WELCOME TO MATHEMATICS WORKSHOP

LET’S TEACH MATHS WITH PASSION!!! A GENERAL ILLUSION-----MATHS IS VERY TOUGH…. LET’S TEACH MATHS WITH PASSION!!!

Let’s Make Teaching Maths Easier……… By Mr. T.Satya Prasad H.O.D.MATHEMATICS

FEW TIPS TO MAKE TEACHING MATHS EASIER:

1.LET’S SHOW THE INVOLVEMENT IN TEACHING 2.ENSURE THAT WHAT YOU HAVE COMMUNICATED TO THE STUDENTS IS EXACTLY WHAT YOU REALLY WANTED TO COMMUNICATE TO THEM. 3.MAKE YOUR CONCEPT CLEAR BEFORE YOU TEACH . 4.DIFFICULTY OF THE PARTICULAR CHAPTER ALSO DEPENDS ON YOUR TEACHING. INVENT NEW WAYS OF MAKING THINGS CLEAR RATHER THAN USING CONVENTIONAL EXAMPLES ONLY. LETS PUT A PAUSE TO FUNDAS……………..

LETS BEGIN WITH… DIVISION

Divisibility DIVISIBILITY RULES Rules

Divisibility Rules Helps you learn shortcuts to tell when a number can be divided by another number with NO remainder.

What is Divisibility? Divisibility means that after dividing, there will be no remainder.

Divisibility by 2 A number is divisible by 2 if the number is even. 18 ÷ 2 = 9 22 ÷ 2 = 11 (Notice that both of these numbers are even.) 21 ÷ 2 = 10 R1 (Not an even number.)

Are these numbers divisible by 2? 127 (Not an even number) 937 4678

Divisibility by 3 A number is divisible by 3 if the sum of the digits is divisible by 3. Is the number 135 divisible by 3? Add the digits: 1 + 3 + 5 = 9 Yes, 135 is divisible by 3 because the sum of the digits is divisible by 3.

Divisibility by 5 A number is divisible by 5 if it ends in 0 or 5. 25 ÷ 5 = 5 23 ÷ 5 = 4 R3

Divisibility by 6 A number is divisible by 6 if it is divisible by both 2 and 3. Is 42 divisible by 6? Is 51 divisible by 6?

Divisibility by A number is divisible by 10 if it ends in 0. 30 ÷ 10 = 3 340 ÷ 10 = 34 67 ÷ 10 = 6 R7 784 ÷ 10 =78 R4

Divisibility By: 2 5 10 1825 346 510 1108

Divisibility by 9 A number is divisible by 9 if the sum of its digits is divisible by 9. 369 is divisible by 9 because 3 + 6 + 9 =18 1 + 8 = 9 AND 9 is divisible by 9.

356,821 The divisibility rules can help YOU !!! Can you tell by just looking at this number if it is divisible by 2? by 5? by 10? by 3 ? by 9? By 6? The divisibility rules can help YOU !!!

After All…DIVISIBILITY Rules!!

Lets move on to… LONG Division

Long Division Before we start this let’s introduce this family somewhat close to division family…… DAD—1.DIVIDE MOM---2.MULTIPLY SIS---SUBTRACT REMO----REPEAT OR REMAINDER BROTHER----------- --BRING DOWN

DAD—1.DIVIDE Step 1 in Long Division 4 1. Divide 2 ) 9 4 7 Divide 2 into first number in the dividend. Think how many 2’s will fit into 9. How many 2’s will go into 9? Write that number directly above the number you divided into.

2 ) 9 4 7 4 8 Step 2 in Long Division 2. Multiply 2 x 4 = 8 MOM---2.MULTIPLY 4 2. Multiply 2 ) 9 4 7 8 Multiply the divisor times the first number in the quotient. 2 x 4 = 8 Write your answer directly under the 9 or the number you just divided into.

2 ) 9 4 7 4 8 1 Step 3 in Long Division 3. Subtract SIS---SUBTRACT 4 3. Subtract 2 ) 9 4 7 8 Draw a line under the 8. Write a subtraction sign next to the 8. 1 Subtract 8 from 9. Write your answer directly below the 8.

2 ) 9 4 7 4 8 1 4 Step 4 in Long Division 4. Bring down Brother Go to the next number in the dividend to the right of the 9. 1 4 Write an arrow under the 4. Bring the 4 down next to the 1.

