Question 12 Marks
Using distributivity of multiplication over addition of whole numbers, find the following products: $736 \times 103$
Answer$736 \times 103 = 736 \times (100 + 3) ($Using distributivity of multiplication over addition of whole numbers$)$
$= (736 \times 100) + (736 \times 3)$
$= 73600 + 2208 = 75808$
View full question & answer→Question 22 Marks
Determine the sum by suitable rearrangements:
$2359 + 1000 + 2641 + 9999$
Answer$2359 + 10001 + 2641 + 9999$
Therefore, $59 + 41 = 100$
And, $99 + 01 = 100$
Therefore, $(2359 + 2641) + (10001 + 9999)$
$= (5000) + (20000)$
$= 25000$
View full question & answer→Question 32 Marks
Find the number which when divided by $58$ gives a quotient $40$ and remainder $31.$
AnswerDividend $=$ Divisor $\times $ Quotient $+$ Remainder Dividend $= 58 \times 40 + 31 = 2320 + 31 = 2351$
View full question & answer→Question 42 Marks
Find the following products. $816 \times 745$
Answer$816 \times 745$
Since, $745 = (750 - 5)$
Therefore, $816 \times (750 - 5) = (816 \times 750) - (816 \times 5) ($Using distributivity of multiplication over subtraction of whole numbers$)$
$= 612000 - 4080 = 607920$
View full question & answer→Question 52 Marks
Find the values of the following using properties:
$24579 \times 93 + 7 \times 24579$
Answer$24579 \times 93 + 7 \times 24579$
$= 24579 \times (93 + 7)$
(Using distributivity of multiplication over addition of whole numbers)
$= 24579 \times 100 = 2457900$
View full question & answer→Question 62 Marks
Determine the sum by suitable rearrangements: $15409 + 178 + 591 + 322$
Answer$15409 + 178 + 591 + 322$
$409 + 91 = 500$ And, $78 + 22 = 100$
Therefore, $(15409 + 591) + (178 + 322) = (16000) + (500) = 16500$
View full question & answer→Question 72 Marks
Find the values of the following using properties: $493 \times 8 + 493 \times 2$
Answer$493 \times 8 + 493 \times 2$
$493 \times (8 + 2) ($Using distributivity of multiplication over addition of whole numbers$)$
$= 493 \times 10 = 4930$
View full question & answer→Question 82 Marks
Divide and check the quotient and remainder: $16135 ÷ 875$
Answer$\frac{16135}{875}$
gives quotient $= 18$ and remainder $= 385.$
Verification: $[$Dividend = Divisor $\times $ Quotient $+$ Remainder$]$
$16135 = 875 \times 18 + 385$
$16135 = 15750 + 385$
$16135 = 16135$
$L.H.S = R.H.S$ View full question & answer→Question 92 Marks
Determine the product of the greatest number of three digits and the smallest number of two digits.
AnswerGreatest $3-$digit number $= 999$
Smallest $2-$digit number $= 10$
Product $= 999 \times 10 = 9990$
Hence, the required product is $9990$
View full question & answer→Question 102 Marks
Find the values of the following using properties: $1568 \times 184 - 1568 \times 84$
Answer$1568 \times 184 - 1568 \times 84 = 1568 \times (184 - 84) ($Using distributivity of multiplication over subtraction of whole numbers$)$
$= 1568 \times 100 = 156800$
View full question & answer→Question 112 Marks
A group housing society constructed $350$ flats. If the cost of construction for each flat is $Rs. 993570,$ what is the total cost of construction of all the flats.
AnswerCost of construction of $1$ flat $= Rs. 993,570$
Total number of flats constructed $= 350$
Total cost of construction of $350$ flats,
$= Rs. (993,570 \times 350)$
$= Rs. 347,749,500$
View full question & answer→Question 122 Marks
Find the following products.
$2032 \times 613$
Answer$2032 \times 613$
Since, $613 = (600 + 13)$
Therefore, $2032 \times (600 + 13)$
$= (2032 \times 600) + ( 2032 \times 13)$
$= 1219200 + 26416$
$= 1245616$
View full question & answer→Question 132 Marks
Find: $\ \ \ 1\ 5\ 9 \ 0\ 8\\\underline{\times\ \ \ \ \ \ 5 \ 4 \ 2\ }\\ \overline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$
AnswerThe product is shown beow:
View full question & answer→Question 142 Marks
Determine the product of: The greatest number of four digits and the smallest number of three digits.
AnswerThe largest four - digit number $= 9999$
The smallest three - digit number$ = 100$
Therefore, Product of the smallest three $-$ digit number and the largest four $-$ digit number $= 9999 \times 100 = 999900$
View full question & answer→Question 152 Marks
Using distributivity of multiplication over addition of whole numbers, find the following products: $816 \times 745$
Answer$258 \times 1008 = 258 \times (1000 + 8)$
(Using distributivity of multiplication over addition of whole numbers)
$= (258 \times 1000) + (258 \times 8) $
$= 258000 + 2064 = 260064$
View full question & answer→Question 162 Marks
Find the difference between the largest number of $4$ digits and the smallest number of $7$ digits.
