Saturday 28 July 2018

Math : Word Problem

Two tankers contain 680 liters and 850 liters of diesel respectively. Find the maximum capacity of a container which can measure the diesel of both tankers in exact number of times.

Given,
Total number of tankers = 2
first tanker contains 680 liters
second tanker contains 850 liters
we have to find,
the maximum capacity of a container which can measure the diesel of both tankers
which means we have to find the HCF (Highest common factor)
lets find the factors for 680 and 850
680 =  2*2*2*5*17
850 = 2*5*5*17
HCF = 2*5*17 = 170
So, 170liters container is common for 680liters tanker and 850 liters tanker to fill the tankers in exact number of times
170 *4 = 680
hence to fill 680 liters tankers, 4 times of 170liters container be used
170 * 5 = 850
hence to fill 850 liters tankers, 5 times of 170 liters container be used.

Friday 6 July 2018

Grade 6 : Math : Exercise 1.2

1. A book exhibition was held for four days in a school. The number of tickets sold at the counter on the first, second, third and final day was respectively 1094, 1812, 2050 and 2751. Find the total number of tickets sold on all the four days?

Given,
Exhibition was held for four days
Number of tickets sold on first day = 1094
Number of tickets sold on second day = 1812
Number of tickets sold on Third day = 2050
Number of tickets sold on fourth day = 2751
now, we have to find the total number of tickets sold on all four days
which implies
we have to add all the four days tickets 
that is,
= 1094 + 1812 + 2050 + 2751
= 7,707 tickets

2. Shekar is a famous cricket player. He has so far scored 6980 runs in test matches. He wishes to complete 10,000 runs. How many more runs does he need?

Given,
Total number of scores Shekar scored = 6980 runs
Number of scores he wants to complete = 10,000 runs
we have to find how many more runs he need
that is, he wants to reach 10,000 runs from 6,980 runs
which implies we have to subtract
= 10,000 - 6,980
=3,020 runs

3. In an election, the successful candidate registered 5,77,500 votes and his nearest rival secured 3,48,700 votes. By what margin did the successful candidate win the election?

Given,
Number of votes successful candidate has secured = 5,77,500 votes
Rival has secured = 3,48,700 votes
we have to find at what margin did the successful candidate win the election
which means in what difference did the successful canditate win
that is, = 5,77,500 - 3,48,700
            = 2,28,800 votes

4. Kirti bookstore solds books worth Rs 2,85,891 in the first week of June and books worth Rs 4,00,768 in the second week of the month. How much was the sale for the two weeks together? In which week was the sale greater and by how much?

Given,
First week, bookstore solds books worth = Rs 2,85,891
Second week, bookstore solds books worth = Rs 4,00,768
The sale for the two weeks together (means add two weeks worth ) 
                                                              = 2,85,891 + 4,00,768
                                                              = Rs 6,86,659
Also we have to find in which week the sale greater
4,00,768 > 2,85,891
so, second week sale is greater
if we find their difference = 4,00,768 - 2,85,891
                                           = Rs 1,14,877 worth greater than first week sale

5. Find the difference between the greatest and the least number that can be written using the digits 6,2,7,4,3 each only once.

Given,
digits given = 6,2,7,4,3
Greatest number using the given digits only once = 76432 (go from highest to lowest)
Least number using the given digits only once = 23467 (from lowest to greatest)
Their difference = 76432 - 23467
                           = 52,965

6. A machine, on an average, manufactures 2,825 screws a day. How many screws did it produce in the month of January 2006?

Given,
A machine manufactures 2,825 screws per day
we have to find how many it produce in the month of january
there are 31 days in January
so, total number of screws it produced in january = 31*2,825
                                                                                = 87,575 Screws

7. A merchant had Rs 78,592 with her. Sha placed an order for purchasing 40 radio sets at Rs 1200 each. How much money will remain with her after purchase?

Given,
Amount merchant had = Rs 78,592
She wanted to purchase 40 radio sets
The cost of one radio set = Rs 1200
so, the cost of 40 radio sets = 40 * 1200
                                           = Rs 48,000
the remaining amount she had after purchasing = 78,592 - 48,000
                                                                            = Rs 30,592