Step 5 in Long Division REMO----REPEAT OR REMAINDER 4 2 ) 9 4 7 8 This is where you decide whether you repeat the 5 steps of division. 1 4 If your divisor can divide into your new number, 14, or if you have numbers in the dividend that have not been brought down, you repeat the 5 steps of division.

2 ) 9 4 7 4 7 8 1 4 Step 1 in Long Division 1. Divide DAD—1.DIVIDE Step 1 in Long Division 4 7 1. Divide 2 ) 9 4 7 8 Divide 2 into your new number, 14. 1 4 Place your answer directly above the 4 in your quotient.

2 ) 9 4 7 4 7 8 1 4 1 4 Step 2 in Long Division 2. Multiply Mom MOM---2.MULTIPLY Step 2 in Long Division 4 7 2. Multiply 2 ) 9 4 7 Mom 8 Multiply your divisor, 2, with your new number in the quotient, 7. 1 4 1 4 Place your answer directly under the 14.

2 ) 9 4 7 4 7 8 1 4 1 4 Step 3 in Long Division 3. Subtract SIS---SUBTRACT Step 3 in Long Division 4 7 3. Subtract 2 ) 9 4 7 8 Draw a line under the bottom 14. 1 4 Draw a subtraction sign. 1 4 Subtract & place answer under the line.

2 ) 9 4 7 4 7 8 1 4 1 4 7 Step 4 in Long Division 4. Bring down Brother 8 Put an arrow under the next number, 7, in the dividend. 1 4 1 4 Bring the 7 down next to the 0. 7

Step 5 in Long Division REMO----REPEAT OR REMAINDER 4 7 2 ) 9 4 7 8 If the 2 will divide into your new number, 7, then repeat the steps of division. 1 4 1 4 7

2 ) 9 4 7 4 7 3 8 1 4 1 4 7 Step 1 in Long Division 1. Divide DAD—1.DIVIDE Step 1 in Long Division 4 7 3 1. Divide 2 ) 9 4 7 8 Divide your divisor, 2, into your new number, 7. 1 4 Place your answer in the quotient next to the 7. 1 4 7

2 ) 9 4 7 4 7 3 8 1 4 1 4 7 6 Step 2 in Long Division 2. Multiply Mom MOM---2.MULTIPLY 4 7 3 2. Multiply 2 ) 9 4 7 8 Mom 1 4 Multiply your divisor, 2, by your new number in the quotient, 3. 1 4 7 Place your answer under the number you brought down, 7. 6

2 ) 9 4 7 4 7 3 8 1 4 1 4 7 6 1 Step 3 in Long Division 3. Subtract SIS---SUBTRACT Step 3 in Long Division 4 7 3 3. Subtract 2 ) 9 4 7 8 Sister 1 4 Draw a line under the number 6. 1 4 7 Place your subtraction sign. 6 Subtract & put your answer directly under the 6. 1

2 ) 9 4 7 4 7 3 8 1 4 1 4 7 6 1 Step 4 in Long Division 4. Bring down Brother 1 4 Look at your dividend to see if there are any more numbers to bring down. 1 4 7 6 If not, move to step 5. 1

2 ) 9 4 7 4 7 3 8 1 4 1 4 7 6 1 Step 5 in Long Division R1 REMO----REPEAT OR REMAINDER 4 7 3 R1 2 ) 9 4 7 8 1 4 Since there are no more numbers to bring down & 2 will not divide into 1, you do not repeat the steps of division. 1 4 7 6 1 The number left over, 1, becomes the remainder.

FINALLY THIS IS HOW IT IS!!!!! 4 7 3 R1 2 ) 9 4 7 8 1 4 1 4 7 6 1

LETS MOVE ON TO….. 2 DIGIT DIVISION

Step 1 in 2 Digit Long Division DAD 4 1. Divide 2 1) 9 4 8 Divide 21 into first number in the dividend. How many 20’s will go into 90? 21 will not go into 9 so you look at 94. Round off 21 and 94 in your head. Now divide 20 into 90 & put your answer above the 4.

