Multidigit Arithmetic Powerpoint.pptx

MULTIDIGIT ARITHMETIC

THIS IS A REVIEW OF HOW TO ADD, SUBTRACT, MULTIPLY, &

DIVIDE MULTIDIGIT NUMBERS

ADDING (SLIDES 5-9)

SUBTRACTING (SLIDES 10- 23)

MULTIPLYING (SLIDES 24-28)

KNOW YOU MATH FACTS

•

_{SUCCESS WITH MULTIDIGIT NUMBERS DEPENDS ON KNOWING}

YOUR MATH FACTS

•

_{IF YOUR MATH FACTS ARE MEMORIZED, YOU KNOW THE}

ANSWER AUTOMATICALLY (WITHOUT THINKING) MUCH LIKE YOU

KNOW THE ANSWER TO THE QUESTION “WHAT IS YOUR NAME.”

VOCABULARY

• _{ADDITION (+) – MEANS TO PUT TOGETHER. THE SUM IS THE ANSWER TO AN ADDITION PROBLEM}

• _{SUBTRACT (-) – MEANS TO REMOVE AN AMOUNT. THE DIFFERENCE IS THE ANSWER TO A}

SUBTRACTION PROBLEM

• _{REGROUP – THE PROCESS OF CHANGING GROUPS OF 1’S INTO 10’S TO MAKE THE PROCESS OF}

ADDING/SUBTRACTING EASIER. THIS IS SOMETIMES CALLED “CARRYING” WITH ADDITION OR “BORROWING” WITH SUBTRACTION.

• _{MULTIPLY (X) – MEANS TO COMBINE AMOUNTS. THE PRODUCT IS THE ANSWER TO A}

MULTIPLICATION PROBLEM

• _{DIVIDE ( – TO SPLIT AN AMOUNT INTO EQUAL PARTS OR GROUPS. THE QUOTIENT IS THE ANSWER}

TO A DIVISION PROBLEM.

• _{REMAINDER – THE AMOUNT LEFT OVER IN A DIVISION PROBLEM.}

PARTS OF A PROBLEM

ADDING MULTIDIGIT NUMBERS

STEPS:

1. STACK THE PROBLEMS (LINE UP THE PLACE VALUE OF EACH DIGIT VERTICALLY

SO THAT THE 1’S ON THE TOP ARE DIRECTLY OVER THE 1’S UNDERNEATH IT

AND SO ARE THE 10’S, 100’S, ETC…)

35,785 + 3,506

2. ADD THE DIGITS IN EACH PLACE VALUE WORKING FROM RIGHT TO LEFT

(THE 1’S FIRST, THE 10’S NEXT, AND SO ON)

3. REGROUP IF NECESSARY

• IF THE ANSWER REQUIRES 2 DIGITS, HOLD THE 1’S AND CARRY THE 10’S

• IN THE EXAMPLE TO THE LEFT SINCE 5+6 AND 7+5 ARE REGROUPED BECAUSE THEIR ANSWERS REQUIRE 2 DIGITS

https://www.youtube.com/watch?v=mAvuom42NyY

Using grid paper will help keep the

#’s alligned

+

7 8 5

5 0 6

+

2 9 1

5,

3

3,

9,

3

1

1

 3 5  7  8  5     3 5  0  6           

1. 71,456 + 13,325 = 2. 64,417 + 22,368 =

3. 54,873 + 7,462 = 4. 48,673 + 3,594 =

84,781

1

Read the problem and identify₂ what is being added, if necessary. Line up the numbers by the place value of their digits, if necessary. Add the digit in each place value. Hint: Start from the ones place.

Compose a number, if needed.

Hint: Move a group of numbers to the next higher place value.

Interpret₃ the sum. “The sum of _______ and _______ is _______.”

Add multi-digit numbers. 1

2 3

a 4

+ 2 3 6 1 4 4 2 6 7 8 86,785

8 6 , 7 8 5

3 , 5 9 4

1

+ +

62,335 52,267

5 4 , 8 7 3 7 , 4 6 2

6 2 , 3 3 5

4 8 , 6 7 3

8 4 , 7 8 1

5 2 , 2 6 7

1 1 1 1 1 1

ADDITION - YOUR TURN #1

1c. 1b.

1a.

