - 5.77

Answer

(i) Writing each of the given numbers with three decimal places, we get:

Given expression = 74.800 + 68.790 - 47.609 - 7.080

$\phantom{74.800 + 68.790-}$= (74.800 + 68.790) - (47.609 + 7.080)

Now,

$\begin{array}{r} \phantom{+}74.800 \\ +\space 68.790 \\ \hline 143.590 \end{array} \qquad \text{and} \qquad \begin{array}{r} \phantom{+}47.609 \\ +\space 7.080 \\ \hline 54.689 \end{array}$

So,

$\begin{array}{r} \phantom{+}143.590 \\ -\space 54.689 \\ \hline 88.901 \end{array}$

Therefore, 74.8 + 68.79 - 47.609 - 7.08 = 88.901.

(ii) Writing each of the given numbers with three decimal places, we get:

Given expression = 68.300 - 102.735 + 217.960 - 37.700

$\phantom{68.300 + 217.960-}$= (68.300 + 217.960) - (102.735 + 37.700)

Now,

$\begin{array}{r} \phantom{+}68.300 \\ +\space 217.960 \\ \hline 286.260 \end{array} \qquad \text{and} \qquad \begin{array}{r} \phantom{+}102.735 \\ +\space 37.700 \\ \hline 140.435 \end{array}$

So,

$\begin{array}{r} \phantom{+}286.260 \\ -\space 140.435 \\ \hline 145.825 \end{array}$

Therefore, 68.3 - 102.735 + 217.96 - 37.7 = 145.825.

(iii) Writing each of the given numbers with three decimal places, we get:

Given expression = 203.500 - 43.760 - 9.890 - 13.086

$\phantom{203.500 + 217.960}$= 203.500 - ( 43.760 + 9.890 + 13.086)

Now,

$\begin{array}{r} \phantom{+}43.760 \\ 9.890 \\ +\space 13.086 \\ \hline 66.736 \end{array}$

So,

$\begin{array}{r} \phantom{+}203.500 \\ -\space 66.736 \\ \hline 136.764 \end{array}$

Therefore, 203.5 - 43.76 - 9.89 - 13.086 = 136.764.

(iv) Writing each of the given numbers with three decimal places, we get:

Given expression = 77.700 - 7.555 - 5.770

$\phantom{203.500 + 217.960}$= 77.700 - ( 7.555 + 5.770)

Now,

$\begin{array}{r} \phantom{+}7.555 \\ +\space 5.770 \\ \hline 13.325 \end{array}$

So,

$\begin{array}{r} \phantom{+}77.700 \\ -\space 13.325 \\ \hline 64.375 \end{array}$

Therefore, 77.7 - 7.555 - 5.77 = 64.375.

What is to be added to 73.6 to get 91.03 ?

Answer

Let the number be x. Then,

73.6 + x = 91.03

Solving for x,

x = 91.03 - 73.6

Rewriting the numbers with two decimal places,

x = 91.03 - 73.60

Writing in column form and subtracting, we get:

$\begin{array}{r} \phantom{+}91.03 \\ -\space 73.60 \\ \hline 17.43 \end{array}$

Therefore, x = 17.43.

What is to be subtracted from 6.1 to get 0.785 ?

Answer

Let the number to be subtracted from 6.1 be x. Then,

6.1 − x = 0.785

Solving for x,

x = 6.1 − 0.785

Rewriting the numbers with three decimal places,

x = 6.100 − 0.785

Writing in column form and subtracting, we get:

$\begin{array}{r} \phantom{+}6.100 \\ -\space 0.785 \\ \hline 5.315 \end{array}$

Therefore, x = 5.315.

By how much should 32.987 be increased to get 60 ?

Answer

Let the required increase be x. Then,

32.987 + x = 60

Solving for x,

x = 60 − 32.987

Rewriting the numbers with three decimal places,

x = 60.000 − 32.987

Writing in column form and subtracting, we get:

$\begin{array}{r} \phantom{+}60.000 \\ -\space 32.987 \\ \hline 27.013 \end{array}$

Therefore, x = 27.013.

By how much should 72.5 be decreased to get 18.76 ?

Answer

Let the required decrease be x. Then,

72.5 − x = 18.76

Solving for x,

x = 72.5 − 18.76

Rewriting the numbers with two decimal places,

x = 72.50 − 18.76

Writing in column form and subtracting, we get:

$\begin{array}{r} \phantom{+}72.50 \\ -\space 18.76 \\ \hline 53.74 \end{array}$

Therefore, x = 53.74.

The sum of two numbers is 34.02. If one of the numbers is 16.268, find the other.

Answer

Let the other number be x. Then,

x + 16.268 = 34.02

Solving for x,

x = 34.02 − 16.268

Rewriting the numbers with three decimal places,

x = 34.020 − 16.268

Writing in column form and subtracting, we get:

$\begin{array}{r} \phantom{+}34.020 \\ -\space 16.268 \\ \hline 17.752 \end{array}$

Therefore, x = 17.752.

Sajjal bought a geometry box for ₹ 139.75 and an exercise book for ₹ 59.60 from a book shop. He gave a 500-rupee note to the shopkeeper. What amount did he get back?

Answer

Cost of geometry box = ₹ 139.75

Cost of exercise book = ₹ 59.60

The total cost is,

$\begin{array}{r} \phantom{+}139.75 \\ +\space 59.60 \\ \hline 199.35 \end{array}$

Money given to the shopkeeper = ₹ 500

Amount returned = 500 − 199.35

Rewriting with two decimal places,

Amount returned = 500.00 − 199.35

Writing in column form and subtracting, we get:

$\begin{array}{r} \phantom{+}500.00 \\ -\space 199.35 \\ \hline 300.65 \end{array}$

Therefore, the amount received back is ₹ 300.65.