Demostration of mathematics concepts using division
- 1. TABLE OF CONTENTS 02 03 Division of Numbers(Grade 3) Fractional Numbers(Grade 4) Patterns in square numbers and triangular numbers(Grade 5) 01
- 3. Topics Covered(Division of Numbers) 1. What is Division? 2. Division is repeated Subtraction 3. Exercise 4. Division on Number line 5. Long Division 6. Dividing 3-digit number 7. Dividing 4-digit number
- 4. What is Division? Division means equal sharing or equal grouping Symbol for Division is ÷
- 6. Equal Sharing Riya Rahul 8 ÷2=4 8 divided by 2 is equal to 4
- 7. Equal Grouping Group of 2 Apples Group of 2 Apples Group of 2 Apples 6 ÷2=3 6 divided by 2 is equal to 3
- 8. Division is repeated subtraction Group of 2 Apples Group of 2 Apples Group of 2 Apples 6 -2=4 4 -2=2 2 -2=0
- 9. Division is repeated Subtraction Instead of subtracting 2 repeatedly three times ,we can write 6÷2=3
- 10. Division Terms 6 ÷ 2 = 3 Dividend Divisor Quotient
- 11. Exercise Share the following equally and write their division fact a) 6 carrots among 3 rabbits 6÷3=2 b) 10 mangoes in 2 baskets 10÷2=5
- 12. Exercise Write the dividend, divisor and quotient for each division fact Division Fact Dividend Divisor Quotient 8 ÷ 2 = 4 8 2 4 12 ÷ 4 = 3 12 4 3 30 ÷ 5 = 6 30 5 6
- 13. Division on number line Find 9 ÷ 3 on number line 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 6 3 0 9 ÷ 3 = 3
- 14. Division on number line Find 10 ÷ 5 on number line 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 0 5 10 ÷ 5 = 2
- 15. Long Division √10 2 5 10 - 0 2 X 1 = 2 2 X 2 = 4 2 X 3 = 6 2 X 4 = 8 2 X 5 = 10 2 X 6 = 12 2 X 7 = 14 2 X 8 = 16 2 X 9 = 18 2 X 10 = 20
- 16. Find quotient by long division √36 5 7 35 - 1 5 X 1 = 5 5 X 2 = 10 5 X 3 = 15 5 X 4 = 20 5 X 5 = 25 5 X 6 = 30 5 X 7 = 35 5 X 8 = 40 5 X 9 = 45 5 X 10 = 50
- 17. Dividing 3- digit number Divide 312 by 4 √312 4 7 28 - 3 4 X 1 = 4 4 X 2 = 8 4 X 3 = 12 4 X 4 = 16 4 X 5 = 20 4 X 6 = 24 4 X 7 = 28 4 X 8 = 32 4 X 9 = 36 4 X 10 = 40 2 32 - 8 0
- 18. Dividing 4- digit number Divide 4137 by 2 √4137 2 2 4 - 01 0 - 0 13 12 - 17 -16 1 2 X 1 = 2 2 X 2 = 4 2 X 3 = 6 2 X 4 = 8 2 X 5 = 10 2 X 6 = 12 2 X 7 = 14 2 X 8 = 16 2 X 9 = 18 2 X 10 = 20 68
- 20. Topics Covered(Fractional Numbers) 1. What is Fraction? 2. Equivalent Fractions 3. Simplifying fractions in simplest form 4. Like/Unlike, Proper, Improper and Mixed Fractions 5. Comparing Fractions
- 21. What is Fraction? Fractions means a part of whole For example: Consider an apple as whole If you give half to your sister then half remains with you and each part is called fraction
- 22. What is Fraction? Fraction is written in the form of Numerator Denominator Number of equal parts taken into consideration for a particular case Total number of equal parts the whole is divided into
- 23. What is Fraction? Half : When the whole is divided into two equal parts, each part is called half Half is written as ½ One Third: When the whole is divided into three equal parts, each part is called One- Third and written as 1/3 One Fourth: When the whole is divided into four equal parts, each part is called One Fourth and written as 1/4
- 24. Exercise Write the fraction for shaded part Answer is 1/3
- 25. Exercise Write the fraction for shaded part Answer is 1/4
- 26. Equivalent Fractions Fractions which represent same portion of whole are called equivalent fractions 1/2 2/4 3/6
- 27. What does simplifying the Fractions means? Simplifying the fraction means reducing the fraction to its lowest form. How to simplify the Fractions Divide numerator and denominator of fraction by common factors till the fraction is in lowest form