Step 2 in 2 Digit Long Division 4 2. Multiply 2 1) 9 4 8 Mom 8 4 Multiply the divisor times the first number in your quotient. 21 x4 84 Write your answer directly under the 94 or the number you just divided into.

Step 3 in 2 Digit Long Division SIS---SUBTRACT Step 3 in 2 Digit Long Division 4 3. Subtract 2 1) 9 4 8 8 4 Draw a line under the 84. Write a subtraction sign next to the 84. 1 Subtract 84 from 94. Write your answer directly below the 84.

Step 4 in 2 Digit Long Division 4. Bring down 2 1) 9 4 8 Brother 8 4 Go to the next number in the dividend to the right of the 4. 1 8 Write an arrow under that number. Bring the 8 down next to the 10.

Step 5 in 2 Digit Long Division REMO----REPEAT OR REMAINDER 4 2 1) 9 4 8 8 4 This is where you decide whether you repeat the 5 steps of division. 1 8 If your divisor can divide into your new number, 108, or if you have numbers in the dividend that have not been brought down, you repeat the 5 steps of division.

Step 1 in 2 Digit Long Division DAD—1.DIVIDE 4 5 2 1) 9 4 8 8 4 Divide 21 into your new number, 108. 1 8 Round 21 and 108 off in your head. Divide 20 into 110 Place your answer directly above the 8 in your quotient.

Step 2 in 2 Digit Long Division MOM---2.MULTIPLY 4 5 2 1) 9 4 8 8 4 Multiply your divisor, 21, with your new number in the quotient, 5. 1 8 1 5 Place your answer directly under the 108.

Step 3 in 2 Digit Long Division SIS---SUBTRACT 4 5 2 1) 9 4 8 8 4 Draw a line under the bottom number, 105. 1 8 Draw a subtraction sign. 1 5 Subtract & place answer under the line. 3

Step 4 in 2 Digit Long Division 5 4. Bring down 2 1) 9 4 8 8 4 Since there is nothing to bring down, go to step five. 1 8 1 5 3

Step 5 in 2 Digit Long Division 4 5 R3 5. Repeat or Remainder 2 1) 9 4 8 8 4 If the 21 will not divide into your new number, 3, & there is nothing to bring down, you are done. 1 8 1 5 3 Write your left over 3 as the remainder next to the 5.

THIS IS HOW IT LOOKS… 4 5 R3 2 1) 9 4 8 8 4 1 8 1 5 3

A DIVISION TEASER……

2 ) 8 0 7 4 Step 1 in Long Division 1. Divide DAD—1.DIVIDE Step 1 in Long Division 4 1. Divide 2 ) 8 0 7 Divide 2 into first number in the dividend. How many 2’s will go into 8? Think how many 2’s will fit into 8. Write that number directly above the number you divided into.

2 ) 8 0 7 4 8 Step 2 in Long Division 2. Multiply 2 x 4 = 8 MOM---2.MULTIPLY Step 2 in Long Division 4 2. Multiply 2 ) 8 0 7 8 Multiply the divisor times the first number in the quotient. 2 x 4 = 8 Write your answer directly under the 8 or the number you just divided into.

2 ) 8 0 7 4 8 Step 3 in Long Division 3. Subtract SIS---SUBTRACT Step 3 in Long Division 4 3. Subtract 2 ) 8 0 7 8 Draw a line under the 8. Write a subtraction sign next to the 8. Subtract 8 from 8. Write your answer directly below the 8.

2 ) 8 0 7 4 8 Step 4 in Long Division 4. Bring down Go to the next number in the dividend to the right of the 8. Write an arrow under the 0. Bring the 0 down next to the 0.

Step 5 in Long Division REMO----REPEAT OR REMAINDER 4 2 ) 8 0 7 8 This is where you decide whether you repeat the 5 steps of division. If your divisor can divide into your new number, 00, or if you have numbers in the dividend that have not been brought down, you repeat the 5 steps of division.

2 ) 8 0 7 4 8 Step 1 in Long Division 1. Divide DAD—1.DIVIDE 4 1. Divide 2 ) 8 0 7 8 Divide 2 into your new number, 00. Place your answer directly above the 0 in your quotient.

2 ) 8 0 7 4 8 Step 2 in Long Division 2. Multiply MOM---2.MULTIPLY Step 2 in Long Division 4 2. Multiply 2 ) 8 0 7 8 Multiply your divisor, 2, with your new number in the quotient, 0. Place your answer directly under the 00.