+ 7 9 5 0 4 7 5

3 1

6 + 5 9 6

6 3 9

6 2

5 + 4 2 7

0 6 4 1 5 8 0 2c. 2b. 2a.

+ 9 2 0 6 6 0 2

2 4

0 + 6 7 9

8 9 4

9 2

4 + 3 3 2

5 4 1 1 7 6 5 3c. 3b. 3a.

+ 5 9 1 1 5 3 1

7 5

5 + 2 3 0

9 6 4 1

8 2

4 + 2 6 6

YOUR TURN #1 – CHECK YOUR ANSWERS

1c. 1b.

1a.

+ 7 9 5 0 4 7 5

3 1

6 + 5 9 6

6 3 9

6 2

5 + 4 2 7

0 6 4 1 5 8 0 2c. 2b. 2a.

+ 9 2 0 6 6 0 2

2 4

0 + 6 7 9

8 9 4

9 2

4 + 3 3 2

5 4 1 1 7 6 5 3c. 3b. 3a.

+ 5 9 1 1 5 3 1

7 5

5 + 2 3 0

9 6 4 1

8 2

4 + 2 6 6

4 4 9 2 7 2 6

9 5 , 3 5 7

1 1

7 5 , 3 2 7 6 8 , 8 7 8

4 9 , 8 6 4 1 0 1 , 7 7 6 _{8 4 , 7 8 1}

1 0 2 , 1 0 8 9 6 , 9 9 6

8 9 , 4 3 0

1 1

1

1 1 1 1 1 1

1 1 1

ESTIMATING TO CHECK

Round each number to

the 100’s place

SUBTRACTING MULTIDIGIT NUMBERS

STEPS:

1. STACK THE NUMBERS VERTICALLY LINING UP THE PLACE VALUE OF EACH DIGIT

• REMEMBER THAT ORDER MATTERS WITH SUBTRACTION SO PUT THE 1ST # ON TOP OF

THE 2ND _#

2. LOOK AT THE ONES.

ASK: CAN WE SUBTRACT?

3. REGROUP AS NEEDED:

1. GO TO THE NEIGHBOR ON THE LEFT AND TAKE ONE AWAY.

2. ADD THE TEN TO THE DIGIT THAT NEEDS REGROUPING.

4. SUBTRACT THE ONES.

5. SUBTRACT THE TENS AND SO ON…

https://www.youtube.com/watch?v=Y6M89-6106I

1. STACK THE PROBLEM (PUT THE 1

ST

NUMBER ON TOP OF THE 2

ND

#)

82 – 53

SUBTRACTION

– A CLOSER LOOK AT EACH

STEP

8 2

-5

3

-

₈₂

53

2. LOOK AT THE ONES.

ASK:

“CAN WE TAKE 3

AWAY FROM

2?”

8 2

-5

3

If we can’t,

then we have to

regroup.

Remember order matters with subtraction. You need

to subtract 2-3 (not 3-2). Always subtract from top to

bottom

3. REGROUP AS NEEDED.

8

2

-5

3

1

:

Go next door

to the tens

and take one

away.

7

2

:

Add the ten

to the ones.

1

4. SUBTRACT THE ONES.

8

2

-5

3

7

1

What is 12 –

3?

9

5. SUBTRACT THE TENS.

8

2

-5

3

7

1

9

What is 7 – 5?

2

MORE EXAMPLES

ESTIMATING TO CHECK

Round each number to

the 100’s

The estimate 5,700 is close so the answer is reasonable.

SUBTRACTING ACROSS ZEROS

METHOD 1

(THE OLD SCHOOL WAY) - BORROW ONE DIGIT AT

A TIME

Start here. There are

not enough.

Since the neighbor to

the left does not have any,

go all the way to the

left to borrow.

