Name : Class:.. Homework Rubric : ( 10 marks ) 8 marks for accuracy.( To be complete and correct ) 1 mark for punctuality. ( To be delivered on time ) 1 mark for organization ( To be clean, neat and tidy ) 1
Lesson QR Code Large numbers Expended & Compact form Multiplying by 1- digit number Multiplying by 2- digit number Divisibility Prime numbers Area of square and rectangle Division Polygons Factors 2
Prime factors Triangle Perimeter I am going to help you to read and write large numbers up to milliard Large numbers Hundred thousands. Millions, ten millions, hundred millions. Milliards (Billions). Operations on large numbers. 3
Greatest no. Add Smallest no. 5 digits 99 999 + 1 6 digits 999 999 + 1 7 digits 9 999 999 + 1 8 digits 99 999 999 + 1 9 digits 999 999 999 + 1 100 000 Hundred thousand 1 000 000 One million 10 000 000 Ten million 100 000 000 Hundred million 1 000 000 000 One milliard 6 digits 7 digits 8 digits 9 digits 10 digits Reading large numbers ( in words ) : 1. 482, 612 : Four hundred eighty two thousands six hundreds and twelve. 2. 62, 070, 004 : Sixty two millions seventy thousands and four. Writing large numbers ( in digits ) : 1. Five millions seven hundreds eleven thousands three hundreds and ninety : 5,7 1 1, 3 9 0 2. Three hundred five millions and eighty eight : 3 0 5, 0 0 0, 0 8 8 4
Exercise (1) 1) Read the following numbers (write in letters): a) 125 400 b) 785 129 690.. c) 3 124 200 059.. d) 18 307 270 987... 2) Write the following numbers ( in digits ) : a) Three million, four hundred thousand and twenty. (...) b) Fifty seven million, five hundred thousand and five. (...) c) Fifty milliard, two hundred forty three million, five hundred thousand and two hundreds. (..) d) Six hundred twenty million and four hundred two. (..) 5
Exercise (2) 1) Read (write in letters): a) 825 039 :.... b) 7 620 500 :..... c) 909 009 066 :... d) 29 000 432 000 :..... 2) Write in digits: a) Four million, two hundred six thousand, seven hundred and thirty. (..) b) Eighty three million, fifty nine thousand, one hundred and sixteen. (...) c) Ninety milliard, fifty four million, seven hundred thousand and eighty (..) d) Fifteen million, five hundred five thousand and five. (.) 6
Exercise (3) 1) Complete the following : a) 456 889 =... thousands +... b) 340 001 =... thousands +... c) 8 789 765 =... m +... ths. +... d) 24 080 034 =... m +... ths +... e) 601 000 567 =... m +... ths +... f) 95 788 445 890 =... ml +... m +... ths +... 2) Write the number : a) 23 ths + 784 =... b) 320 ths + 81 =... c) 6 m + 345 ths + 600 =... d) 23 m + 78 ths + 2 =... e) 46 ml + 343 m + 100 ths =... 7
Exercise (4) 1) Choose the correct answer: 1) The place value of the digit 2 in the number 245 080 701 is a) millions b) ten millions c) hundred millions 2) The place value of the digit 8 in the number 8 235 001 is a) thousands b) millions c) ten millions 3) The place value of the digit 6 in the number 64 579 328 is a) millions b) hundred thousands c) ten millions 4) The value of the digit 4 in the number 4 536 789 is. a) 4 000 000 b) 4 000 c) 40 000 000 5) The value of the digit 9 in the number 945 200 300 is a) 9 000 000 b) 900 000 000 c) 90 000 000 6) The value of the digit 5 in the number 2 456 300 is. a) 5 000 000 b) 50 000 000 c) 50 000 8
Exercise (5) 1) Complete in an expanded form: a) 526 453 = 500 000 +...+...+...+...+... b) 8 234 098 =... m +... H th +...T th +...th +... h +... t +... u c) 7 675 039 = + +.. +.+.+ d) 4 603 121 = + +.. +.+.+. 2) Complete in a compact form = write in digits a)... = 100 000 + 70 000 + 6 000 + 500 + 20 + 1. b)... = 700 000 + 6 000 + 30 + 6. c)... = 800 000 + 40 000 + 900 + 70 + 5. d)... = 6 Tm + 7m + 3 H th + 7 H m + 6 T + 1 9
Exercise (6) 1)Complete each of the following : a) 148 357 = 100 000 +... + 8 000 +... +...+ b)...= 20 000 000 + 400 000 + 50 000 + 3 000 + 60 + 9. c) 8 532 674 109 =... ml +... m +... ths +... d) 97 000 590 =... Tm +... m +... h +... t +... u. e)...= 37 millions, 150 thousands, 478. 2)Write the place value of the underlined digit : a) 2 888 786 489 =... b) 140 609 300 =... c) 36 549 201 =... 10
More exercise to solve 3) Write the value of the underlined digit : a) 6 030 154 291 =... b) 5 146 079 385 =... c) 256 005 000 =... d) 9 865 500 000 =... 4) Write the following in letters : a) 95 005 050... b) 5 012 700 000.... 5) Write the following in digits : a) Eight milliard, two hundred twenty million and sixteen (..) b) Fifteen million and five thousand (.) 11
Exercise (7) 1)Complete the following : a) 8 tens =... b) 350 x 10 =... c) 18 hundreds =... d) 90 thousands =... e) 150 x 1000 =... f)... tens = 30000 g) 2 560 x 100 =... h) 9 000 =... thousands. i) 6 000 thousands =... millions. j) 340 millions =... thousands. k)600 T th =... m =...th. l) 20 000 th =... m =...T m. 12