2 ) 8 0 7 4 8 Step 3 in Long Division 3. Subtract SIS---SUBTRACT Step 3 in Long Division 4 3. Subtract 2 ) 8 0 7 8 Draw a line under the bottom 14. Draw a subtraction sign. Subtract & place answer under the line.

2 ) 8 0 7 4 8 7 Step 4 in Long Division Put an arrow under BROTHER----------- --BRING DOWN Step 4 in Long Division 4 2 ) 8 0 7 8 Put an arrow under the next number, 7, in the dividend. Bring the 7 down next to the 0. 7

Step 5 in Long Division REMO----REPEAT OR REMAINDER 4 2 ) 8 0 7 8 If the 2 will divide into your new number, 7, then repeat the steps of division. 7

2 ) 8 0 7 4 3 8 7 Step 1 in Long Division 1. Divide DAD—1.DIVIDE Step 1 in Long Division 4 3 1. Divide 2 ) 8 0 7 8 Divide your divisor, 2, into your new number, 7. Place your answer in the quotient next to the 7. 7

2 ) 8 0 7 4 3 8 7 6 Step 2 in Long Division 2. Multiply MOM---2.MULTIPLY 4 3 2. Multiply 2 ) 8 0 7 8 Multiply your divisor, 2, by your new number in the quotient, 3. 7 Place your answer under the number you brought down, 7. 6

2 ) 8 0 7 4 3 8 7 6 1 Step 3 in Long Division 3. Subtract 3 3. Subtract 2 ) 8 0 7 8 SIS---SUBTRACT Draw a line under the number 6. 7 Place your subtraction sign. 6 Subtract & put your answer directly under the 6. 1

2 ) 8 0 7 4 3 8 7 6 1 Step 4 in Long Division 4. Bring down BROTHER----------- --BRING DOWN Step 4 in Long Division 4 3 4. Bring down 2 ) 8 0 7 8 Look at your dividend to see if there are any more numbers to bring down. 7 6 If not, move to step 5. 1

2 ) 8 0 7 4 3 8 7 6 1 R1 Step 5 in Long Division 3 R1 REMO----REPEAT OR REMAINDER 2 ) 8 0 7 8 Since there are no more numbers to bring down & 2 will not divide into 1, you do not repeat the steps of division. 7 6 1 The number left over, 1, becomes the remainder.

THIS IS HOW IT LOOKS… 4 3 R1 2 ) 8 0 7 8 7 6 1

LET’S SEE WHAT ARE PRIME NUMBERS

Prime Numbers Eratosthenes’ Sieve

Eratosthenes’ Sieve A sieve has holes in it and is used to filter out the juice. Eratosthenes’s sieve filters out numbers to find the prime numbers.

Definition Factor – a number that is multiplied by another to give a product. 7 x 8 = 56 Factors

7 Definition 7 is prime because the only numbers Prime Number – a number that has only two factors, itself and 1. 7 7 is prime because the only numbers that will divide into it evenly are 1 and 7.

Definition Factor – a number that divides evenly into another. 56 ÷ 8 = 7 Factor

Hundreds Chart On graph paper, make a chart of the numbers from 1 to 100, with 10 numbers in each row.

Hundreds Chart 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

1 – Cross out 1; it is not prime 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

2 – Leave 2; cross out multiples of 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

2 6 7 Total of digits = 15 3 divides evenly into 15 Hint For Next Step To find multiples of 3, add the digits of a number; see if you can divide this number evenly by 3; then the number is a multiple of 3. 2 6 7 Total of digits = 15 3 divides evenly into 15 267 is a multiple of 3

2 – Leave 2; cross out multiples of 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

3– Leave 3; cross out multiples of 3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

Hint For the Next Step To find the multiples of 5 look for numbers that end with the digit 0 and 5. 385 is a multiple of 5 & 890 is a multiple of 5 because the last digit ends with 0 or 5.