Monday 25 June 2018

Problems based on the divisibility test

1. Replace the sign ___ by the smallest number to make them divisible by the given number.

a. 7158__ by 6

By the divisibility test,
if the number is divisible by 2 and 3 then that number is divisible by 6.
if the given number is divisible by 2 the units place must be 0 , 2, 4 , 6 , or 8.
if the given number is divisible by 3 then first we have to add the digits 7+1+5+8=21
21 is divisible by 3
so we can replace the sign by 0 since 71580(unit place 0) which is divisible by 2 and 71580(add will get 21) which is divisible by 3.
hence 71580 is divisible by 6

b. 8152__ by 4

By the divisibility test,
if the last two digits is divisible by 4 then that number is divisible by 4.
if we replace the sign by 0 then the last two digits be 20 which is divisible by 4.
hence 81520 is divisible by 4

c. 86__72 by 11

By the divisibility test,
the sum of the numbers in odd place = 8 + __+2  = 10+__
sum of the numbers in even place = 6 + 7  = 13
10+__  - 13 = 0 (since the difference must be either 0 or divisible by 11)
[we have to write the smallest possible number hence we choose 0]
so __ be 3
13-13=0
hence 86372 is divisible by 11

d. 631__24 by 8

By the divisibility test,
if the last three digit is divisible by 8 then that number is divisible by 8.
__24 , 24 itself is divisible by 8 hence we can replace the sign by 0
hence 631024 is divisible by 8.

2. State whether the following sentences are true or false.

a. 231648 is divisible by 4 and 8

Divisible by 4
lets consider last two digits 48 which is divisible by 4.
Divisible by 8
lets consider last three digits 648 which is divisible by 8
hence 231648 is divisible by 4 and 8 TRUE

b. 976575 is divisible by 3 and 15

Divisible by 3
lets add all the digits 9+7+6+5+7+5=39 which is divisible by 3
Divisible by 15
if the number is divisible by 3 and 5 then that number is divisible by 15
we already found that number number is divisible by 3
the unit place is 5 so the given number is divisible by 5 
hence it is divisible by 15
976575 is divisible by 3 and 15 TRUE


c. 567835 is divisible by 5 and 25  

Divisible by 5
the unit place in the given number 5, so the given number is divisible by 5
Divisible by 25
if the last two digits are 00,50 or 75 then that number is divisible by 25
here the last two digits is 35, so 567835 is not divisible by 25
567835 is divisible by 5 and 25 FALSE  

3. What digit you add each time to make the numbers on the Violet divisible by the numbers given in the RED

a. 67984311 by 2,3,4,5,6,8,9,10

Divisible by 2
if we add last digit as 0 then according to the divisibility test,
679843110 is divisible by 2

Divisible by 3
lets add all the digits 6+7+9+8+4+3+1+1+__ = 39+__
39 itself is divisible by 3
hence we can replace the sign as 0
679843110 is divisible by 3

Divisible by 4
the last two digits 1__, if we replace sign by 2 then 12 which is divisible by 4
hence 679843112 is divisible by 4

Divisible by 5
the last digit must be either 0 or 5
hence it can be 679843110 or 679843115 which are divisible by 5

Divisible by 6
According to the divisibility test,
the number must be divisible by both 2 and 3
if we add 0 that is 679843110 is divisible by both 2 and 3.
hence 679843110 is divisible by 6

Divisible by 8
lets consider the last three digits 11__ ,
110,111 are not divisible by 8
112 is divisible by 8
hence 679843112 is divisible by 8

Divisible by 9
Sum of the digits = 39 + __ 
39 is not divisible by 9
if we add 6 to 39 which gives 45 and 45 be divisible by 9
hence 679843116 is divisible by 9

Divisible by 10
the last digit must be 0
hence 679843110 is divisible by 10 

 

Tests for Divisibility

Divisibility by 2

If we observe a few multiples of 2 to be 2,4,6,8,10,12,14,...
that is the unit place of these numbers are like 0 , 2 , 4 , 6 , 8.
hence we can conclude that a number is divisible by 2 if that number has any of the digits
 0 , 2 , 4 , 6 ,or  8 in its units place.

Divisibility by 3

If the sum of the digits is a multiple of 3, then the number is divisible by 3.
Example
669 , here first we have to add all the digits
6+6+9 = 21
21 is divisible by 3
hence 669 is divisible by 3

Divisibility by 4

A number with 3 or more digits is divisible by 4 if the last two digits of the given number is divisible by 4.
Example
8216
lets consider the last two digits
16 which is divisible by 4
hence 8216 is divisible by 4

Divisibility by 5

A number which has either 0 or 5 in its units place then that number is divisible by 5.

Divisibility by 6

If the number is divisible by 2 and 3 both then that number is divisible by 6

Divisibility by 8

If the number formed by the last three digits is divisible by 8 then that number is divisible by 8.

Example
86512
lets consider the last three digits 512 which is divisible by 8.
hence 86512 is divisible by 8

Divisibility by 9

If the sum of the digits of the given number is divisible by 9 then that number is divisible by 9.