2) Choose the correct answer: 1) 90 hundreds =.. a) 9 000 b) 90 000 c) 900 000 d) 900 2) 17 tens =.. a) 1 700 b) 170 c) 17 000 d) 170 000 3) 45 thousands =. a) 4 500 b) 450 c) 45 000 d) 450 000 4) 23 X 100 =. a) 2 300 b) 23 000 c) 230 d) 230 000 5) 920 X 1000 =. a) 92 000 b) 920 000 c) 9 200 000 d) 9 200 6) 83 000 = hundreds. a) 830 000 b) 830 c) 8 300 d) 83 000 7) 15 000 =...thousands. a) 150 b) 1 500 c) 15 d) 15 000 8) 7 000 hundreds =..ten thousands. a) 7 000 b) 70 c) 700 d) 70 000 9) 250 millions =.thousands. a) 250 000 b) 25 000 c) 2 500 d) 25 000 000 10) 80 000 thousands = millions. a) 8 000 b) 80 000 c) 80 d) 800 000 13
Compare by putting >, < or = a) 37 457 310 73 419 546. b) 150 258 214 150 258 213. c) 9 854 705 1 012 314. d) 271 400 336 271 400 663. e) 7 100 600 200 8 000 000 000. f) 1 000 000 000 999 999 999 + 2. g) 1 307 458 210 1 703 458 210. h) 6 420 111 715 998 777 999. i) 45 hundreds 45 thousands. j) 200 millions 2 milliards. k) 48 ten hundreds 480 ten thousands. l) 969 696 969 969 969 969. 14
Arrange the following numbers 1) Arrange in an ascending order : a) 765 432, 7 352 967, 65 047 321, 6 835 764. The order is :...,...,...,... b) 24 571 207, 24 571 702, 724 571 072, 24 571 270. The order is :...,...,...,... c) 18 millions, 18 thousands, 1 800 00 tens, 18 hundreds. The order is :...,...,...,... 2)Arrange in a descending order : a) 94 987 145, 965 852 664, 9 325 997, 9 654 784. The order is :...,...,...,... b) 833 322 165, 833 400 001, 833 322 156, 83 987 654. The order is :...,...,...,... c) 20 thousands, 200 tens, 2 hundred thousands, 2 million. The order is :...,...,...,... 15
1) Write the greatest & the smallest numbers in each : a) 6, 2, 8, 5, 1, 7 I will help you in forming numbers Greatest. Smallest b) 5, 0, 8, 3, 7, 2 Greatest. Smallest c) 9, 3, 7, 2, 4, 8, 5 Greatest Smallest 2) Complete each of the following : a) The smallest 7-digits number is... b) The greatest 8-digits number is... c) The smallest number formed from 7 different digits is... d) The greatest number formed from 8 different digits is... e) The smallest 9-digit number is... f) The greatest 9-digit number is... g) The smallest odd number formed from 7 digits is... 16
More exercise to solve Choose the correct answer : 1) 6 milliard, 47 million and 257 = a) 647 000 257 b) 6 047 000 257 c) 647 257 2) 3000 millions =. a) 3 000 000 b) 30 000 000 c) 3 000 000 000 3) One milliard is the smallest number formed from. digits a) 7 b) 10 c) 9 d) 12 4) The greatest 10-digit number formed from the digits from 0 to 9 is. a) 1 234 567 890 b) 9 087 654 321 c)9 876 543 210 5) Which number is closest to one million a) 909 999 b) 990 999 c) 900 009 17
Add and subtract 1) Choose the correct answer: 1) 847 215 + 204 684 =... a) 1 051 899 b) 1 510 783 c) 1 051 896 2) 1 547 643 + 3 849 768 =... a) 5 497 543 b) 5 397 411 c) 5 397 311 3) 7 547 643 3 849 768 =. a) 3 997 875 b) 7 697 875 c) 3 697 875 4) 94 763 500 28 979 649 =. a) 65 783 451 b) 65 783 851 c) 65 780 149 18
Can you find the missing numbers Choose the correct answer: a) 9 238 146 - = 657 389 ( 8 580 757, 8 569 757, 9 678 757 ) b).. + 2 123 456 = 3 924 125 ( 1 900 669, 1 800 669, 1 800 779 ) c).. - 378 945 = 378 945 ( 857 870, 757 840, 757 890 ) d) 1 000 000 +... = 1 234 678 ( 354 678, 234 678, 234 654 ) e) 9 256 000 -. = 5 312 989 ( 3 943 011, 4 943 021, 3 945 011 ) f) - 4 808 199 = 3 121 703 ( 7 992 902, 7 929 902, 8 929 902 ) 19
General exercise 1) Put >, < or = : a) 999 999 + 1 1 million b) 1 000 001 1 ten million c) 9 876 543 the greatest 7-digit number d) 1 000 000 the smallest 7 different digit no. 2) Choose the correct answer : 1) 235 million, 180 thousand and 65 =... a) 235 175 065 b) 235 180 065 c)325 180 065 2) The value of the digit 7 in the no. 4 876 554 009 is... a) 700 000 000 b) 700 000 c) 70 000 000 3) The smallest 8 different digits number is... a) 10 000 000 b) 12 345 678 c) 10 234 567 20
4) 100 000 000 + 2 000 000 + 30 000 + 600 + 2 =. a) 102 030 602 b) 132 030 620 c) 120 030 602 5) The place value of 8 in 67 899 655 is... a) million b) hundred thousand c) ten thousand 3 ) Arrange in a descending order : 3 521 764, 994 318, 5 764 849 and 2 millions. The order is :...,...,...,... 4) Find : The greatest and the smallest numbers can be formed from all of the following digits [ 7, 2, 8, 3, 5, 9 and 4 ] Then find : their sum and the difference between the two numbers.. 21
Can you solve this 1) Complete in the same pattern : a) 4 500, 4 600,...,...,... b) 76 100, 76 150,...,...,... c) 18 760, 18 750,...,...,... d) 25 000, 24 500,...,...,... 2) Calculate each of the following : a) The difference between 6 322 346 and 1 466 830. b) Take away 5 678 000 from 6 000 000.. c) A number if added to it 300 000 the result will be 1 million.... 22
d) A number if added to 7 812 159 the sum will be 9 209 312... e) A number if it is subtracted from million the difference will be 209 312. f).. 25 000 = 57 000 g) 79 540 + = 99 685 23