4– Leave 5; cross out multiples of 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

5– Leave 7; cross out multiples of 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

6–Leave 11; cross out multiples of 11 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

All the numbers left are prime 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

The Prime Numbers from 1 to 100 are as follows: 2,3,5,7,11,13,17,19, 23,31,37,41,43,47, 53,59,61,67,71,73, 79,83,89,97

HECTIC Division

Dividing Difficult Large Numbers 31) 1719 31 will not go into 1 31 will not go into 17 31 will go into 171

Dividing Difficult Large Numbers 31) 1719 To figure what your first number will be cover the 1 in 31 & the 1 in 171.

Dividing Difficult Large Numbers 31) 1719 Now ask how many 3’s will go into 17.

Dividing Difficult Large Numbers 5 31) 1719 Be sure to put that number directly above the 1 not the 7.

Dividing Difficult Large Numbers 5 31) 1719 Now multiply the 5 x 31 and place it under the 171.

Dividing Difficult Large Numbers 5 31) 1719 155 31 x5 16 9 155

Dividing Difficult Large Numbers 5 31) 1719 155 16 9 Now cover up the 1 in 31 & the 9 in 169

Dividing Difficult Large Numbers 5 6 31) 1719 155 16 9 Now multiply 31 x 6.

Dividing Difficult Large Numbers 5 6 31) 1719 155 31 x6 16 9 186 186

Dividing Difficult Large Numbers 5 5 31) 1719 155 16 9 Subtract & your answer is 55R14 155 14

Can you identify the fractions? Fraction Finder Can you identify the fractions?

What fraction of this shape is yellow?

What fraction of this shape is yellow? 1 4

What fraction of this shape is yellow?

What fraction of this shape is yellow? 4 9

What fraction of this shape is yellow?

What fraction of this shape is yellow? 1 2

What fraction of this shape is yellow?

What fraction of this shape is yellow? 3 6 or 1 2

What fraction of this shape is green?

What fraction of this shape is green? 2 4 or 1 2

What fraction of this shape is blue?

What fraction of this shape is blue? 1 6

What fraction of this shape is pink?

What fraction of this shape is pink? 6 12 or 1 2

What fraction of this shape is purple?

What fraction of this shape is purple? 1 6

What fraction of this shape is green?

What fraction of this shape is green? 4 or 1 whole

What fraction of this shape is RED?

What fraction of this shape is RED? 1 2

What fraction of this shape is red?

What fraction of this shape is red? 2 12

LET’S CHECK Fractions HOW THEY LOOK LIKE!!!

3 4 Parts of a Fraction = the number of parts = the total number of parts that equal a whole

Parts of a Fraction 3 = numerator 4 = denominator

Which number is circled? 3 4 = denominator

Which number is circled? 3 = numerator 4

¾ looks like 1/4 1/4 3 4 1/4

¾ looks like 1/4 3 1/4 4 1/4

¾ looks like 1/4 1/4 3 4 1/4

What fraction of the balls are red? 1 4

What fraction of the balls are blue? 3 4

What fraction of the balls are green? 1 6

What fraction of the balls are purple? 4 6

What fraction of the rectangle is purple? 4 6

What fraction of the rectangle is purple? 2 6

What fraction of the pie is purple? 4 4

What fraction of the pie is purple? 3 4

What fraction of the musical instruments have strings? 2 5

What fraction of the fish have stripes? 3 5

What fraction of the pins are knocked down? 3 10

Let’s go the other way round

How many halves are in a whole? 2 1/2 1/2

How many quarters are in a whole? 1/4 1/4 4

How many eighths are in a whole? 1/8 1/8 1/8 1/8 8 1/8 1/8 1/8 1/8

How many eighths are in a quarter? 1/8 2 1/4

How many eighths are in a half? 1/8 1/8 1/8 1/8 4 1/2

How many quarters are in a half? 1/4 2 1/2 1/4

How many thirds are in a whole? 1/3 1/3 3 1/3

How many sixths are in a whole? 1/6 1/6 6 1/6 1/6 1/6 1/6

How many sixths are in a third? 1/6 2 1/6 1/3

How many sixths are in a half? 1/6 3 1/6 1/2 1/6

How many fifths are in a whole? 1/5 1/5 5 1/5 1/5 1/5

How many tenths are in a whole? 1/10 1/10 1/10 1/10 10 1/10 1/10 1/10 1/10 1/10 1/10

