Good Afternoon!Today we will be learning about Order of Operations.

Let’s warm up :

1) Estimate 6 x 44.

2) Estimate 236 x 46.

3) Divide 114 by 3.

4) Estimate 376 % 415) 625

X 17

1) 240

2) 10,000

3) 38

4) 10

5) 10,625

Let’s first review what we learnt in the previous sessions before proceeding further.

Factor: Number that is multiplied to give a product.Product: Number that is obtained by multiplying numbers.Multiplication by a whole number is REPEATED

ADDITION. There are several properties of Multiplication.

1) COMMUTATIVE PROPERTY:

We can change the order of the factors and the product stays the

same. EXAMPLE: 4 x 3 = 12

3 x 4 = 122) IDENTITY PROPERTY:

We can multiply a number by 1 and the product is the

number. EXAMPLE: 3 x 1 = 3

3) ZERO PROPERTY:

We can multiply a number by 0 and the product is

zero. EXAMPLE: 7 x 0 = 0

We learnt about the following terms:

Multiple: It is the product of a number and any whole number. Even numbers: Whole numbers that are divisible by 2 are even

numbers.Odd numbers: Whole numbers that are not divisible by 2 are odd numbers.Prime numbers: Numbers whose factors are only 1 and the

number itself are prime numbers. Composite numbers: All the non-prime numbers except 0 and 1, are Composite Numbers.

Find 7 x 3.

Use a Known Fact

7 groups of 3 = 7 groups of 2 plus 7 7 x 3 = 7 x 2 +

7 = 14 + 7 = 21

Double a Known Fact

Find 8 x 6.

8 x 6 = (4 x 6 ) + (4 x 6)

= 24 + 24 = 48

8 groups of 6 = 4 groups of 6 + 4 groups of 6

Find 236 x 46We multiply numbers by first lining up

the digits in the following manner:

236X 461416

23

Multiply by the ones. Regroup

Wherever necessary

.

STEP 1:

STEP 2:

Regroup Whereve

r necessar

y.

236X 461416

23

9440

12

Multiply by the tens.

236X 461416

23

+9440

12

10856

STEP 3:

Then, add the products.

Hence, 236 x 46 = 10,856

Multiplication is an operation on two numbers to find a product. Like 3 x 4 = 12.

While multiplying, we can change the grouping of the factors and the product stays the same.

EXAMPLE: 2 x (3 x 4) = (2 x 3) x 4

ASSOCIATIVE PROPERTY:

Estimate 6 x 44.

By Estimate, we mean an answer that is close to the exact answer.

While estimating products, we round the greater factor.

6 x 44.

6 x 40 =240

Round to the nearest

tens.

Overestimate: It is estimate greater than the exact answer.Underestimate: It is estimate less than the exact

answer.

Divide 114 by 3.

STEP 1:

3 114

3

-92

3 tens in each

group.

2 tens left

11 tens, 4 ones9 tens

used

STEP 2:

3 114

3

-924

Bring down 4 ones.

24 ones in all.

STEP 3:

3 114

38

-924-24

0

8 ones in each

group.

24 ones used.

0 ones left.

Estimate: 36 x 54

By Estimate, we mean an answer that is close to the exact answer.

While estimating products, we round each factor.36 x 54.

40 x 50 =2,000

Round to the nearest

tens.Hence, the estimated value of 40 x 50 is

2,000.

Round to the nearest

tens.

We can apply the concept of Place value to find the solution of multiples of 10.

42 ones % 6 = 7 ones 42 tens % 6 = 7 tens 42 hundreds % 6 = 7 hundreds

42 % 6 = 7420 % 6 = 70

4,200 % 6 = 700

Numbers that are close to the number in a problem and are easy to divide mentally are

Compatible Numbers.

The objective of finding Compatible numbers is the Estimation of Quotients.

Compatible numbers help to find the multiple that is closest to the dividend, so it is easier to divide mentally.

Estimate 123 % 4120 % 4 = 30

120 and 4 are compatible numbers.

Estimate 356 % 41

356 is closer to 360.So, 360 % 40 =

9The basic

fact is: 36 % 4 = 9

The estimate of 356 % 40 is 9.

41 is closer to 40.