Wow story problems Read and solve each of the following : a) A merchant has 600 000 L. E., he bought a piece of land for 251 000 L.E. How much money was left with him?.... b) Shady bought a red car for 24 319 L.E and his brother Kareem bought a blue car that costs 98 570 L.E. How much money did they both pay?..... c) Sarah travelled 7 314 842 Km by a plane, she also travelled 243 117 Km by a train.how many Km did she travel all this trip?... 24
d) A merchant bought 1 356 789 pens. He sold 923 868 of them.find the number of pens he has now.... e) A factory produced 2 987 543 toys in one year. The next year, the factory produced 3 267 594 toys. Find the difference between the productions in both years..... f) The number of population in one city is 4 567 765 people and in another city is 5 456 343 people, how many people live in the two cities? 25
The relation between two straight lines Remember the types of lines : Straight Line Ray Line Segment No start & no end 1 Start & no end 1 start & 1 end Remember the types of angles : Acute angle Right angle Obtuse angle Straight angle Between Exactly Between Exactly 0 & 90 90 90 & 180 180 This year we are going to study the relation between any two straight lines whether they are going to meet at a point or they are never going to meet. Learn these new words : Intersect : meet at a point. Point of intersection : The point where any two lines meet 26
Relation between two straight lines : A. Intersecting and perpendicular ( ) lines : C 1. Point of intersection is N. 90 2. AB CD. A B 3. 4 angles. 4. Each angle is right angle ( 90 ). D B. Intersecting and not perpendicular lines : 1. Point of intersection is M. X 2. XY intersect ZL. Z L 3. 4 angles ( no right angles ). M 4. 2 acute angles & 2 obtuse angles. Y C. Parallel lines ( // ) : D S 1. No point of intersection. 2. DE // ST. 3. Never intersect. 4. No angles. E O 27
Can you solve this? 1)Write intersecting ¬, perpendicular or parallel : 1. 2. 3. 4............. 2)Use the figure to complete using ( ) or ( // ) : a) AB DE A F B b) CF DE c) CD FA d) CE CF D C E 3) Use the figure to complete : a) AB //.. b) AB.at point A A B c) AD // M D C d) AD at point D e) AC intersects. at point 28
4) Choose the correct answer : a) Any two straight lines that never intersect are called. ( perpendicular, parallel, intersecting and not perpendicular ) b) Any two lines that intersect at a point and make four right angles are called. ( parallel, intersecting and not perpendicular, perpendicular ) c) The two intersecting lines intersect at. ( one point, two points, zero points ) d)the two parallel lines intersect at.. ( two points, zero point, one point ) e) The two intersecting lines make.. angles. ( 2, 4, 5 ) f) If one angle at the intersecting point of the two lines is right angle then the two lines are called ( parallel, perpendicular, intersecting and not perpendicular ) g)the two perpendicular lines form 4.. angles. ( acute, obtuse, right ) 29
Try to draw 1)Draw the perpendicular NZ on the given straight line XY, then complete : m ( XNZ ) = m (... ) =... 2)Draw a O, then complete : from the point M on DC to intersect it at point m ( MOC ) = m (... ) =... 3)Draw a straight line parallel to AB the point L. and passing through 4) In the figure shown : 1) Draw CD AB at point M. 2) Find measure of angle AMC. 30
5) Using the figure opposite,then complete : AB AB XY... BC ( or // )... YZ ( or // )... BC ( or // ) AY intersects with BZ at the point... YC intersects with BX at the point... 6) Choose the correct answer : AB AE BC.(DC.( BD // ( CD, AD, AB, AE, XY ), BC ), AD ) DC // ( AE, AB, XY ) 7) Using the opposite figure,then complete: AF //.. AD.. or. AB //. CE AE. intersects CE at the point 31
Can you solve this 1) Choose the correct answer : 1) The place value of the digit 7 in 375 214 is. a) hundred b) thousand c) ten thousand 2) 543 543 218 + 149 738 512 =... a) 690 280 173 b) 693 281 730 c) 703 281 730 3) 45 000, 45 500,... a) 47 000 b) 46 000 c) 45 750 4) The two lines form... right angles. a) 4 b) 3 c) 2 5) The two lines which cannot intersect are called... a) perpendicular b) parallel c) intersecting but not perpendicular 6) The smallest 10-digit number is... a) million b) milliard c) ten thousand 32
7) 543 214 -... = 271 599. a) 271 615 b) 271 800 c) 28 340 8) 3 m + 876 th + 5 h + 9 u =... a) 8 763 509 b)3 876 509 c) 3 860 059 2)Put ( > ), ( < ) or ( = ): a) 132 045 93 245 b) The smallest 7-digits One million. c) 99 999 + 2 100 000. d) The measure of an acute angle Obtuse angle. 3) Arrange in an ascending order : 7 524 832, 7 245 832, 7 452 382 and 745 832. The order is...,...,...,... 33
4)Using the figure opposite,then complete : AB BC AD... DC ( or // )... DE ( or // )... BC ( or // ) AD intersects with DC at the point... DE intersects BC with at the point... Well done 34
Multiplication 1)Find the product of each of the following : 2 6 0 8 X 4.. 2) Choose the correct answer: a) 3 425 X 6 =.. ( 20 550, 20 650, 50 550 ) a) 73 540 X 4 = ( 294 750, 294 160, 394 160 ) b) 34 567 X 3 =. ( 103 705, 305 701, 103 701 ) c) 3 246 X 30 =... ( 98 480, 97 380, 95 380 ) d) 54 320 X 20 = ( 1 086 400, 1 086 600, 1 086 450 ) 35