AnswerThe largest four - digit number is $9999.$
The smallest seven - digit number is $1000000.$
Therefore, difference between them $= 1000000 - 9999 = 990001$
View full question & answer→Question 172 Marks
Study the following pattern: $1 =\frac{1\times2}{2}$ $1+2=\frac{2\times3}{2}$ $1+2+3=\frac{3\times4}{2}$ $1+2+3+4=\frac{4\times5}{2}<$ By observing the above pattern, find: $2 + 4 + 6 + 8 + 10 + ............... + 100$
Answer$2 + 4 + 6 + 8 + 10 +… + 100$
This can also be written as $2 \times (1 + 2 + 3 + 4 + … + 49 + 50)$
Now, $(1 + 2 + 3 + 4 + … + 49 + 50 ) = 50 \times 512 = 1275$
Therefore, $(2 + 4 + 6 + 8 + 10 + … + 100) = 2 \times 1275 = 2550$
View full question & answer→Question 182 Marks
Divide and check the quotient and remainder: $7772 ÷ 58$
Answer$\frac{7772}{58}=134$
Verification: $[$Dividend $=$ Divisor $\times $ Quotient $+$ Remainder $]$
$7772 = 58 \times 134 + 0 7772 = 7772$
$L.H.S = R.H.S$ View full question & answer→Question 192 Marks
Study the following pattern: $1 =\frac{1\times2}{2}$
$1+2=\frac{2\times3}{2}$
$1+2+3=\frac{3\times4}{2}$
$1+2+3+4=\frac{4\times5}{2}<$ By observing the above pattern, find: $50 + 51 + 52 +$ _________ $+ 100$
Answer$50 + 51 + 52 + … + 100$
This can also be written as $(1 + 2 + 3 + … + 99 + 100) - (1 + 2 + 3 + 4 + … + 47 + 49)$
Now, $(1 + 2 + 3 + … + 99 + 100 ) = 100 \times 1012$
And, $(1 + 2 + 3 + 4 + … + 47 + 49 ) = 49 \times 502$
So, $(50 + 51 + 52 + … + 100 ) = 100 \times 1012 - 49 \times 502 = 5050 - 1225 = 3825$
View full question & answer→Question 202 Marks
Divide and check the quotient and remainder:
$6906 ÷ 35$
Answer$\frac{6906}{35}$
gives quotient $= 197$ and
remainder $= 11$
Verification: $[$Dividend $=$ Divisor $\times $ Quotient $+$ Remainder$] $
$6906 = 35 \times 197 + 11 $
$6906 = 6895 + 11 $
$6906 = 6906 $
$L.H.S = R.H.S$ View full question & answer→Question 212 Marks
Find the values of the following using properties: $15625 \times 15625 - 15625 \times 5625$
Answer$15625 \times 15625 - 15625 \times 5625 = 15625 \times (15625 - 5625)$
(Using distributivity of multiplication over subtraction of whole numbers)
$= 15625 \times 10000 = 156250000$
View full question & answer→Question 222 Marks
Find a number which when divided by $35$ gives the quotient $20$ and remainder $18.$
AnswerDividend $=$ Divisor $\times $ Quotient $+$ Remainder
Dividend $= 35 \times 20 + 18$
$= 700 + 18$
$= 718$
View full question & answer→Question 232 Marks
Divide and check the quotient and remainder: $16025 ÷ 1000$
Answer$\frac{16025}{1000}$ gives quotient remainder $= 25$
Verification: $[$Dividend $=$ Divisor $\times $ Quotient $+$ Remainder$] $
$16025 = 1000 \times 16 + 25 $
$16025 = 16000 + 25 $
$16025 = 16025 $
$L.H.S = R.H.S$ View full question & answer→Question 242 Marks
Study the following pattern:
$1\times1+2\times2=\frac{2\times3\times5}{6}$
$1\times1+2\times2+3\times3=\frac{3\times4\times7}{6}$
$1\times1+2\times2+3\times3+4\times4=\frac{4\times5\times9}{6}$
By observing the above pattern, write next two steps.
