BOOKLET FOR CHAPTER 1, 2 & 3
PEARSON
HIRA PRASAD | RAJESH HASSIJA
MATHS ACE
CONTENTS
1. NUMBERS 4- digit numbers
Place value & Face value Even and Odd numbers Successor and Predecessor Skip counting
Comparison of Numbers
Ascending and Descending order
Forming greatest and smallest numbers Rounding off numbers
Roman numerals 2. ADDITION
Addition of 4-digit numbers
Addition of Three or More numbers (with regrouping) Properties of addition
Some special properties of addition Estimating the sum
Horizontal addition Applications in real life 3. SUBTRACTIONS
Subtraction of 4-digit numbers Subtraction with regrouping Subtracting with zeros
Addition and subtraction together Properties of subtraction
Estimating the difference Application in real life Mixed bag
Real life application on addition and subtraction
4. ANSWER SHEET
NUMBERS
WARM UP:
1.Choose the correct option.
1. 100 Comes after 99
a)89 b)98 c)100 d)101 2.The number name for 609 is six hundred nine.
a) six hundred nine b) nine hundred six c) sixty-nine d) ninety- six
3.The largest 3-digit number is 999 and the smallest 2-digit number is 10
a)990,11 b)999,10 c)10,999 d)100,10 4.The number that comes before 506 is …………..
a)505 b)507 c)500 d)509 5.The place value of 6 in 468 is ………..
a)600 b)60 c)6 d)66 6. ………….. come in between 456 and 458
a)455 b)457 c)459 d)447 4-DIGIT NUMBER
We know that 999 is the greatest 3-digit number. When we add 1 to 999, we obtain 1000, which is the smallest 4-digit number.
999 (greatest 3-digit number) + 1 = (smallest 4-digit number) We read 1000 as one thousand.
NUMBERS GREATER THAN 1000
We can get numbers greater than 1000 by adding 1 at every step.
9999 is the greatest 4-digit number. When we add 1 to it, we get 10,000 9999 + 1 = 10,000
We read 10,000 as ten thousand. It is the smallest 5 digit number.
We also know that, 10 ones = 1 Ten = 10
10 Tens = 1 hundred = 100 Similarly,
10 Hundreds = 1 Thousand = 1000
Let us represent this on the abacus.
Forming and reading 4-digit numbers.
Look at the following blocks. Can you find out numbers on these blocks
The numbers shown by these blocks is
We read 3248 as three thousand two hundred forty-eight.
Let us represent 3248 on the abacus.
Example: Which number is formed by the following blocks ?
Answer: The blocks show the number
4583 is read as four thousand five hundred eighty-three.
Example: Which number is formed by the following blocks?
Answer: The blocks show the number
3079 is read as three thousand seventy-nine.
Example 3: Which number is shown by the following abacus?
Solution:
The abacus show the number
Answer: 7308 is read as seven thousand three hundred eight.
EXERCISE 1.1
1. Write the number names. Three have been done for you.
a) 1479 : One thousand four hundred seventy nine b) 3682 : Three thousand six hundred eighty two c) 6514 : Six thousand five hundred fourteen d) 7490 :……….
e) 7847 :………..
f) 3064 :………..
g) 9708 :………..
2. Write the numbers. Three have been done for you.
a) Seven thousand two hundred fifteen 7215 b) Eight thousand three hundred one 8301 c) Nine thousand thirteen 9013 d) Four thousand five hundred twelve ………
e) Nine thousand ………
f) One thousand six hundred seventy seven ……….
g) Three thousand six hundred fourteen ……….
3. Fill in the missing numbers and complete the number grids. Also say these numbers while writing.
a)
1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 b)
3221 3225
3232 3237
3250
3253
3265
c)
9951 9956
9962 9967
9973 9978
9984 9989
9995 10,000
4. Write the numbers. Two have been done for you.
a) 4 Thousand + 5 Hundreds + 6 Tens + 2 Ones 4562 b) 8 Thousand + 3 Hundreds + 1 Ones 8031 c) 9 Thousands + 1 Ten + 3 Ones ………
d) 4 Thousands + 5 Hundreds + 1 Ten + 2 Ones ……….
e) 9 Thousands ……….
5.Write the numbers formed from each of the following blocks.
6.Read the abacus. Then write the numeral and the number name. Two have been done .
7.Show the following numbers on the abacus. One has been done for you.
PLACE VALUE AND FACE VALUE:
The place value of a digit in a number depends on the place it occupies in the number.
The face value of a digit in a number is the digit itself irrespective of the place it occupies.
Let us consider 4832. Write place value and face value of each digit of this number.
2 is in ones place 3 is in tens place 8 is in hundreds place
4 is in thousand place
(* indicates multiplication in the above table) Example: Write the place value of each digit. a) 1375 b) 8269
EXPANDED FORM AND STANDARD FORM OF A NUMBER
A number when written as a sum of the place values of all its digits is said to be in its expanded form.
The standard form of a number is obtained by adding the place value of each digit. For example,
7864 = Standard form 7000+800+60+4 = Expanded form
Th H T O 4 8 3 2
PLACE VALUE FACE VALUE 2 * 1 = 2 2
3 * 10 = 3 30 8 * 100 = 800 800 4 * 1000 = 4000 4000
Example: Write the expanded form of 5298.
Solution: Let us write the place value of each digit of this number.
Answer: 5298 is the standard form of 5000+200+90+8.