1)Find the product of each of the following : a) 4 835 X 26 = 1) Start from the unit 2) Cross the carry up Multiplying by a 2-digit number 3) Multiply the ten digit 4) Put zero under the unit 5) Then add b) 357 X 50 =.. c) 6 765 x 24 = 36
2) Choose the correct answer : 1) 75 X 23 = a) 1 725 b) 1 735 c) 1 745 d) 2 725 2) 58 X 22 = a) 1 256 b) 1 266 c) 1 276 d) 1 340 3) 116 X 12 =.. a) 1 382 b) 1 392 c) 1 372 d) 1 382 4) 228 X 24 =... a) 5 472 b) 5 372 c) 5 272 d) 5 572 37
Can you help me to solve this story Read and solve the following : a) Mohamed saves P.T 3 455 monthly. How much money he saves in 9 months?... b) A theatre has 45 rows each consists of 38 seats. How many seats are there in this theatre?... c) A man bought 67 lamps for 88 P.T for each. What is the total price of the lamp?... 38
d) In each sack there are 124 apples. How many apples are there in 45 sacks?... e) A man bought 98 meters of cloth for 45 L.E per meter. Find the total cost?... f) If a packet of paper contains 98 papers. How many papers are there in 509 packets?... g) Weal read 9 books of 540 pages each, how many pages did he read?.... h) A school has 19 classes of 45 pupils each, find the number of pupils in this school...... 39
e.g. : The multiple of a number means to add this number each time to the answer starting from ZERO. - Multiples of 1 = 0, 1, 2, 3, 4, 5,... ( +1 each time ) - Multiples of 2 = 0, 2, 4, 6, 8, 10,... ( +2 each time ) - Multiples of 3 = 0, 3, 6, 9, 12, 15,... ( +3 each time ) - Multiples of 4 = 0, 4, 8, 12, 16, 20,... ( +4 each time ) - Multiples of 5 = 0, 5, 10, 15, 20, 25,... ( +5 each time ) - Multiples of 10 = 0, 10, 20, 30, 40, 50,... (+10 each time) If 6 x 4 = 24 we can say 24 is a multiple of 4 & a multiple of 6. Remarks : ZERO is the common multiple of all numbers. Any number is a multiple of itself. All EVEN numbers with units digit 0, 2, 4, 6, 8 are multiples of 2. Numbers with units digit 0 or 5 are multiples of 5. Numbers with units digit 0 are multiples of 10. Any number is a multiple of 2 & 3 is a multiple of 6. Any number is a multiple of 2 & 5 is a multiple of 10. Any number is a multiple of 3 & 5 is a multiple of 15. 40
Can we solve this together? 1) Write : a) All multiples of 2 between 17 and 29.... b) All multiples of 10 less than 56.... c) All multiples of 8 less than 45.... d) All multiples of 3 between 10 and 20. e) All multiples of 5 between 14 and 44. f) All multiples of 2 that are less than 10. 2) Choose the correct answer : a) The number.... is a multiple of all numbers. ( 0, 1, 2, 3 ) b) The number.... is a multiple of 9. ( 19, 40, 50, 18 ) c) The number 35 is a multiple of ( 3, 2, 4, 7 ) d) The number is a multiple of both 3 and 5. (12,18, 24, 30 ) 41
More multiples 3)Circle : a) The multiples of 2 in : [ 17, 12, 36, 23, 60, 15] b) The multiples of 3 in : [ 23, 18, 40, 15, 17, 27] c) The multiples of 5 in : [21, 30, 44, 48, 95,115] d) The multiples of 11 in : [29, 33, 69, 77, 99, 96] 4) Answer the following: a)ahmed has an amount of money between 40 and 50 pounds, that is a multiple of 5. How much is this amount?... b)if the no. of the students in a class lies between 20 & 30 is a multiple of 2 & 3.Find the no. of the students. which c)sally has an amount of sweets between 10 and 20 sweets, that is a multiple of 3 and 5. How many sweets does she have?.. 42
5) Find the common multiple between 2 and 4 less than 14 : 2 0, 2, 4, 6, 8, 10, 12 4 0, _, 4, _, 8,, 12 The common multiples are ( 4, 8, 12 ) 6) Find the common multiple between 5 and 10 less than 40 :..... 7) Find the common multiple between 4and 8 less than 35:..... 43
Polygon The Polygon: It is a group of closed lines formed from three or more line segments. The Vertex : It is the point of intersection of any two adjacent sides. The Diagonal : It is the line segment that joins any two non-consecutive vertices. In any polygon : No. of sides = No. of angles = No. of vertices 44
Polygon Triangle No. of sides No. of vertices No. of angles 3 3 3 Quadrilateral 4 4 4 Pentagon 5 5 5 Hexagon 6 6 6 Heptagon Octagon 7 7 7 8 8 8 45
1)Complete: More polygons 1) A group of closed lines formed from three or more line segments is called.. 2) The vertex of the polygon is the....of any two adjacent sides. 3) The line segment that joins any two non-consecutive vertices is called 4) Numbers of sides of polygon = number of its...... and number of its... 5) The triangle has sides. 6) The 4- sided polygon is called... 46
7) The hexagon is a polygon with..sides. 8) The pentagon is a.... sided polygon. 9) The... is a polygon which has 8 sides. 10) The polygon which has 7 sides is called..... 2)Choose the correct answer: a) The polygon which has four sides is called a. ( hexagon, pentagon, quadrilateral ) b) The hexagon is a polygon with.. sides. ( 5, 6, 4 ) c) The number of vertices of the pentagon =.. ( 5, 7, 3 ) d) The polygon which has 7 sides is called a. ( octagon, heptagon, hexagon ) 47