Example
504
lets add all the digits
5+0+4 = 9 which is divisible by 9
hence 504 is divisible by 9

Divisibility by 10

If the number has 0 in its units place then that number is divisible by 10

Divisibility by 11

First we have to find the difference between the sum of the digits at odd places (from the right side)
and the sum of the digits at even places of the number.If the difference is either 0 or that number is divisible by 11 then the given number is divisible by 11.
Example
61809
9+8+6 = 23
0+1=1
their difference = 23-1 = 22 which is divisible by 11
hence 61809 is divisible by 11



Sunday 10 June 2018

Math : Grade 5 : Exercise 2E

Solve. Use models to help you.

1. a. 612 + ______ = 948

Given,
What number if we add with 612 will give you 948
so, if we subtract 612 from 948 we will get the number
that is, 948 - 612 = 336

b. 7394 + ________ = 12642

12642 - 7394 = 5,248

c. ______ - 847 = 1238

Given,
what if we subtract 847 from what number will get 1238
so, if we add 847 with 1238 we will get that number
that is, 847 + 1238 = 2,085

d. ___________ - 9162 = 1811

9162 + 1811 = 10,973

e. 9408 - _______ = 1138

Given
If we subtract a number from 9408 will get 1138
so, if we subtract 1138 from 9408 will get that number
that is, 9408 - 1138 = 8,270

f. 49584 - _______ = 23175

49584 - 23175 = 26,409

2. a. What must add to 18345 to make it 19624?

Given
_______ + 18345 = 19624
that is, 19624 - 18345 = 1,279

b. If you subtract 23146 from a number , you are left with 35906. Find the number.

Given
__________ - 23146 = 35906
that is, 35906 + 23146 = 59,052

c. Find the number which must be subtracted from 83196 to leave 11422.

Given
83196 - _______ = 11422
that is, 83196 - 11422 = 71,774

d. The sum of two numbers is 40132. If one number is 29184, find the other number.

Given
29184 + _______ = 40132
that is, 40132 - 29184 = 10,948

3. a. Khalid wants to buy a board game that cost Rs 501. He has Rs 479. How much more money does he need?

Given
Cost of a board game = Rs 501
Amount he had = Rs 479
we have to find how much more money he need.
that is, 479 + _______ = 501
so, 501 - 479 = 22
Hence he need Rs22

b. Harshita's stamp album can hold 1,500 stamps. So far she has pasted 785 stamps in it. How many more stamps can she paste in it?

Given
Number of stamps album can hold = 1,500
Number of stamps she pasted = 785
we have to find how many more stamps she can paste
that is, 785 + ______ = 1,500
so, 1500 - 785 = 715
hence she can paste 715 more

c. A large library has lent out 1,785 books. It has 7,816 books left. How many books does the library have in all?

Given,
Number of books has lent out = 1,785
number of books left = 7,816
total number of books the library have = 1,785 + 7,816
                                                              = 9,601
hence the library have 9601 books

d. An art exhibition had 915 pieces of art on show. Some of them got sold but there were 211 unsold pieces. How many pieces were sold?

Given
Number of pieces of art on show = 915
number of pieces unsold = 211
we have to find number of sold out pieces.
number of pieces were sold = 915 - 211
                                             = 704
hence 704 pieces were sold

Wednesday 6 June 2018

Math : Grade 5 : Exercise 2D


1 Solve using addition, subtraction, multiplication or division

a. The Sunshine club newspaper printed 33,530 copies in a year. Of these 28,395 copies were distributed. How many were not distributed?

Given,
Total copies printed in a year = 33,530
Number of copies distributed = 28,395
We have to find the number of copies which are not distributed
That is,
Number of copies not distributed = Total copies - Number of copies distributed
                            = 33,530 - 28,395
                            = 5,135
Hence 5,135 copies weren’t distributed.

b. The odometer on a van showed 53,811 km in the beginning of October. After being used for three months it showed 84,209 km in December. If it had traveled 21,614 km in October and November, how much distance did it cover in the month of December?

Given,
In the beginning of October the odometer showed = 53,811 km
In December it showed = 84,209 km
Therefore,
Distance traveled from October to December = 84,209 - 53,811
                                   = 30,398km
Also given,
Distance traveled in October and November = 21,614km
We have to find
The distance it cover in the month = total distance from October to December - distance covered in October and November
                            = 30,398 - 21,614
                            = 8,784 km

c. Sushil’s car traveled 25,384 km in one year and suraj’s car traveled 30,001 km in the same year. How many kilometer less did Sushil’s car run?

Given,
Distance traveled by Sushil’s car = 25,384 km
Distance traveled by Suraj’s car = 30,001 km
We have to find,
Number of Kilometer less did Sushil’s car run = Distance traveled by Suraj’s car - Distance traveled by Sushil’s car
                                     = 30,001 - 25,384
                                     = 4,617 km

d. Mr Shenoy had Rs3,25,765. He borrowed Rs1,12,700 to buy a new car. How much did the car cost?