Example: Write the following numbers in the standard form.
a)6000+700+40+8 b)9000+400+80+2 c)5000+300+4 d)8000+20+2 Solution: a)6000+700+40+8 = 6748
b)9000+400+80+2 = 9482 c)5000+300+4 = 5304 d)8000+20+2 = 8022 Exercise 1.2:
1.Write the place value of the digits which are underlined.
a)4521 500 e)5452 ………
b)8340 8000 f)2739 ………
c)9471 70 g)3465 ………
d)8340 ……… h)7109 ………
2.Write the place value of each digits. Two has been done
Th H T O
6 8 2 5
Th H T O 4 0 7 3
Th H T O
3 9 7 5
5 70 900 3000 3
70 0 4000
Th H T O
8 2 9 2
3.Write the face value of the digits which are underlined.
a)1301 3 b)2572 7 c)3406 …………. d)3999 …………
e)7129 …………. f)5053 …………
4.Write the given number in expanded form. Two have been done for you.
a)1675 = 1000+600+70+5 b)3829 =3000+800+20+9 c)7036 = ………. d)6920 = ………..
e)5325 =………. f)9546 = ………
g)4567 =……….. h)6789 = ………
5.Write the numbers in compact form . Two have been done for you.
a)2000+500+30+20= 2532 b)6000+100+70+40=6174 c]1000+0+0+3= …………. d]400+70+5 = ………
e]1000+400+60+1=…………. f]5000+100+80+9 =……….
6.Build numbers using the given clues. One has been done for you.
a] 4 Tens b] 6 Hundreds c] 2 Ones 1 Thousand 8 Ones 8 Hundreds 5 Ones 5 Thousands 0 Tens 7 Hundreds 3 Tens 9 Thousand
7. Fill in the blanks. One has been done for you . a] In 8326, 3 is in hundreds place.
b] in 1909, 1 is in the ………place.
c] In 5281, 8 is in the………place.
d]In 3559,9 is in the ……….place.
EVEN AND ODD NUMBERS:
The numbers which make perfect pairs are called even numbers .For example, 2,4,6,8……..
are all even numbers the numbers which do not make perfect pair are called odd numbers . For example, 1,3,5,7,……..are all odd numbers.
Even numbers have 0,2,4,6 or 8 at the ones place. For example , the numbers 3890,7772 ,8974,5378 have 0,2,4,6 or 8at the ones place . So they are even numbers .
Odd numbers have 1,3,5,7,9 at the ones place. For example the number 2461,4803,6825, 9729and 4687have 1,3,5,7,9 at the ones place so they are odd numbers.
Exercise1.3:
1.Tick the even numbers and cross odd numbers.
2356 7853 4701 6780 7778 3489 2801 1745
5433 7505 4444 2907 9820 2132 9987 2.Write all even numbers between the following numbers . a)7 and 25 b)151 and 171
3. Write all the numbers
a) all odd numbers between 36 and 52 Answer : 37,39,41,43,45,47,49,51.
b)all odd numbers between 458 and 480.
c)any ten odd numbers between 2000 and 3000.
d)any ten even numbers between 5000 and 6000.
Answer: 5002, 5004, 5006, 5008, 5010, 5012, 5014, 5016, 5018, 5020.
SUCCESSOR AND PREDECESSOR :
To get the successor of a number , add 1 to the number
To get the predecessor pf a number, subtract 1 from the number.
Successor of 5729 = 5729+1=5730.
Predecessor of 5729=5729-1=5728.
Exercise1.4
1.Write the successor of the following number. Three have been done for you.
a)4893 4894 b)5309 5310 c)7979 ………
d)2815………… e)6749 ……… f)3009……….
g)7408………… h)3872 3873 i)9110 ………..
2.Write the predecessor of the following numbers. Three have been done for you.
a)3566 3567 b)9763 9764 c)…………5031 d)………9270 e) ……… 6725 f) ………….3026 g)9,999 10,000 h)………. 3880 i) ………….7010
SKIP COUNTING:
Skip counting is counting forwards or backward by any other than one.
Example: Skip count forwards by 2.
+2 +2 +2 +2
7342 , 7344 , 7346 , 7348 , 7350 , ………
Example: Skip count backwards by 7.
-7 -7 -7 -7
1139, 1132, 1125, 1118, 1111, ……….
COMPARISON OF NUMBERS :
We compare two numbers to find out which is greater or smaller of the two numbers .If two numbers are exactly the same we say that they are equal.
We use the following signs for comparing two numbers .
>greater than 9153>762 5232>4011 8103>7500
<less than 211<9211 3125<4005 8005<8008
=equal to 6719=6719 3415=3415 9800=9800 ASCENDING ORDER AND DESCENDING ORDER
The arrangement of number from the smallest to the greatest is called ascending order.
3496 < 3523 < 4906 < 5349 Smallest Greatest Ascending order
The arrangement of numbers from greatest to the smallest is called descending order.
5349 > 4906 > 3523 > 3496 Greatest Smallest Descending order
Example : Arrange these numbers in ascending order and then in descending order.
2148,2418,2128,2182
Solution : All these numbers have same digit 2 in the Thousand place.
Therefore, we compare Hundreds, Tens and Ones digits.