How many tenths are in a fifth? 1/10 1/10 2 1/5

How many tenths are in a half? 1/10 1/10 5 1/10 1/2 1/10 1/10

You Be the Designer

1 2 = 2 4 Equivalent Fractions Name the same amount but have different numerators and denominators. 1 2 1 1 = 4 2 4 2 1 4

1 2 = 2 4 Equivalent Fractions Are sometimes called equal fractions: two or more fractions that name the same number. 1 2 1 1 = 4 2 4 2 1 4

Equivalent Fraction Models 1 2 3 = = 2 4 6

Equivalent Fraction Models 1 4 = 5 = 2 8 10

Equivalent Fraction Models 1 4 = 2 8

Equivalent Fraction Models 3 6 = 4 8

Equivalent Fraction Models 2 4 = 3 6

What are the missing numbers? 1 2 3 = = 2 4 6

What are the missing numbers? 1 4 = 5 = 2 8 10

What are the missing numbers? 1 4 = 2 8

What are the missing numbers? 3 6 = 4 8

What are the missing numbers? 2 4 = 3 6

To Find Equivalent Fractions Multiply the numerator and the denominator by the same number. 1 3 3 x = 3 3 9

To Find Equivalent Fractions Divide the numerator and the denominator by the same number. 4 4 1 ÷ = 12 4 3

Fractions -----LET’S Simplifying Fractions

Factor A number that divides evenly into another. Factors of 24 are 1,2, 3, 4, 6, 8, 12 and 24.

What are the factors of 9? Factors of 9 are 1, 3 and 9.

What are the factors of 10? Factors of 10 are 1, 5 and 10.

What are the factors of 7? Factors of 7 are 1 and 7.

What are the factors of 56? Factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.

Common Factor When two numbers have the same factor it is called a common factor. A common factor of 12 and 6 is 3.

Name a Common Factor of 9 and 27? 1, 3, 9

Name a Common Factor of 4 and 8? 1, 2, 4

Name a Common Factor of 4 and 8? 1, 2, 4

Name a Common Factor of 15 and 30? 1, 3, 5, 15

Name a Common Factor of 12 and 48? 1, 2, 3, 4, 6, 12

Name a Common Factor of 9 and 21? 1, 3, 9,

Name a Common Factor of 10 and 25? 1, 5, 10

Name a Common Factor of 3 and 4? 1

Simplest Form When the only common factor of the numerator and denominator is 1, the fraction is in simplest form. 3 1 3 ÷ = 4 1 4

Greatest Common Factor The greatest common factor is the largest factor between two numbers. 12 = 1, 2, 3, 4, 6, 12 18 = 1, 2, 3, 6, 9, 18

What is the Greatest Common Factor? 8 = 1, 2, 4, 8 12 = 1, 2, 3, 4, 6, 12

What is the Greatest Common Factor? 8 = 1, 2, 4, 8 14 = 1, 2, 7,14

What is the Greatest Common Factor? 6 = 1, 2, 3, 6 18 = 1, 2, 3, 6, 9, 15

What is the Greatest Common Factor? 6 = 1, 2, 3, 6 12 = 1, 2, 3, 4, 6, 12

What is the Greatest Common Factor? 8 = 1, 2, 4, 8 16 = 1, 2, 4, 8, 16

What is the Greatest Common Factor? 8 = 1, 2, 4, 8 10 = 1, 2, 5, 10

What is the Greatest Common Factor? 3 = 1, 3 6 = 1, 2, 3, 6

What is the Greatest Common Factor? 4 = 1, 2, 4 6 = 1, 2, 3, 6

What is the Greatest Common Factor? 7 = 1, 7, 21 = 1, 3, 7, 21

What is the Greatest Common Factor? 15 = 1, 3, 5, 15 24 = 1, 2, 3, 8, 12, 24

How to Find the Simplest Form of a Fraction Find the greatest common factor of the numerator and the denominator and divide both the numerator and the denominator by that number. 12 6 2 ÷ = 18 6 3