Polygons having 4 sides, 4 vertices & 4 angles : The Square The Rectangle - 4 equal sides. - 4 right angles. - 2 diagonals. - The 2 diagonals are equal, bisect each other and. The Rhombus - Each 2 opposite sides are equal. - 4 right angles. - 2 diagonals. - The 2 diagonals are equal, bisect each other and not. The Parallelogram - 4 equal sides. - No right angles. - 2 diagonals. - The 2 diagonals are not equal, but bisect each other and. - Each 2 opposite sides are equal and parallel. - No right angles. - 2 diagonals. - The 2 diagonals are not equal, not but bisect each other. The Trapezium It has only 2 opposite sides parallel and not equal. 48
Answer the following 1)Write the name of each polygon : 1 2 3 4 5............... 2) Complete : a) In the parallelogram each two opposite sides are..... and..... b) In the rhombus the four sides are and the four angles are... c) In the square each angle is a... angle. d) Any quadrilateral has... diagonals. e) The trapezium has only 2 sides are... and not..... f) The 2 diagonals of the rhombus are... and not... g) The 2 diagonals of the rectangle are... and not..... 49
3)Choose the correct answer: 1)The measure of any angle of a square equals. a) 45 b) 90 c)150 2)Number of sides of any polygon does not equal number of its. a) diagonal b) angles c) vertices 3)The two diagonals are perpendicular in a) square and rhombus. b) parallelogram and rectangle. c) square and rectangle. 4) The two diagonals in.. and.. are equal in length. a) square and parallelogram. b) square and rhombus. c) rectangle and square. 50
1] Choose the correct answer : 1) The number 3 milliard, 45 million, 473 thousand is written as.. a) 3 045 473 000 b) 4 300 473 000 c) 3 450 473 000 2) The diagonals are equal in length in and a) rectangle rhombus b) square rectangle c) square rhombus 3) The place value of digit 5 in the 5612816 is. a) milliard b) ten thousand c) million 4) The smallest number formed from 7digits from the digits 5,8,4,7,0,2,3 is a) 2 340 578 b) 2 034 578 c) 8 754 320 5) The milliard is the smallest number formed from.digits. a) 10 b) 9 c) 7 6) The two straight lines that never intersect is called. a) parallel b) perpendicular c) intersecting but not 7)Ten million, five hundred seventy two thousand = a) 10 207 200 b) 10 510 072 c) 10 572 000 8)The geometric figure which its four sides are equal in length is called.. a) trapezium b) parallelogram c) rhombus 51
9) 8752013 + 439815 =.. a) 9 191 828 b) 9 567 828 c) 8 191 800 10) 7256312 7056300 = a) 500 014 b) 200 012 c) 200 125 11) 436 x 52 = a) 26 765 b) 22 765 c) 22 672 12) The smallest different 8- digit number is a) 10 234 567 b) 12 345 678 c) 87 654 321 52
2] Put <, > or = : a) 3 milliards..475956432. b) 7423856 5018738..2415117. c) 3 x 14..90 x 2. d) 75 thousand 750 hundred. 3] a) Find the greatest and smallest number formed from 6 digits using the following digits : 7, 0, 2,5, 9, 4 Then calculate the difference between them.. b)sarah bought 24 meters of cloth for L.E 64 each, Find the total price that she paid?.. 53
8 4 = 2 Dividend Divisor Quotient 54
1) Find the quotient ( result of division) a) 684 2 =.. b) 933 3 =.. c) 742 2 =.. d) 2460 20 = 55
2) Choose the correct answer : a) 6 5 8 2 =.. ( 234, 329, 229 ) b) 6126 6 = ( 121, 1021, 1210 ) c) 2 524 4 =.. ( 631, 618, 531 ) 56
Find the quotient a) 5250 50 =.. b) 4880 80 =.. 57
2) Choose the correct answer : a) 7525 25 =. ( 304, 301, 340 ) b) 4896 24 =.. ( 204, 205, 240 ) c) 6464 16 =.. ( 440, 450, 404 ) 58
More and more division 1) Choose the correct answer : a) 7852 26 =.. ( 320, 302, 402 ) b) 7839 39 =.. ( 211, 210, 201 ) c) 64128 32 =.. ( 2 005, 2 400, 2 004 ) 59
2) Put the sign ( > ), ( < ), ( = ) : a) 842 2 42 X 10 b) 9 744 42 9 744 X 42 c) 2 412 12 220 d) 15015 15 16016 16 60
Word problems a) A farmer bought 15 Fadden for 1950 pounds, what is the price of each Fadden?.... b) A hotel has168 rooms, divided equally among a number of floors, each floor has 12 rooms. How many floors are there in the hotel? c) Sarah saved L.E 2065 in 5 months, calculate how much money She saved in each month? 61
d) If 756 pupils in a school are distributed equally among 18 classes, find the number of pupils in each class? e) A runner covers 7380 meters in 6 hours, calculate how long he covers in one hour?.... f) Ahmed bought a TV set for L.E 1 660, he paid L.E 340 and the rest was divided on 24 equal instalments, find the value of each instalment?.. 62
Any number is divisible by another if the remainder of the division is ZERO. 30 3 = 10 & R= 0 Then, 30 is divisible by 3 and by 10 because, 30 is a multiple of 3 and a multiple 10. 30 4 = 7 & R= 2 Then, 30 is not divisible by 4 nor by 7 because, 30 is not a multiple of 4 nor a multiple of 7. Remarks : Any number is divisible by itself. All the multiples of any number are divisible by this number. All EVEN numbers are divisible by 2. Numbers with units digit 0 or 5 are divisible by 5. Numbers with units digit 0 are divisible by 10. A number is divisible by 3 if the Sum of its digits is divisible by 3. 63