The ascending order of the numbers is : 2128 < 2148 < 2182 < 2418
The descending order of the numbers is : 2418 > 2182 > 2148 > 2128
Exercise 1.5
1.Skip count backwards. One has been done for you.
a) count by 5s
5554, 5549, 5544, 5539, 5534, 5529, 5524
(in the above question we subtract 5 from the previous one to get the next number) b) count by 9s
8564, 8555, …………., ………….., …………., …………., ………
2. Skip count forwards. One has been done for you.
a) count by 7s
6087, 6094, 6101, 6108, 6115, 6122, 6129
Th H T O 2 1 4 8 2 4 1 8 2 1 2 8 2 1 8 2
(in the above question we add 7 to the previous one to get the next number) b) count by 3s
997, 1000, …………, …………, …………., …………., ………
3. Look at the numbers carefully and fill in the blanks with sign > , < or =. Few have been done for you.
a) 5631 < 6533 b) 5732 > 2475 c) 6923 < 7984 d) 6773…...4816 e) 6578…...5760 f) 3752…..4064 g) 2639…..8941 h) 7900…..7900 i) 7461…...4678
4. Write the numbers in ascending order. Few have been done for you.
a) 1954, 6793, 6397, 9145 1954 < 6397 < 6793 < 9145 b) 2879, 4836, 2761, 2144 2144 < 2761 < 2879 < 4836 c) 1038, 4982, 6721, 7730 1038 < 4982 < 6721 < 7730 d) 3623, 4527, 7524, 6118 ………..
e) 3289, 6568, 1216, 1849 ……….
f) 5910, 5019, 5901, 5001 ……….
5. Arrange the numbers in descending order. Few have been done for you.
a) 2387, 5872, 3798, 4367 5872 > 4367 > 3798 > 2387 b) 4893, 3067, 8267, 6738 8267 > 6738 > 4893 > 3067 c) 1047, 3803, 3280, 1784 ……….
d) 8745, 7854, 7746, 7986 ……….
e) 2877, 8967, 4773, 3452 ……….
6. Underline the greatest number. Three have been done for you.
a) 2831 8234 8934 3867 b) 7098 8943 3506 5667 c) 2067 2078 2065 2068 d) 5200 5202 5220 5022 e) 4398 1056 3489 8934 f) 7461 7641 7436 7761
7. Underline the smallest number. Three have been done for you.
a) 3211 2375 3221 2131 b) 8351 8315 8531 8647 c) 6732 6832 4651 6823 d) 7811 8711 6781 9831 e) 6211 6702 7635 7810 f) 4734 7443 5443 6132
FORMING GREATEST AND SMALLEST NUMBERS.
To form the greatest number, rearrange the digits in descending order.
To form the smallest number, rearrange the digits in ascending order. If you get 0 at the extreme left, then exchange its place with the number on its right.
Example: Form the greatest 4-digit number using the digits 1, 9, 6 and 8 without repeating the digits.
Solution: The descending order of the digits is 9, 8, 6, 1.
Answer: The greatest number is 9861.
Example: Form the greatest and smallest 4-digit numbers using the digits 2, 4, 8 and 0 without repeating the digits.
Solution: The descending order of the digits is 8, 4, 2, 0.
Thus, the greatest number is 8420.
The ascending order of the digits is 0, 2, 4, 8.
Answer: The smallest number is 2048.
Exercise 1.6
1. Form the greatest number and smallest number using the following digits only once.
Few have been done for you.
Digits Greatest number
Smallest number a)1,5,4,2 5421 1245 b)5,6,9 965 569 c)4,3,8,7
d)6,8,7,5 8765 5678 e)3,2,1,9 9321 1239 f)9,6,0,7
2. Write the greatest 4-digit number by changing the position of digits in the following numbers. Few have been done for you.
a) 3175
Solution: The descending order of the digits is 7,5,3,1.
The greatest number is 7531.
b) 6471
Solution: The descending order of the digits is 7,6,4,1 The greatest number is 7641.
c) 4156 d) 4449 e) 7650 f) 9863
Solution: The descending order of the digits is 9,8,6,3.
The greatest number is 9863.
g) 8144 h) 1305
ROUNDING OFF NUMBERS
ROUNDING OFF TO NEAREST TENS
To round off to nearest tens, see the digit at the ones place.
Rule 1: If it is 5 or greater than 5, then the number will be rounded up.
Rule 2: If it is 4 or less, then the number will be rounded down.
ROUNDING OFF TO NEAREST HUNDREDS
To round off to nearest hundreds see the digit at the tens place.
Rule 1: If 5 or number greater than 5, then the number will be rounded up.
Rule 2: If it is 4 or less then the number will be rounded down.
ROUNDING OFF TO NEAREST THOUSANDS
To round a number to nearest thousands, see the digit at the hundreds place.
Rule 1: If it is 5 or number greater than 5, then the number will be rounded up.
Rule 2: If it is 4 or less then the number will be rounded down.
Exercise 1.7
1. Round the following numbers to the nearest tens. Some are done for you.
a) 43----40 (because 3 is less than 5) b) 67----70 (because 7 is greater than 5) c) 156----
d) 389---- e) 674----
2. Round the following numbers to the nearest hundreds. Some are done for you.
a) 265----300(because 6 is greater than 5) b) 872----900(because 7 is greater than 5) c) 957----
d) 989---- e) 354----
3. Round off the numbers to the nearest thousands.
a) 2343----2000(because 3 is smaller than 5) b) 5667----6000 (because 6 is greater than 5) c) 8156----
d) 4389----
e) 7674----
ROMAN NUMERALS
The Roman numerals with their corresponding Hindu-Arabic numerals are given below:
Roman numerals I V X L C D M
Hindu-Arabic numerals 1 5 10 50 100 500 1000 RULES FOR WRITING ROMAN NUMERALS UPTO 39
Rule 1: If a numeral is repeated it means addition. A roman numeral can be repeated up to a maximum of three times. ‘V’ is never repeated.