Simplify or Reduce This Fraction 12 6 2 ÷ = 18 6 3

Simplify or Reduce This Fraction 9 3 3 ÷ = 21 3 7

Simplify or Reduce This Fraction 12 4 3 ÷ = 20 4 5

Simplify or Reduce This Fraction 10 5 2 ÷ = 15 5 3

Simplify or Reduce This Fraction 10 2 5 ÷ = 16 2 8

Simplify or Reduce This Fraction 12 4 3 ÷ = 16 4 4

Simplify or Reduce This Fraction 3 3 1 ÷ = 12 3 4

Simplify or Reduce This Fraction 2 2 1 ÷ = 8 2 4

Simplify or Reduce This Fraction 2 2 1 ÷ = 4 2 2

Simplify or Reduce This Fraction 6 3 2 ÷ = 9 3 3

Simplify or Reduce This Fraction 6 2 3 ÷ = 8 2 4

Fractions VII Adding Like Denominators

3 4 Parts of a Fraction = the number of parts = the total number of parts that equal a whole

Parts of a Fraction 3 = numerator 4 = denominator

Adding Like Denominators Only add the numerators 1/4 1/4 3 1 4 + = 4 4 4 1/4 1/4

Simplify Your Answer 4 1 = 4

Add these fractions 1/5 1/5 3 1 4 + = 1/5 5 5 5 1/5

Add these fractions 1/4 1/4 2 1 3 + = 4 4 4 1/4

Add these fractions 1 1 1 6 6 6 3 2 5 + = 6 6 6 1 1 6 6

Add these fractions 1 1 1 6 6 6 2 2 4 + = 6 6 6 1 6

Simplify Your Answer 4 2 2 ÷ = 6 2 3

Add these fractions 5 3 8 + = 12 12 12

Simplify Your Answer 8 4 2 ÷ = 12 4 3

Add these fractions 1 3 4 + = 10 10 10

Simplify Your Answer 4 2 2 ÷ = 10 2 5

Add these fractions 4 3 7 + = 4 4 9 9 9

Add these fractions 3 1 4 + = 5 5 8 8 8

Simplify Your Answer 4 4 1 5 ÷ 5 = 8 4 2

Add these fractions 2 1 3 + 4 3 = 7 9 9 9

Simplify Your Answer 3 3 1 7 ÷ 7 = 9 3 3

Fractions----- Adding Unlike Denominators

Some multiples of 3 & 6 6, 12, 18, 24, 30, 36, 42 Common Multiple A number that is a multiple of two or more numbers. Some multiples of 3 & 6 6, 12, 18, 24, 30, 36, 42

Least Common Multiple The smallest common multiple of a set of two or more numbers. 5 = 5, 10, 15, 20, 25, 30 6 = 6, 12, 18, 24, 30, 36

Shortcut for Finding the Least Common Denominator or Least Common Multiple Check to see if the smaller denominator divides evenly into the larger denominator. If it does, use the larger denominator for your LCD or LCM. 1 3 will divide evenly into 9, so 9 is your LCD or LCM. 3 1 + 9

To Add or Subtract Fractions With Unlike Denominators Find the multiples of each denominator. 1 5 = 5, 10, 15, 20, 25, 30 1 + 10 = 10, 20, 30, 40, 50

To Add or Subtract Fractions With Unlike Denominators Compare the lists of multiples. Circle the common multiples between the two lists. 1 5 = 5, 10, 15, 20, 25, 30 1 + 10 = 10, 20, 30, 40, 50

To Add or Subtract Fractions With Unlike Denominators Use the lowest common multiple as the denominator. 1 5 = 5, 10, 15 ,20 ,25 ,30 1 + 10 = 10, 20, 30, 40, 50

To Add or Subtract Fractions With Unlike Denominators This number is also called the least common denominator. 1 5 = 5, 10, 15 ,20 ,25 ,30 1 + 10 = 10, 20, 30, 40, 50

To Add or Subtract Fractions With Unlike Denominators Rewrite the fractions using the least common denominator or least common multiple. 1 5 10 1 + 10 10

To Add or Subtract Fractions With Unlike Denominators Find the equivalent fractions for 1/5 & 1/10 with 10 as the denominator. You know that 1/10 is equal to 1/10 so Put a 1 over the Bottom 10. 1 5 10 1 1 + 10 10

To Add or Subtract Fractions With Unlike Denominators Find the equivalent fractions for 1/5 & 1/10 with 10 as the denominator. To find the top number, ask yourself what do you multiply the 5 by to get 10. 1 5 10 1 1 + 10 10