- 28. Example 21/63 (21÷3)/(63÷3) It is further reduced by dividing both numerator and denominator by 3 So we get 7÷21 which is further reduced to 1/3
- 29. Like,Unlike Fractions Fractions which have same denominator are called like Fractions Example 1/7 , 2/7 , 5/7 are Like fractions Fractions which have different denominator are called unlike Fractions Example 1/7 , 2/8 , 5/9 are unlike fractions
- 30. How to compare Like Fractions Since their denominators are same,we only need to compare numerators Example 2/7 5/7 2/7 < 5/7
- 31. How to compare Unlike Fractions Since their denominators are different , use cross multiplication technique to compare Example 2/5 3/8 2x8 3x5 16 15 16>15 So 2/5>3/8
- 32. Proper and Improper Fractions Mixed Fraction Fraction which have numerator less than denominator are called Proper Fractions Example 2/5 4/7 9/11 Fraction which have numerator greater than denominator are called Improper Fractions Example 6/5 9/7 16/11 Fractions which have two parts – a whole number followed by proper fraction are called mixed fraction Example 2 1 7 Rule to solve mixed fraction (Divisor x Quotient)+Remainder/Divisor
- 33. PATTERNS IN SQUARE NUMBERS AND TRIANGULAR NUMBERS
- 34. Square Number A square number can be obtained by multiplying the number by itself 1x1=1 2x2=4 3x3=9 4x4=16…..
- 35. Pattern of Square Number We can understand pattern of square number by using dots 1x1=1 2x2=4 3x3=9
- 36. Sum of Consecutive Odd numbers to get Square Number This is another way to create pattern of square number 1 1+3=2x2 1+3+5=3x3
- 37. Sum of Consecutive Odd numbers to get Square Number Write the sum without adding Odd Numbers Product Sum 1+3+5+7+9 5x5 25 1+3+5+7+9+11 6x6 36 1+3+5+7+9+11+13 7x7 49
- 38. How to find difference of Square Numbers 1) 3x3-2x2 9-4=5 2) 129x129-128x128 16641-16384 257 Lets see shortcut method for above examples 1) 3x3-2x2 Take first number ie 3 + take first number ie 2 3+2=5 2)129x129-128x128 129+128=257
- 39. Exercise Find the next square number a) 121 121=11x11 So, next square number is 12x12=144 b) 256 256=16x16 So, next square number is 17x17=289
- 40. Exercise Express the following square numbers as the sum of consecutive odd numbers 81 81=9x9 So,81 is the sum of first 9 consecutive odd numbers 1+3+5+7+9+11+13+15+17
- 41. Exercise If 4 is first square number, which is the 5th one? 1st 2x2=4 2nd 3x3=9 3rd 4x4=16 4th 5x5=25 5th 6x6=36
- 42. Triangular Number The triangular number pattern is the representation of the numbers in the form of equilateral triangle
- 43. Pattern of Triangular Number We can understand pattern of triangular number by using dots 1 3 6 1st Triangular number=1 2nd Triangular number=1+2=3 3rd Triangular number=1+2+3=6….
- 44. Exercise Find the 5th Triangular number (5x6)/2=15(shortcut method) 1+2+3+4+5 =15(Long method) Find the 11th Triangular number (11x12)/2=66(shortcut method) 1+2+3+4+5+6+7+8+9+10+11=66(Long method)
- 45. Exercise Find the next triangular number 10,15,____ First find the difference 15-10=5 Next add 1 to the difference answer Next add 6 to 15 to get next triangular number 15+6=21 final answer
- 46. Exercise If 3 is the first triangular number, which the 5th one? 1st triangular number 1+2=3 2nd triangular number 1+2+3=6 3rd triangular number 1+2+3+4=10 4th triangular number 1+2+3+4+5=15 5th triangular number 1+2+3+4+5+6=21
- 47. Exercise Name two numbers which are square as well as triangular numbers 1,3,6,10,15,21,28,36,45,55…. 1 is triangular as well as square number 36 is triangular as well as square number
- 48. THANK YOU