EXAMPLES
II = 1 + 1 = 2 III = 1 + 1 + 1 = 3 XX = 10 + 10 = 20
Rule 2: If a smaller numeral is written after a larger numeral, their values are added.
EXAMPLES
VI = 5 + 1 = 6 XI = 10 + 1 = 11 XV = 10 + 5 = 15
Rule 3: If a smaller numeral is written before a larger numeral, its value is subtracted from the value of the larger numeral.
EXAMPLES
IV = 5 – 1 = 4 IX = 10 – 1 = 9 Example: Write as Roman numerals.
a)21 b)14 c)37
Solution: First write the number in groups of Tens and Ones. Then write their corresponding Roman numeral.
a)21 = 10+10+1 = XXI b)14 = 10+4 = XIV c)37= 10+10+10+7 = XXXVII
Example: Write Roman numerals as Hindu-Arabic numerals a) XVII=10+5+1+1=17 b) XII=10+1+1=12
C)XXIX=10+10+(10-1) =29 Exercise 1.8
1.Write the Hindu-Arabic numerals for each of the following.
a) III = 1+1+1=3 g) XXV---
b) XIV = 10+(5-1) =14 h) XIX =10+(10-1) =19 c) V--- I) XXVII---
d) XII--- j) IX--- e) X--- k) XXX--- f) XVI--- l) XV--- 2. Write Roman numerals for the following.
a) 7--- b) 9--- c) 17---- d) 25---
e) 18---- f) 24---
g) 21---- h) 28=10+10+5+1+1+1=XXVIII i) 32--- j) 36=10+10+10+5+1=XXXVI
4. Fill in the blanks. Some are done for you.
a) VI = 5 + 1 = 6 b) IX = 10 - 1 = 9 c) XV= 10 + 5 = 15 d) XXXIV = 30 + 5 = 35 e) XVIII =……. + 8 = ………
f) XI = ……... + 1 = ……….
g) XXIX = ……. + 9 = ………
h) XXIII = 20 + ……. = ………
5. Fill in the blank with >, < or =. some are done for you.
a) XIII < 15 b) XI = 9 c) XXXV > 23 d) X < 11
e) XXIX………29 f) XVIII………18 g) XIV………...16 h) XXXVI…….37 i) XXIV……….26
MENTAL MATHS Fill in the blanks.
1. What is the product of an even number and an odd number---even or odd?
Solution: For example, 2*3 = 6 4*7=28
This shows that the product of odd and even number is even.
2. Hi. I am a 4-digit number. Three of my digits are same and the sum of all four digits is 1. I am ……….
Solution: Sum of all the four digits = 1 =1+0+0+0 (As three of the digits are same so, three digits can only be 0 so that sum remains 1)
3. 9050 is ………(smaller/greater) than 9055.
4. The greater the number of digits the ………. Is the number.
5. A 5-digit number begins with the ………. Place.
(thousands/ten thousands)
2. ADDITION
LITTLE ANGELS is a small school in Jaisalmer. The school has 120 boys and 132 girls.
What is the total number of students in the school?
……….
For finding the answer, we need to add 120 boys and 132 girls. Putting together two or more numbers is called adding. The numbers being added are called addends. The answer of addition is called the sum.
ADDENDS ADDENDS
SUM 1.Add the following. Two have been done for you.
H T O
5 4 3 3
8 7
H T O 6 7 3 2 1 5
2.Fill in the blanks. Two have been done for you.
a)37+………=37 b)47+13=15+45 c)96+………=97 d)50+0=25+25 3.Add the following on the number line.
a) 6+3+4= 13
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
b)8+7+2= 17
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 4.Add the following numbers. Three have been done for you.
H T O 1 2 0 1 3 2 2 5 2
H T O 1 7 5 3 2 4 4 9 9 H T O 1 5 4 6 4 1
5.Add the following numbers. Three have been done for you
REMEMBER: Arrange the digits at their correct place value. Always start adding from ones digits.
6.Arrange the number in columns and add in your notebook.
a)253+422 b)352+248 c)569+455 d)582+259 e)278+265+743 f)891+340+146 g)825+597 h)707+523+79 e)
ADDITION OF 4-DIGIT NUMBERS:
ADDITION WITHOUT REGROUPING (In mathematics, ’regrouping’ is also known as
‘carrying over’.
Example: Add 2453 and 2316.
Solution:
Step1: Place the numbers in the columns correctly.
Add the Ones.
3+6=9 Ones
Th H T O 2 7 8 2 5 6 7 4 3 1 2 7 7
Th H T O 8 9 1 3 4 0 1 4 6 1 3 7 7
Write 9 under the Ones column.
Step2: Add the Tens 5+1=6 Tens
Write 6 under the Tens column.
Step3:Add the hundreds 4+3=7 Hundreds.
Write 7 under the hundreds column.
Step4: Add the thousands.
2+2=4 thousands
Write 4 under the thousand column.
Answer: Sum=4769.
ADDITION WITH REGROUPING:
Example: Add 3659 and 1487.
Solution:
Step1: Add the Ones.9+7=16 Ones = 1 Tens + 6 Ones.