Given,
Amount Mr Shenoy had to buy a new car = Rs 3,25,765
Amount he borrowed to buy a new car = Rs 1,12,700
Total amount of the car cost = 3,25,765 + 1,12,700
                       = Rs 4,38,465

e. Sriram won 75 tournaments. The prize money totals up to Rs 2,25,000. If he received the same amount for every tournament, how much had he earned per tournament?

Given,
Total number of tournaments = 75
Total Prize money = Rs 2,25,000
Amount he earned per tournament = total prize money / total number of tournaments
                              = 2,25,000 / 75
                              = Rs 3,000

f. A school needs 24,510 pencils a year. How many boxes of 25 must the school buy?

Total pencils school needs a year = 24,510
A box contains 25 pencils each
Hence total number of boxes school needs = 24,510 / 25
                                   = 980.4
Boxes should not be in decimal.
Hence 981 boxes so that no more pencils remains.

g. The toy store had 20 boxes of dolls and 25 boxes of teddy bears. Each box holds 24 of each. How many dolls and teddy bears did the toy store have in all?

Given,
Number of boxes of dolls = 20
Number of boxes of teddy = 25
Each box contains 24 of respective toys.
Total number of dolls = number of boxes of dolls * number of dolls per box
                  = 20 * 24
                  = 480 dolls
Total number of teddy = number of boxes of teddy * number of teddy per box
                   = 25 * 24
                   = 600 teddy bears
Hence total number of toys = 480 dolls + 600 teddy bears
                       = 1080 toys

Monday 30 April 2018

Math : Grade 5 : Exercise 2C

1. Find the selling price or cost price of each of these products with the help of a model.

a. Terracota pot from west bengal.
Cost price = Rs 315
Loss = Rs 38
Selling Price=?

here, given Loss and cost price
We know that,  Loss = Cost Price - Selling Price
here, we have to find Selling Price
hence Selling Price = Cost Price - Loss
lets substitute the given values
Selling Price = Rs 315 - Rs 38
                      = Rs 277

b. Stool from Punjab.
Selling Price = Rs 690
Loss = Rs 57
Cost Price = ?

Cost Price = Loss + Selling Price
Cost Price = Rs 57 + Rs 690
                  = Rs 747

c. Shawl from Nagaland.
Selling Price = Rs 1,560
Loss = Rs 350
Cost Price = ?

Cost Price = Loss + Selling Price
Cost Price = Rs 350 + Rs 1,560
                  = Rs 1,910

d. Kanjeevaram saree from Tamil Nadu.
Cost Price = Rs 7,880
Profit = Rs 1,090
Selling Price = ?

Profit = Selling Price - Cost Price
Selling Price = Profit + Cost Price
                      = Rs 1,090 + Rs 7,880
                      = Rs 8,970

2. Complete the table.


Selling Price
Profit
Loss
Cost Price
a
Rs 2,385
Rs 195
-
Rs 2,385 - Rs 195 = Rs 2,190
b
Rs 1,900
-
Rs 628
Rs 1,900 + Rs 628 = Rs 2,528
c
Rs 8,630
-
Rs 1,020
Rs 8,630 + Rs 1,020 = Rs 9,650
d
Rs 74,365
Rs 2,315
-
Rs 74,365 - Rs 2,315 = Rs 72,050

 

Note : Cost Price = Loss + Selling Price , Cost Price = Selling Price - Profit.         

3. Complete the table.


Cost Price
Profit
Loss
Selling Price
a
Rs 1,095
-
Rs 89
Rs 1,095 - Rs 89 = Rs 1,006
b
Rs 3,586
Rs 369
-
Rs 3,586 + Rs 369 = Rs 3,955
c
Rs 9,980
-
Rs 3551
Rs 9,980- Rs 3551 = Rs 6,429
d
Rs 15,381
Rs 1,395
-
Rs 15,381 + Rs 1,395 = Rs 16,776
 

Note : Selling Price = Cost Price + Profit , Selling Price = Cost Price - Loss.

4. Solve

a. Rashid incurred a loss of Rs 590 on a chair he sold at Rs 1,280. What was the cost price of the chair?

Given, Loss = Rs 590 and selling price = Rs 1,280
Cost Price = Selling Price + Loss
                 = Rs 1,280 + Rs 590
                 = Rs 1,870

b. Ali made a profit of Rs 3,200 on a sofa set he bought for Rs 15,290. At what price did he sell it?

Given, Profit = Rs 3,200 and cost price = Rs 15,290
Selling Price = Cost Price + Profit
                     = Rs 15,290 + Rs 3,200
                     = Rs 18,490

c. A dozen books are sold at Rs 1,648 at a profit of Rs 120. What is the cost price of the books?

Given, profit = Rs 120 and Selling Price = Rs 1,648
Cost Price = Selling Price - Profit
                 = Rs 1,648 - Rs 120
                 = Rs 1,528