Answer the following 1) Choose the correct answer : a) All the multiples of 5 is divisible by ( 2, 5, 10 ) b) 40 is not divisible by... ( 4, 3, 8 ) c) 23 5 = 4, r =3 then 23 is by 5. (divisible, not divisible) d) 35 is divisible by both ( 2&5, 3& 5, 5&7 ) 2)Complete : a) 42 is divisible by 6 because 42 is a...of 6. b) 3 x 5 =...then it is divisible by both of...and... c) 2 x 7 =...then it is a multiple both of...and... d) 25 and 30 are divisible by... 3)Match : a) 12 is divisible by 2 & 5 b) 40 is divisible by 11 & 5 c) 55 is divisible by 3 & 2 64
4)Use these numbers to complete the following : 24, 15, 18, 50, 12, 40, 32 a) Numbers are divisible by 3 are :.... b) Numbers are divisible by 4 are :.... 5)Choose the correct answer: a) The number is said to be divisible by 3 if the sum of its digits is divisible by.. ( 2, 3, 5 ) b) 42 is divisible by ( 2, 5, 4 ) c) 75 is divisible by ( 4, 2, 5 ) d) 1 401 is divisible by.. ( 6, 3, 5 ) 6) Circle the numbers which are : a) Divisible by 2 ( 15, 18, 102, 5 224 ) b) Divisible by 3 ( 33, 1 256, 732, 1 278 ) c) Divisible by 5 ( 125, 3 123, 1 460, 330 ) d) Divisible by 2, 3 and 5 ( 165, 600, 630, 735 ) 65
A B It is a polygon having 3 sides, 3 vertices & 3 angles. m ( A ) + m ( B ) + m ( C ) = 180. C The sum of the measures of the interior angles of any triangle = 180. Types Of Triangles a)according to the measure of ANGLES : Right-angled Acute-angled Obtuse-angled X A D Y Z B C E F It has one right angle and 2 acute angles. Remarks : The three angles are acute angles. It has one obtuse angle and 2 acute angles. Any triangle has at least two acute angles. In the right-angled, the sum of the two acute angles is 90. 66
b) According to the length of SIDES : Equilateral Isosceles Scalene A X D B C Y Z E F - 3 sides are equal in length. AB = BC = CA - 3 angles are equal in measure. - each angle = 60. - 2 sides are equal in length. XY = XZ - 2 angles are equal in measure. m Y ) = m ( Z ) - 3 sides are different in length. AB BC CA - 3 angles are different in measure. Remarks : In any the sum of the length of any two sides is greater than the length of the third side We can draw a triangle if : given the lengths of 2 sides and measure of 1 angle OR given the measures of 2 angles and the length of 1 side 67
Find the measure of the third angle of each of the following triangles: m ( < C ) =. m ( < M ) =. m ( < T ) =. m ( < Q ) =. m ( < D ) =. m ( < K ) =. 68
1) Complete a) The triangle is a...that has...sides and...angles. b) In any triangle the sum of its angles =... c) Any triangle there are at least two...angles. d) In the right angled, the sum of the 2 acute angles =... e) We can draw the triangle given...or...... f) When the three sides of the triangle are equal in length it is called an.... triangle. g) The triangle whose sides length are 5cm, 5cm and 8cm is a/an.... triangle. h) If one angle of a triangle is an obtuse angle then it is called a/an.... triangle. i) The with angles 70,20 and 90 is called.... j) In ABC, if m( A) = m( B)=50, then m( C) =... k) In XYZ, if m( X )= m( Y )= m( Z ) then its type is.... l) The obtuse angled triangle has... acute angles. m) The whose sides are 3 cm,4 cm and 5 cm is.... 69
2) Choose the correct answer : 1) m( E) = 30, m( F) = 40 and m( G) = 110, then this is (a-an) angled triangle. a) Right b) obtuse c) acute 2) m( S) = 51, m( T) = 67 and m(u) = 62, then this is (a-an) angled triangle. a) Right b) obtuse c) acute 3) If AB = 6c.m, BC = 7c.m and CA = 6c.m, then this is (a-an). triangle. a) Equilateral b) isosceles c) scalene 4) If XY = 4c.m,YZ = 8c.m and ZX = 5c.m, then this is (a-an).. triangle. a)scalene b) isosceles c) equilateral 5) If NO = 3c.m, OR = 3c.m and RN = 3c.m, then this is (a-an) triangle. a) Isosceles b) equilateral c) scalene 70
Draw a) The triangle XYZ in which ZX = 10c.m, m( Z)= 60 and m( X) = 30, then find the length of YZ and the type of the triangle according to the lengths of its sides. b)the LMN in which LM = 6cm and m( L) = m( M) =45. Find: a) The length of NL and NM. b) Without using the protractor m( N). c)the type of the triangle according to the measures of its angles and the lengths of its sides. 71
2 x 3 = 6 Factor Factor Product To Find the factors of 6 : 1 X 6 2 X 3 then, 6 has 4 factors which are ( 1, 2, 3, 6 ) To Find the factors of 16 : 1 X 16 2 X 8 4 X 4 then, 16 has 5 factors which are ( 1, 2, 4, 8, 16 ) don t repeat 4 Remarks : One is a factor of all numbers. Each number is a factor of itself. The largest factor of any number is the number itself. One is the only number that has one factor. The numbers that have only 3 factors are 4, 9, 49 25 72
Answer the following 1) Find the factors of each of the following : a) 4... b) 7... c) 15... d) 14... e) 27... 73