AnswerThe next two steps are as follows:
$1 \times 1 + 2 \times 2 + 3 \times 3 + 4 \times 4 + 5 \times 5$
$= 5 \times 6 \times 116$
$= 55$
$1 \times 1+ 2 \times 2 + 3 \times 3 + 4 \times 4 + 5 \times 5 + 6 \times 6$
$= 6 \times 7 \times 136$
$= 91$
View full question & answer→Question 252 Marks
$i.\ 6 \times 2 - 5 = 7$
$ii.\ 7 \times 3 - 12 = 9$
$iii.\ 8 \times 4 - 21 = 11$
$iv.\ 9 \times 5 - 32 = 13$
$v.\ \_ \times \_ -\_\_ = \_\_$
$vi.\ \_ \times \_ - \_\_ = \_\_$
$vii.\ \_ \times \_ - \_\_ = \_\_$
Answer$i.\ 6 \times 2 - 5 = 7$
$ii.\ 7 \times 3 - 12 = 9$
$iii.\ 8 \times 4 - 21 = 11$
$iv.\ 9 \times 5 - 32 = 13$
$v.\ 10 \times 6 - 45 = 15$
$vi.\ 11 \times 7 - 60 = 17$
$vii.\ 12 \times 8 - 77 = 19$
View full question & answer→Question 262 Marks
Without drawing a diagram, find. $10th$ square number.
AnswerA square number can easily be remembered by the following rule
$N^{th}$ square number $= n \times n$
10th square number $= 10 \times 10 = 100$
View full question & answer→Question 272 Marks
The population of a town was $59000$. In one year it was increased by $4563$ due to new births. However, $9218$ persons died or left the town during the year. What was the population at the end of the year$?$
AnswerPopulation of the town $= 59000$
Increase in the population $= 4536$
Decrease in the population$ = 9218$
New population $= 59000 + 4536 - 9218 = 54318$
View full question & answer→Question 282 Marks
Rohit deposited $Rs. 125000$ in his savings bank account. Later he withdrew $Rs. 35425$ from it. How much money was left in his account$?$
AnswerMoney deposited by Rohit $= Rs. 125000$
Money withdrawn by Rohit $= Rs. 35425$
$\therefore$ Money left in the account $= Rs. (125000 - 35425) = Rs. 89575$
View full question & answer→Question 292 Marks
What are the whole numbers which when multiplied with itself gives the same number?
AnswerThere are two numbers which when multiplied with themselves give the same numbers.
$i.\ 0 \times 0 = 0$
$ii.\ 1 \times 1 = 1$
View full question & answer→Question 302 Marks
The digits of $6$ and $9$ of the number $36490$ are interchanged. Find the difference between the original number and the new number.
AnswerOriginal number $= 39460$
New number $= -36490$
Difference $= 39460 - 36490 = 2970$
View full question & answer→Question 312 Marks
Can a rectangular number also be a square number$?$
AnswerYes, a rectangular number can also be a square number.
For example, $16$ is a square number also a rectangular number.
View full question & answer→Question 322 Marks
Write the first four products of two numbers with difference $4$ starting from in the following order:
Answer$1, 2, 3, 4, 5, 6 ....1 \times 5 = 5 (5 - 1 = 4)$
$2 \times 6 = 12 (6 - 2 =4)$
$3 \times 7 = 21 (7 - 3 = 4)$
$4 \times 8 = 32 (8 - 4 = 4)$
View full question & answer→Question 332 Marks
The annual fee charged from a student of class $VI$ in a school is $Rs. 8880.$ If there are, in all, $235$ students in class $VI,$ find the total collection.
AnswerFees charged from $1$ student $= Rs. 8880$
Therefore, Fees charged from $235$ students, $= Rs. 8880 \times 235 = 2086800$
Thus, the total collection from class $VI$ students is $Rs. 2086800.$
View full question & answer→Question 342 Marks
What is the difference between the largest number of five digits and smallest number of six digits?
AnswerThe largest five - digit number is $99999.$ The smallest six - digit number is $100000.$ Therefore, difference between them $= 100000 - 99999 = 1$
View full question & answer→Question 352 Marks
Find the following products. $736 \times 93$
Answer$736 \times 93$
Since, $93 = (100 - 7)$
Therefore, $736 \times (100 - 7) = (736 \times 100) - (736 \times 7)$
$($Using distributivity of multiplication over subtraction of whole numbers$)$
$= 73600 - 5152 = 68448$
View full question & answer→Question 362 Marks
Simpliry $754 \times 845 + 754 \times 155$ by using distributivity of multiplication over addition.
AnswerDistributive law of multiplication over addition: $a (b + c) = a \times b + a \times c$
$\therefore 754 \times 845 + 754 \times 155$
$= 754(845 + 155)$
$= 754 \times 1000 = 754000$
Hence, $754 \times 845 + 754 \times 155 = 754000.$
View full question & answer→Question 372 Marks
The population of a town is $96209.$ If the number of men is $29642$ and that of women is $29167,$ determine the number of children.
AnswerTotal population of the town $= 96209$
Number of men $= 29642$
Number of women $= 29167$
Sum of men and women $= (29642 + 29167) = 58809$
Therefore, Number of children in the town $= ($Total population$) - ($Sum of men and women$)$
$= 96209 - 58809 = 37400$
View full question & answer→