Write 6 under the Ones column and carry 1 Ten to the Tens place.
Step2: Add the Tens.5+8+1(carry over) =14 Tens =1 Hundred +4Tens
Write 4 under the Tens column and carry over 1 Hundred to the Hundreds place.
Step3: Add the Hundred 6+4+1(carry over) = 11Hundreds=1Thousand +1 Hundred.
Write 1 under the hundred column and carry over 1 thousand to the Thousand Place.
Step4: Add the thousands.3+1+1(carryover)=5 thousands Write 5 under the thousands place.
Answer: Sum=5146.
Exercise2.1:
1. Add the following numbers. Two have been done for you.
2. Add the following numbers. Three have been done for you.
3.Write each of the following in expanded form and add.
a) 3434+4335
Solution: Place the number in column correctly and write their expanded forms. Then add
Ones, Ten, Hundreds and Thousand separately.
3Thousands 4Hundreds 3Tens 4Ones
4Thousands 3Hundreds 3Tens 5Ones 7Thousands 7Hundreds 6Tens 9Ones
b)2390+1229 c)7803+1173 d)9201+7826 e)4818+6213 f)3890+5639 g)4921+2804
4.Arrange the numbers in the columns and add in your notebook.
a)2817+2993 b)3675+2678 c)962+5298 d)4892+2743 e)3542+1902 f)4567+3698 g)2853+5907 h)2707+3523 ADDITION OF THREE OR MORE NUMBERS (with regrouping):
Exercise2.2
Th H T O 3 4 3 4 4 3 3 5 7 7 6 9
1.Add the following numbers. Three have been done for you.
2.Arrange the numbers in column and add in your notebook.
a)2187+2539+425 b)1012+2678+3675 c)3246+5032+962 d)1026+4892+2743
e)3453+1879+112 Th H T O 1 1 1
3 4 5 3
1 8 7 9
1 1 2 5 4 4 4 f)2345+2225+3695
Th H T O 1 1 1
2 3 4 5
2 2 2 5
3 6 9 5
8 2 6 5
PROPERTIES OF ADDITION:
ORDER PROPERTY OF ADDITION:
The sum of two numbers remain the same even if we change the order of the numbers.
This is called the order property of the addition.
We see that the answer is same in both the cases.
We can say that 2893+2917=2917+2893.
GROUPING PROPERTY OF ADDITION:
When adding 3 or more numbers the numbers cam be grouped in any way. The same remain the same. This is called the grouping property of addition.
Let us add 456+378+175.We can group this number in various ways 1.Group 378 and 175 together using brackets. Add their sum to 456.
2.Group 456 and 378 together and add their sum to 175.
3.Group 456 and 175 together at their sum to 378.
The answer remains same in all the three cases.
ADDITION OF ZERO:
When we add 0 to a number the sum is the number itself.
962+0=962 5298+0=5298 ADDITION OF 1:
When we add 1 to the number, the sum is the successor of the number.
896+1=897 897 is the successor of 896 1564+1=1547 1547 is the successor of 1546 Execise2.3:
Fill in the blanks:
1)569+872=872+569 2)2789+3241=3241+2789 3)………+7892=7892+4723 4)7652+9002=………+7652
5)1920+672+………=672+2453+1920 6)4567+……..+5390=7461+5390+4567 7)2378+7890+3122=3122+7890+2378 8)1221+6677+8899=6677+8899+1221 9)4747+……..+7937=……….+5382+4747 SOME SPECIAL PROPERTIES OF ADDITION:
1. Numbers ending in zero(s) can be added easily.
2. 10 added to any number increases the value of digit in tens place by one.
3. 100 added to any number increases the value of the digit at the hundreds place by 1.
4. 1000 added to any number increases the value of the digit at the thousands place by 1.
ESTIMATING THE SUM
To estimate the sum of two given numbers, we round off the given numbers and then find their sum.
HORIZONTAL ADDITION
You have learnt to add numbers vertically by placing them in columns.
Now let us learn to add numbers horizontally.
Example: Add 643 and 132 horizontally.
Solution:
Step1: Add the Ones 3Ones + 2Ones= 5Ones Step2: Add the Tens.
4Tens + 3Tens = 7Tens Step3: Add the Hundreds
6Hundreds + 1Hundred= 7Hundreds Answer: Sum = 775.
Exercise 2.4:
1.Estimate the sum.
a)4282+66540
Answer: Rounding off 4282 to nearest 1000 we get 4000.
Rounding off 6554 to nearest 1000 we get 7000.
Adding 4000 and 7000 = 4000+7000= 11000 b)5437+4783
Answer: Rounding off 5437 to nearest 1000 we get 5000.
Rounding off 4783 to nearest 1000 we get 5000.
Adding 5000 and 5000= 5000+5000=10000.
H T O 6 4 3
H T O 1 3 2
c)8668+3459 d)108+253+3788 e)339+420+582 f)1256+2390+3555 2.Add the following numbers horizontally.
a)263+643 Solution:
Step1: Add the Ones
3Ones+3Ones=6Ones.
Step2: Add the Tens
6Tens=4Tens=10Tens Step3: Add the Hundreds
6Hundreds+2Hundred=8Hundreds Answer: Sum=906
b)401+230 c)782+567 d)986+342 e)853+395 f)609+554
APPLICATION IN REAL LIFE Exercise2.5:
Solve these addition stories.
1.A farmer grew 1879 pumpkins last year. This year he grew 762 pumpkins more.How many Pumpkins did he grow this year?