2) Put ( ) or (x) : a) 3 is factor of 72 ( ) b) 2 is factor of 34 ( ) c) 3, 2 are factors of 32 ( ) d) 18 has 6 factors ( ) 3) Find the factors of each of the following : a) 6... b) 5... c) 12... d) 24... 74
3) Choose the correct answer : a) 5 is a factor of. ( 54, 50, 53 ) b) 3 is a factor of. ( 53, 163, 354 ) c) 2 is a factor of. ( 21, 201, 210 ) d) 2 and 5 are the factors of ( 601, 610, 106 ) e) 2 and 3 are the factors of ( 124, 224, 126 ) f) The number 11 has factors. ( 2, 3, 5 ) g) The number 12 has factors. ( 6, 9, 8 ) h).. is a factor of all numbers. ( 0, 1, 2 ) i) is a factor of 20 ( 5, 8, 40 ) j). Is a factor of 9 ( 0, 3, 18 ) 4) Write: a) Four numbers that have only 3 factors... b)the two 1-digit numbers which have 3 factors... 75
5) Find the common factor between 6 and 8 : The factors of 6: 1 X 6 The factors of 8: 1 X 8 2 X 4 2 x 3 The factors of 6 are ( 1, 2, 3, 6 ) The factors of 8 are ( 1, 2, _, _, 4, 8 ) The common factor is ( 2 ) 6) Find the common factor between 6 and 12 :.......... 76
Factors of : 2 = 1 x 2, 3 = 1 x 3, 5 = 1 x 5, 7 = 1 x 7 Ex : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37... etc. are called ʺPrime Numbersʺ. Remarks : Prime number has 2 factors only ( 1 and the number itself ). Zero is not prime number because all numbers are factors of it One is not prime number because it has 1 factor only. 2 is the smallest prime number. 2 is the only even prime number. All prime numbers are odd except 2. 3 is the smallest odd prime number. The only prime number between 90 and 100 is 97. Not all odd numbers are prime (ex. 9, 15, 21, ) 77
Can you solve this? 1) Complete : a) The smallest prime number is... b) One is not a prime number because... c) The only even prime number is..... d)... is a number that has only one factor. e)...,..., are numbers that each of them has 3 factors. f) All prime numbers are...except... 2) Put ( ) or (x): a) Zero is a prime number. ( ) b) All prime numbers are even numbers. ( ) c) 2 is the only even prime number. ( ) d) All prime numbers are odd numbers. ( ) e) 97 is only the prime number between 90 and 100. ( ) f) 1 is the smallest prime number. ( ) 78
3)Write : a) The prime numbers less than 30.... b) Write all non-prime numbers between 5 and 23.... 4)Choose the correct answer : a).. is a prime number. ( 16, 11, 21 ) b) The smallest prime number is ( 0, 1, 2 ) c) The smallest odd prime number is. ( 1, 2, 3 ) d) The prime number between 20 and 25 is.. ( 21, 23, 24 ) e).is not a prime number. ( 1, 3, 5 ) f) The number 108 is divisible by the two prime numbers 3 and. ( 9, 7, 2 ) 79
1)Factorize each number to its prime numbers : a) 12 2 b) 16 c) 24 6 2 3 3 1 12 = 2 x 2 x 3 16 =... 24 =... d) 21 e) 25 f) 18 21 =... 25 =... 18 =. 80
Factorize 12 and 16, then find their H.C.F and L.C.M. 12 2 16 2 6 2 8 2 3 3 4 2 1 2 2 1 12 = 2 x 2 x 3 16 = 2 x 2 x _ x 2 x 2 H.C.F = 2 x 2 = 4. L.C.M = 2 x 2 x 3 x 2 x 2 = 48 1) Find the H.C.F and the L.C.M. a) 6 8 b) 8 12 6 =... 8 =... 8 =... 12=... H.C.F =... H.C.F =... L.C.M =... L.C.M = 81
c) 16 20 d) 18 27 16 =... 1 8 =... 20 =... 27 =... H.C.F =... H.C.F =... L.C.M =... L.C.M =... e) 6 12 f) 24 30 6 =... 24 =... 12 =... 30 =... H.C.F =... H.C.F =... L.C.M =.. L.C.M =... 82
1) Complete: a) The quadrilateral whose 4 sides are equal in length and it has 4 right angles is called... b) All the... of the square are equal in measure. c) The measure of each angle of the square =..... d) The diagonals of the square are...,... and... e) All the... of the square are equal in length. f) In the square all angles are...angles. 2) Draw : A square ABCD in which AB = 4 cm. 83
A) The Perimeter of any polygon equals the sum of its sides length. Since, The Square has 4 equal sides then its perimeter = S + S + S + S Therefore, We can deduce the following Rule : Perimeter of the square = Side x 4 P = S x 4 B ) The Area of any geometrical figure is the no. of equal parts forming that figure. Area of the square = Side x Side A = S x S 84
1) Find: Can you solve this a) The perimeter of a square whose side length is 6 cm.... b) The perimeter of a square whose side length is 4 cm.... c) The area of a square whose side length is 8 cm.... d) The area of a square whose side length is 5 c.m. 2) Choose the correct answer : a) The perimeter of a square whose side length is 5 is. ( 25, 20, 24 ) b) The perimeter of a square whose side length is 7 is. ( 28, 30, 24 ) c) The area of a square whose side length is 3 cm.. ( 12, 9, 4 ) d) The area of a square whose side length is 8 cm.. 85 ( 32, 64, 24 )
3)Find the perimeter and the area of each of the following : a) A square whose side length is 2 cm. Perimeter =. Area = b) A square whose side length is 5 cm. Perimeter =. Area = c) A square whose side length is 6 cm. Perimeter =. Area = d) A square of side length 3 cm. Perimeter =. Area = 86
I can help you to draw a rectangle 1) Complete : a) In the rectangle the diagonals are.. in length. b) All the...of the rectangle are equal in measure. c) The measure of each angle of the rectangle =.....º d) The diagonals of the rectangle are....,... and... e) In the rectangle, all angles are...angles. 2) Draw : A rectangle XYZL with length 6 cm and width 4 cm. Then join XZ and YL. 87