Let’s start now with the Order of Operations

ARITHMETIC EXPRESSION: It is an expression consisting of numbers, grouping symbols and arithmetic operation symbols.

To evaluate these expressions, a specific Order of Expressions is followed.

When a numerical expression involves two or more operations, there is a specific order in which these operations must be

performed.

4 – (3 + 2) is an arithmetic expression.

Evaluate 3 + 4 x 2

3 + 4 x 2 = 7 x 2 = 14

or

3 + 4 x 2 = 3 + 8 = 11

Two people may interpreted the problem differently this problem like

Here, the correct answer is 11.Let’s see how.

When a numerical expression involves two or more operations, there is a specific order in which these

operations must be performed.The order is:

Parenthesis

Exponents

Multiplication

Division

Add

Subtract

P

E

M

D

A

S

Please Excuse (My Dear) (Aunt Sally).

Parenthesis, Exponents, (Multiplication/Division) then (Add/Subtract)OR that is, PEMDAS for short .

This phrase will help you understand the order.

The reason (multiplication & division) and (add & subtract) are grouped is when those operations are

next to each other you do the math from left to right.

You do not necessarily do addition first if it is written next to subtraction. 

To solve an expression you need to follow the rules for the Order of Operation.

Evaluate: 3 + (3 x 4) - 1

Rule 1:

First, do operations inside the parenthesis ( ).

3 + (3 x 4) - 1

Rule 2:

Then do multiplication and division in order from left to right. 3 + 12 - 1

Rule 3:

Finally, do addition and subtraction in order from left to right.

15 - 1

14

There is no more

multiplication or

division.

Is 8 x (3 + 6) equal to 7 x (17 - 6) ?

The value 8 x (3 + 6) = 72 is less than 7 x (17 - 6) = 77.

Hence, not equal.

First of all, we evaluate

8 x (3 + 6)

= 8 x 9

= 72

Then, we evaluate

7 x (17 - 6)

= 7 x 11

= 77

BREAK

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Assignments

Simplify:

1) (4 + 5) + (3 x6) - 8

2) (48 % 6) + 9

3) 15 % 5 x 8 - 4

4) (42 % 7) % 3

5) 7 + 12 x 2

6) 3 + 6 x (5 + 4) ÷ 3 - 7

1) 19 4) 2

2) 17 5) 31

3) 20 6) 14

7) Is 3 + (45 - 7 ) equal to 3 x (14 - 1) ?

8) Is 10 % 2 + 8 equal to 5 x 2 + 3 ?

9) Is 6 x (9 + 2) equal to 8 x (13 - 6) ?

7) No. 3 + (45 - 7 ) > 3 x (14 - 1)

8) Yes.

9) No. 6 x (9 + 2) > 8 x (13 - 6)

10) Elena bought 4 cards for $3 each and 2 pens for $6 each. How much did she spend in all?

10) 48

Very Good!Let's Review

ARITHMETIC EXPRESSION: It is an expression consisting of numbers, grouping symbols and arithmetic operation symbols.

To evaluate these expressions, a specific Order of Expressions is followed.

When a numerical expression involves two or more operations, there is a specific order in which these operations must be

performed.

4 – (3 + 2) is an arithmetic expression.

Parenthesis, Exponents, (Multiplication/Division) then (Add/Subtract)OR that is, PEMDAS for short .

Please Excuse (My Dear) (Aunt Sally).

This phrase will help you understand the order.

To solve an expression you need to follow the rules for the Order of Operation.

Evaluate: 3 + (3 x 4) - 1

Rule 1:

First, do operations inside the parenthesis ( ).

3 + (3 x 4) - 1

Rule 2:

Then do multiplication and division in order from left to right. 3 + 12 - 1

Rule 3:

Finally, do addition and subtraction in order from left to right.

15 - 1

14

There is no more

multiplication or

division.

Is 8 x (3 + 6) equal to 7 x (17 - 6) ?

The value 8 x (3 + 6) = 72 is less than 7 x (17 - 6) = 77.

Hence, not equal.

First of all, we evaluate

8 x (3 + 6)

= 8 x 9

= 72

Then, we evaluate

7 x (17 - 6)

= 7 x 11

= 77

You have done a nice job.See you in the next session.