Solution: Pumpkins grown by farmer last year=1879
Number of pumpkins grown by farmer this year more than last year=762 Total number of pumpkins grown this year = 1879+762=2641.
2.A toy shop sold 2654 toys last month and 3578 toys this month. How many toys were Sold in both the months together?
Solution: Number of toys sold last month=2654 Number of toys sold this month=3578
Total number of toys sold altogether=2654+3578=6232
3.A car dealer sold 2634 cars in the year 2010,2458 cars in 2011 and 3562 cars in the year 2012. How many cars in all did he sell together in these three years?
Solution: Cars sold in 2010 = 2634 Cars sold in 2011 = 2458 Cars sold in 2012 = 3562
Cars sold in the three years = 2634+2458+3562=8654
4.In a particular month a fruit seller sold 5234 apples and 3896 bananas. How many apples and bananas did he sell together in the month?
Solution: Number of apples sold = 5234
Number of bananas sold =3896
Total number of apples and bananas sold in the month = 5234+3896=9130.
5.In an orchard, there are 1293 peach trees, 2367 apple trees and 1658 apricot trees. Find the total number of trees in orchard.
Solution: Number of peach trees in an orchard= 1293 Number of apple trees in an orchard=2367 Number of apricot trees in an orchard=1658
Total number of trees in an orchard = 1293+2367+1658=5318
6.Jisha bought a pair of jeans for Rs.3987, a top for Rs1654 and a muffler for Rs.1114. How much did Jisha spend in all?
7.Rakesh runs 1480metres in his first race ,2667 metres in his second race and 1629 in his third race. How far did he run in all.
8.Sakshi bought set of story books for Rs.1765, a set of craft books for Rs.1409 and an encyclopaedia for Rs.2784. Find out the total amount of money she spent.
9.A farmer produces 2358 bags of wheat, 1236 bags of millet and 1405bags of rice. Find The total number of bags of grains?
10.A shopkeeper sold 4227 cartons of tomato juice, 2424 cartons of carrot juice and 2273 cartons of apple juice. Find out how many cartons of juice did the shopkeeper sell?
11. A gardner planted 3257 saplings in a park on Monday, 1452 saplings on Tuesday and 2741 saplings on Wednesday. Find out the total number of saplings the gardner planted in these three days.
12. Garima has Rs.8545 in her bank account. She deposited Rs.2570 on Monday and Rs.2630 on Wednesday. How much money is there now in her account?
MENTAL MATHS
Tick the correct answer.
1. 900 + 1000 + 1 =?
a) 9991 b) 9091 c) 1901 d) 1910
2. 3867 girls and 133 boys went on a picnic. How many children were there on picnic?
a) 4033 b) 4000 c) 4133 d) 4313
3. A shopkeeper had a sale of Rs.2098 on Monday, Rs1000 on Tuesday and Rs.1002 on Wednesday. Find his total sale.
a) 5000 b) 4100 c) 4098 d) 4010
SUBTRACTION
There were 764 animals and birds in a zoo and out of these 251 were birds.
How many were animals?...
To find the answer, we have to do subtraction.
Remaining number of animals = 764 – 251 = 513 7 6 4
-2 5 1
5 1 3 Difference Subtraction is taking away some objects from a group.
We always subtract a smaller number from a bigger number and the answer we get after subtracting, is called the difference.
REMEMBER: In subtraction, the bigger number is called minuend. The number to be Subtracted is called subtrahend.
1. Write the subtraction facts for the following. Three have been done for you.
a) If 29 + 51 = 80 then 80 - 29 = 51 and 80 - 51 = 29
b) If 41 + 55 = 96 then 96 - …….. = ……. and 96 -……. = ……..
c) If 36 + 64 = 100 then 100 - 64 = 36 and 100 - 36 = 64.
d) If 138 = 200 = 338 then 338 - …….. = …….. and 338 - …….. = ……...
e) If 163 + 267 = 430 then 430 - 267 = 163 and 430 - 163 = 267.
2.Fill in the blanks.
a) 32-21=………….
b) …….. – 1 = 81 c) 64 - …… = 64 d) 700 – 100 = 600 e) 47 - ….. = 1 f) …… - 0= 63 g)700 – 1 = 699 . h)79 - ……. = 78 i)360 - 60 = 300.
3. Subtract.
4.Write in columns and subtract.
a)758-426
H T O 7 5 8 4 2 6 3 3 2
b)689-566 c)483-150 d)159-124 e)901-658 f)632-583 g)347-299 h)843-680 i)532-189 SUBTRACTION OF 4-DIGIT NUMBERS
SUBTRACTION WITHOUT REGROUPING Example: Subtract 1425 from 2468.
Solution:
Step1: Place the numbers in columns correctly. Subtract the Ones.
8 – 5 = 3 Ones
Write 3 under the Ones columns Step2: Subtract the Tens.
6 – 2 = 4 Tens
Write 4 under the Tens column.
Step3: Subtract the Hundreds.
4 – 4 = 0 Hundreds
Write 0 under the Hundreds column.
Step4: Subtract the Thousands.
2 – 1 = 1 Thousand
Write 1 under the Thousands column.
Answer: Difference = 1043.
REGROUPING THOUSANDS, HUNDREDS, TENS AND ONES Example: Subtract 5869 from 7150.
Solution:
Step1: Subtract the Ones. We cannot subtract 9 Ones from 0 Ones.Therefore we regroup Tens into Ones.