A ) The Perimeter of any polygon equals the sum of its sides length. Since, The Rectangle has 2 equal lengths ( L ) and 2 equal widths ( W ) then its perimeter = L + W + L + W Therefore, We can deduce the following Rule : Perimeter = (L + W) x 2 B ) The Area of any geometrical figure is the no. of equal parts forming that figure. Area = L x W 88
1)Find the perimeter and the area of each of the following : a) A rectangle whose length 5cm and width 2cm. Perimeter =. Area = b) A rectangle with dimension 6cm and 4 cm. Perimeter =. Area = c) A rectangle whose length 5 cm and width 3 cm. Perimeter =. Area = d) A rectangle with dimension 3 cm and 7cm. Perimeter =. Area = 89
1) Which is greater the area of a square with side length 5 cm or a rectangle with dimensions 4 cm and 6 cm. 2) Which is greater the perimeter of a rectangle with dimensions 7 cm and 3 c.m or a square with side length 4 cm 3) Find the area of the shaded part in the given figure: The area of the rectangle = The area of the square= The area of the shaded part = 90
1) Which is greater the area of a square with side length 6 c.m or a rectangle with dimensions 6 c.m and 5 c.m. 2) Which is greater the perimeter of a rectangle with dimensions 4 cm and 2 cm or a square with side length 3 cm 3) Find the area of the shaded part in the given figure: The area of the rectangle =. The area of the square=. The area of the shaded part = 91
1) Complete : a) 4 dm =... cm =... mm. b)... dm = 20 cm =... mm. c) 4 km =... m =... dm. d) 6 m =... cm =... dm. e) 8cm =... mm. f) 45 km =... m =... cm. g) 25 dm =... cm =... mm. h) 450 cm =... dm. i) 2300 m =... dm. j) 8 km =... m =...dm 92
2) Complete: a) 5 km =.. m b) 700 mm = dm c) 90 m =.. cm d) 450 cm =.. dm e) 87 dm =. mm f) 250 000 m =.. km g) 3 m = dm =. cm h). Km = 1000 m =. Cm i) 530 000 dm =. Km 93
2) Choose 1) 5 m =.cm a) 5 000 b) 500 c) 50 000 d) 500 000 2) 6 m = dm a) 60 b) 600 c) 6 000 d) 60 000 3) 9 m = mm a) 900 b) 90 000 c) 9 000 d) 90 4). Km = 4 000 m a) 400 b) 4 c) 4 000 d) 40 000 5) 800 000 dm =.. km a) 8 b) 800 c) 80 d) 8 000 6) 4 km =.cm a) 4 000 b) 40 000 c) 400 000 d) 40 7) mm = 50 dm a) 5 000 b) 500 c) 5 d) 50 000 94
Exam (1) 1)Choose the correct answer : 1)The smallest prime number is.. a) 0 b) 1 c) 2 d) 3 2) The numbers 3, 5, 7 and 9 is called number a) even b) prime c) odd d) common 3) The number. Is divisible by each of 2 and 5 a) 72 b) 100 c) 25 d) 28 4) The quadrilateral whose four sides are equal in length is. a) trapezium b) rectangle c) rhombus d) parallelogram 5) If 756 pupils in a school are distributed equally among 18 classes Find the number of each class by.. a) Addition b) division c) multiplication d) subtraction 6) The smallest number formed from 8 digits is a) 10 000 000 b) 10 234 567 c) 10 000 001 95
7) If the measure of the angles of the triangle are 60, 40 and 80, then the triangle is angled a) Right b) obtuse c) acute d) straight 8) 2 dm = cm a) 2 b) 200 c) 20 d) 2 000 9) 345 15 =.. a) 23 b) 32 c) 24 d) 25 10) The common factor of all numbers is a) 1 b) 0 c) 2 d) 3 11) H.C.F of 12 and 18 is.. a) 12 b) 6 c) 36 d) 2 12) 1 024 32 =. a) 32 b) 34 c) 42 d) 24 96
13) The perimeter of a square of side length 5 cm is..cm a) 20 b) 25 c) 10 d) 23 14). Is a common factor of all numbers a) 0 b) 1 c) 2 d) 3 15) 8 Km = m a) 80 b) 800 c) 80 000 d) 8 000 16) The triangle whose side lengths are 3cm,7cm and 5cm is... triangle. a) Scalene b) equilateral c) isosceles d) acute 17) The rectangle whose dimensions are 7cm and 3cm, then its perimeter is cm a) 7 b) 17 c) 20 d) 15 18) The L.C.M of 6 and 9 is. a) 15 b) 12 c) 27 d) 18 97
19) 288 x 12. 288 12 a) > b) = c) d) > 20) Number of vertices in the hexagon is a) 5 b) 6 c) 7 21) The diagonals of rectangle are and not.. a) equal perpendicular b) perpendicular equal 22) The place value of the digit 8 in the number 147385 is a) million b) ten c) hundred 23) 32605108.. 23511998. a) > b) < c) = 24) The polygon that has 5 sides is called. a) octagon b)hexagon c) pentagon 25) 950000 324067 = a) 324076 b) 625933 c) 675933 2) Complete: a) All factors of 12 are.,..,,, and b) The L.C.M of the numbers 8 and 12 is 98
c).. is a common factor of all numbers. d) The number is divisible by 5 if its unit digit is or e) The area of the square whose side length is 6 cm =. 3) a) Draw XYZ in which XY = 5cm, m( X) = 45 and m( Y) = 45, Then 1) find m( Z) 2)The type of the triangle according to the measures of its angles? b) A hotel contains 192 rooms divided equally by a number of floors, each floor contains 16 room. How many floors are there in this hotel?...... 99
4]Use the opposite figure, then complete : AB AB XY... BC ( or // )... YZ ( or // )... BC ( or // ) AY intersects with BZ at the point... YC intersects with BX at the point... 100