To Add or Subtract Fractions With Unlike Denominators Find the equivalent fractions for 1/5 & 1/10 with 10 as the denominator. That’s right 2. Since you are looking for the equivalent fraction you know the top number must also be multiplied by 2. 1 x 2 = 5 10 x 2 = 1 1 + 10 10

To Add or Subtract Fractions With Unlike Denominators Find the equivalent fractions for 1/5 & 1/10 with 10 as the denominator. 1 2 x 2 = To find the top number just multiply 2 x 1 to get your equivalent fraction. 5 10 x 2 = 1 1 + 10 10

To Add or Subtract Fractions With Unlike Denominators Now just add the numerators. 1 2 x 2 = 5 10 x 2 = Remember when adding fractions you never add the denominators. 1 1 + 10 10 3 10

1 2 8 1 + 8 8 Add these Fractions Use the short cut to find the Least Common Denominator (LCD). 1 2 8 1 + 8 8

1 2 8 1 + 8 8 Add these Fractions x 4 = x 1 = Now find the equivalent fractions for 1/2 & 1/8. 1 2 8 x 4 = 1 + 8 x 1 = 8 Ask what do you multiply 2 by to get 8 and what do you multiply 8 by to get 8.

1 2 8 1 + 8 8 Add these Fractions x 4 = x 4 = x 1 = x 1 = Since you are writing equivalent fractions, now multiply the top numbers by the same number you did in the bottom. 1 x 4 = 2 8 x 4 = 1 x 1 = + 8 x 1 = 8

1 4 2 8 1 1 + 8 8 Add these Fractions x 4 = x 4 = x 1 = x 1 = Now multiply across. x 4 = 2 8 x 4 = 1 1 x 1 = + 8 x 1 = 8

1 4 2 8 1 1 + 8 8 5 8 Add these Fractions x 4 = x 4 = x 1 = x 1 = Add your new numerators. x 4 = 2 8 x 4 = 1 1 x 1 = + 8 x 1 = 8 5 8

2 5 15 1 + 3 15 Add these Fractions Find the common Multiples for 5 and 3. Write This number As your new denominator. 2 5 15 1 + 3 15

2 5 15 1 + 3 15 Add these Fractions x 3 = x 5 = Ask yourself what you multiply the bottom number by to get 15. 2 5 15 x 3 = 1 + 3 x 5 = 15

2 5 15 1 + 3 15 Add these Fractions x 3 = x 3 = x 5 = x 5 = Multiply the top number by the same number you did in the bottom. 2 x 3 = 5 15 x 3 = 1 x 5 = + 3 x 5 = 15

2 6 5 15 1 5 + 3 15 Add these Fractions x 3 = x 3 = x 5 = x 5 = Multiply across. 2 6 x 3 = 5 15 x 3 = 1 5 x 5 = + 3 x 5 = 15

2 6 5 15 1 5 + 3 15 11 15 Add these Fractions x 3 = x 3 = x 5 = x 5 = Now add your new numerators. 2 6 x 3 = 5 15 x 3 = 1 5 x 5 = + 3 x 5 = 15 11 15

Add these Fractions 1 2 x 2 = 6 12 x 2 = 1 3 x 3 = + 4 x 3 = 12 5 12

Add these Fractions 5 20 x 4 = 6 24 x 4 = 1 3 x 3 = + 8 x 3 = 24 23 24

Add these Fractions 2 6 x 3 = 3 9 x 3 = 1 1 x 1 = + 9 x 1 = 9 7 9

4 12 5 15 2 10 + 3 15 22 15 Add these Fractions x 3 = x 3 = x 5 =

Simplify Your Answer 7 1 15 22 15) 22 15 15 7

Roman Numerals

Let’s learn the Roman Numerals: I = 1 V = 5 X = 10 L = 50 C = 100 D = 500 M = 1000

Click on the number that matches the Roman Numeral.

LXIII A. 53 B. 63 C. 113

OOPS! Try again!

You are correct! LXIII = 50+10+3 = 63 Remember: L=50; X=10; III=3

2.DCXXIV A. 624 B. 1624 C. 5524

OOPS! Try again!

You are correct! DCXXIV= 500+100+20+4= 624

3. CCL A. 150 B. 250 C. 550

OOPS! Try again!

You are correct! CCL = 100+100+50=250

THANK YOU