5 Tens + 0 Ones = 4 Tens +10 Ones 10 – 9 = 1 One .
Write 1 under the Ones column.
Step2: Subtract the Tens. We cannot subtract 6 Tens from 4 Tens .Therefore we regroup Hundreds into Tens.’
1 Hundred + 4 Tens = 0 Hundreds =14 Tens 14 – 6 = 8 Tens.
Write 8 under the Tens column
Step3: Subtract the Hundreds. We cannot subtract 8 Hundreds from 0 Hundreds.
Therefore we regroup Thousands into Hundreds
7 Thousands = 0 Hundreds= 6 Thousands = 10 Hundreds 10 – 2 = 2 Hundreds
Write 2 under the Hundreds column.
Step4: Subtract the Thousands.
6 – 5 = 1 Thousands
Write 1 under the Thousands column.
Answer: Difference = 1281.
EXERCISE 3.1:
1.Subtract without regrouping.
2.Subtract with regrouping:
3. Subtract the following in your notebook by rearranging in columns.
a)278 from 5623 b)1254 from 7841 Th H T O
5 6 2 3 2 7 8 5 3 4 5
c)5698 from 8201 d)4897 from 9874 e)5669 from8447 f)2512 from 8456
SUBTRACTING FROM ZEROS
When subtracting larger whole numbers start in the Ones column and move left. However sometimes we cannot subtract from the column we are in. So, we need to borrow from the column to the left.
But there are times when the number to the is a zero. When this happens you must borrow from the next 2 places to the left.
REMEMBER:
1. Always start subtracting from the ones column and move your way left.
2. If you cannot subtract from the column you are in you need to borrow one from the Column to the left .
3. But if there is a zero in the next column, borrow from the next two columns to the Left.
EXERCISE3.2
1. Find the difference.
2. Arrange these numbers in column and subtract.
a) 6889 from 9000
b)4590 from 9890 c)890 from 6004
Th H T O 9 0 0 0 6 8 8 9 2 1 1 1
ADDITION AND SUBTRACTION TOGETHER Example: Solve 669+180-472+233
Solution: Add 669 and 180. Then subtract 472 from there sum and add 233 to the difference to get the answer.
Answer: Thus, 669+180-472+233=610 CHECKING SUBTRACTION THROUGH ADDITION
To check subtraction add the difference to the smaller number. You should get bigger number as the answer.
Example: Subtract 366 from 981.
Solution: Check:
Exercise 3.3
1. Solve the following:
a) 508-194+103 H T O 4 10 5 0 8 1 9 4 3 1 4
b) 437+345-683+111 c) 652-584+241+132 d) 874-132-245+435 e) 302+254-369
2.Find the difference. Then check the answer through addition.
a) 605-263 b) 689-354 c) 9605-8272
H T O 3 1 4 1 0 3 4 1 7
CHECK:
d) 3785-3702
PROPERTIES OF SUBTRACTION
When we subtract 0 from a number, the difference is the number itself.
When we subtract 1 from a number, the difference is the predecessor of the number.
When we subtract the number from itself, the difference is always 0.
EXERCISE3.4:
1.Fill in the blanks:
a) 872 – 872 =0 b) 2789 – 0 = 2789 c) 7893 – 1 = 7892 d) 8765 – 8765 = …………
e) 1920 - ……….. = 1920 f) 5672 – 1 = ………….
ESTIMATING THE DIFFERENCE
Rounding off helps in estimating the difference.
Exercise3.5:
1.Estimate by rounding to nearest tens.
a) 87 – 23
Solution: Rounding off 87 to nearest tens = 90 Rounding off 23 to nearest tens = 20 Estimated the difference = 90-20=70 b)167–94
c)546-231
2. Estimate by rounding to nearest hundreds.
a)654 – 114
Solution: Rounding off 654 to nearest hundreds = 700 Rounding off 114 to nearest hundreds = 100 Estimating the difference = 700 – 100 = 600.
b)786 – 231 c)857-673 APPLICATION IN REAL LIFE
EXERCISE3.6:
Th H T O 5 10 9 6 0 5 8 2 7 2 1 3 3 3
Th H T O 1 1 3 3 3 8 2 7 2 9 6 0 5
1.Soham had a collection of 2764 stamps. He gave away 1402 stamps. How many stamps were left.
Solution: Number of stamps Soham had= 2764 Number of stamps he gave away= 1402.
Number of stamps left = 2764 – 1402 = 1362
2.A runner a has to run 1275 steps in a marathon. He has finished 1145 steps. How many Steps are left?
Solution: Number of steps runner has to run = 1275 Number of steps he had finished =1145 Number of steps left = 1275 – 1145 = 130.
3.There are 9948 students in a school. On the first day, 1029 students were absent. How Many students were present on the first day?
Solution: Number of students in a school = 9948
Number of students absent on first day in school = 1029
Number of students present on first day in school = 9948 – 1029 = 8919
4.A factory made 7648 water bottles in a month. 2975 bottles were damaged. How many Bottles can be used?
Solution: Number of bottles made in a month = 7648 Number of bottles damaged this month =2975
Number of bottles that can be used = 7648 – 2975 = 4673
5.There were 2865 red and green beads in a box. The number of red beads was 1567 How many beads were green?
Solution: Total number of beads = 2865 Number of red beads = 1567
Number of green beads in a box = 2865 – 1567 = 1298
6.3893 students study at New Modern Era School and 2895 at Saint John School. How many more students study at the New Modern Era School?
7.Preeti loves to collect old coins. She has a collection of 8264 coins, out of which 5075 are of India. How many are of other countries?
8.Of a total of 3605 bottles of juice, 2850 were supplied to the school canteen. How many bottles of juice were not delivered?
9.A gardener planted 3006 saplings in a park. Heavy rains damaged 1769 saplings. How Many saplings were saved?
10.Out of 7526 flats in a new colony, 3839 flats are sold. How many flats are still unsold?
MIXED BAG
In real life, sometimes we perform both addition and subtraction.
Exercise3.7:
a) 3809+4526-1678-2546 b) 3205-2417+6325-4754 c) 6852-5624+2140-986 d) 549+2365-4102+7892-876 Solution:
Step1: Group the first number and all the numbers with + sign together (549+2365+7892)
Add these numbers.
Step2: Group the all numbers with – sign together.
- (4102+876)
Add these numbers.
Step3: Subtract the sum of the second group (- numbers) from the sum of the first group (+ numbers)
Tth Th H T O 1 2 1 5 4 9 2 3 6 5 7 8 9 2 1 0 8 0 6
Th H T O 4 1 0 2
8 7 6 4 9 7 8
Tth Th H T O 0 9 7 9 16 1 0 8 0 6
4 9 7 8 5 8 2 8 e) 2364-1358+4512-569-3698 Solution:
Step1: Group the first number and all the numbers with + sign together.
(2364+4512)
Add these numbers.
Th H T O 2 3 6 4 4 5 1 2 6 8 7 6
Step2: Group all numbers with – sign.
- (1358+569+3698) Add these numbers.
Th H T O 1 2 2 1 3 5 8
5 6 9 3 6 9 8 5 6 2 5
Step3: Subtract the sum of the second group (- numbers) from the sum of the first Group numbers (+ numbers).
Th H T O 6 8 7 6 5 6 2 5 1 2 5 1 f) 4521+569-2315-1946 g) 3698-2514-3305+5987 h) 5223-3547+2578-1946
REAL LIFE APPLICATION OF ADDITION AND SUBTRACTION:
Exercise3.8:
1. The total capacity of an auditorium is 2000.498 people arrive half an hour before the show and 865 people arrive just before the show begins. How many seats are
unoccupied?
Solution: Total capacity of auditorium = 2000.
Number of people that arrived half an hour before = 498
Number of people that arrived just before the show begin = 865 Total seats occupied = 498 + 865 =1363
Number of seats unoccupied = Total seats – occupied seats =2000-1363=637
2. Ramu reads 341 pages of a book and 116 pages on the next day and 287 pages on the third day. How many pages are left if there are 1753 pages in the book?
Solution: Number of pages read on the first day = 341 Number of pages read on second day = 116 Number of pages read on third day = 287
Total pages read by him = 341 + 116 + 287 = 744 Total number of pages in the book = 1753
Number of pages left to read = total pages – pages read by him = 1753 – 744 = 1009
3. In a drawing competition, 7725 students participated. Out of these, 2349 are from class 2, 2783 from class 3 and the rest were from class 4. Find number of students who participated in class 4?
Solution: Total number of students who participated = 7725 Number of students from class 2 = 2349
Number of students from class 3 = 2783
Total number of students of class 2 and 3 = 5132
Number of students of class 4 = Total number of students – total students Of class 2 and 3
= 7735 – 5132 = 2593.
4. A florist sold 5637 roses and 2893 sunflowers in 2010. He sold 4052 roses and 1974 sunflowers in 2011. How many less flowers did he sell in 2010 than in 2011?
Solution: Number of flowers sold in 2010 = 5637 roses + 2893 sunflowers = 8530.
Number of flowers sold in 2011 = 4052 roses + 1974 sunflowers = 6026.
Number of flowers sold less in 2011 = number of flowers sold in 2010 – Number of flowers sold in 2011 = 8530-6026=2504.
5. In a factory, there are 1785 workers. 957 workers come in the first shift, 496 workers come in second shift and rest come in the third shift. How many workers come in the third shift?
6. Rahul had Rs.9970 with him. He purchased books for Rs.5640, a briefcase for Rs.1855 and a set of CDs for Rs.850. How much money is he left with?
7. Gunjan saved Rs.5600 from her salary. Out of that, she bought a wrist watch for Rs.2895. Her sister gifted her Rs.2100 on her birthday. How much money is left with Gunjan now?
8. Subtract the sum of 2534 and 1890 from 8542.
9. What must be added to the sum of 5672 and 2892 to get 9267?
Solution: First number= 5672 Second number= 2892 Third number=?
Sum of first number and second number=5672+2892=8564 Total sum of all numbers =9267
Third number = Total sum – sum of first number and second number =9267 – 8564 = 703.
So, the required number= 703.
10. Subtract the sum of 2516 and 4472 from the sum of 2906 and 5265.
MENTAL MATHS
Tick the correct answer:
1. What should be subtracted from 666 to get 222?
a)222 b)666 c)333 d)444 2. One less than the 4-digit number is
a)1000 b)900 c)999 d) none of these 3. 3410 – 210 + 1000 is equal to
a)3500 b)4200 c)3610 d) none of these 4. The difference of the smallest 3-digit numbers is
a)999 b)100 c)900 d) none of these 5. If 1 is subtracted from a number, we get
a) its predecessor b) its successor c)0 d)1