Regroup one digit at a time. Until you reach the digit you are

subtracting

Another Example:

SUBTRACTING ACROSS ZEROS

METHOD 2

– THE BOXING STRATEGY

•

_{LOOK SEVERAL DIGITS AHEAD & CHUNK/BOX THIS SET}

5 0 0 2

- 1 4 8

4 9 9

₁₂

SUBTRACTION – YOUR TURN #2

1. 725 - 68 = 2. 3,789 - 509 =

3. 707 - 361 = 4. 8,000 – 5,274 =

-

--

3 , 7 8 9 5 0 9

7 0 7

3 6 1 5 , 2 7 4 8 , 0 0 0

YOUR TURN #2 – CHECK YOUR ANSWERS

1. 725 - 68 = 2. 3,789 - 509 =

3. 707 - 361 = 4. 8,000 – 5,274 =

-

--

3 , 7 8 9 5 0 9

7 0 7

3 6 1 5 , 2 7 4 8 , 0 0 0

3 , 2 8 0

2 , 7 2 6 6 5 7

3 4 6

7 9 9 10 6 10

6 12 15 11

MULTIDIGIT MULTIPLICATION

STEPS:

1. STACK THE NUMBERS VERTICALLY LINING UP THE PLACE VALUE OF EACH DIGIT

2. MULTIPLY THE ONES DIGIT

• REGROUP AS NECESSARY (NOTE – ANY REGROUPED AMOUNTS ARE ADDED DURING MULTIPLICATION) 3. INSERT A ZERO AS A PLACEHOLDER FOR YOUR NEXT PARTIAL PRODUCT

4. MULTIPLY THE TENS DIGIT

• REGROUP AS NECESSARY

5. INSERT 2 ZEROS AS PLACEHOLDERS IN YOUR NEXT PARTIAL PRODUCT

6. MULTIPLY THE 100’S DIGIT

7. CONTINUE THE PROCESS OF ADDING PLACEHOLDER TO MULTIPLY EACH PLACE VALUE

• THE 10’S DIGIT HAS ONE PLACEHOLDER

• THE 100’S DIGIT HAS TWO PLACEHOLDERS

• THE 1000’S DIGIT HAS THREE PLACEHOLDERS

• AND SO ON…

8. ADD THE PARTIAL PRODUCTS

https://www.youtube.com/watch?v=FJ5qLWP3Fqo

Note: The number of placeholder used matches the number of

zero’s for each place value. https://www.youtube.com/watch?v=RVYwunbpMHA

MULTIDIGIT BY ONE DIGIT

Add the regrouped amount

This is 6 x 3 which is 18, plus

the regrouped amount (18 +

5 = 23)

Add the regrouped amount

This is 7 x 6 which is 42, plus

the regrouped amount (42 +

2 = 44)

MULTIDIGIT BY TWO DIGITS

the ones

Step 2 – Use a placeholder and multiply the tens

Step 3 – Add the partial products

DON’T FORGET THE PLACEHOLDERS

CCSS 5th _{Grade Numbers and Base Ten 5.0}

Multiply using the multiplication algorithm. Lesson to be used by EDI-trained teachers only.

©2013 All rights reserved.

Skill Development/Guided Practice (continued)

Skill Development/Guided Practice (continued)

7.

8.

4 9 3

2 5 1



5 7 9

1 3 4



The multiplication algorithm is a step-by-step method for solving a multiplication problem. • The multiplication algorithm involves multiplying by place value then adding the

partial products.

Partial products are the smaller products obtained when multiplying by place value.

Multiply by place values beginning with the ones place. Write digits in the correct place value.

Add digits in the same place value as needed. Add the partial products.

Interpret the multiplication problem. “______ times ______ is equal to _______.”

Multiply using the multiplication algorithm. 1

2 a b 3

How did I/you multiply by place values?

How did I/you multiply by place values?

CFU

CFU

1

Use 2 placeholders when multiplying the 100’s digit.

LONG DIVISION STEPS

D D M S C B R

1. DASHES

2. DIVIDE

3. MULTIPLY

4. SUBTRACT

5. CHECK

6. BRING DOWN

7. REPEAT (OR REMAINDER)

Dude, does

McDonalds

sell

cheesebur

gers

regularly?

https://www.youtube.com/watch?v=LGqBQrUYua4

This is a sample

long division problem

6

8 9 2

1 4 8 r 4

-6

2 9

-2 4

5 2

-4 8

4

Quotient

Divisor

Dividend

Answer

Number doing the dividing.

Number being divided

STEP BY STEP – A CLOSER LOOK

STEP 1 – DASHES

a) STARTING AT THE LEFT, UNCOVER 1 DIGIT OF THE DIVIDEND AT A TIME

b) ASK “CAN I DIVIDE THE DIVISOR BY THIS DIGIT?”

c) ONCE THE 1

DASH IS PLACED, USE DASHES OVER ALL THE DIGITS TO

THE RIGHT

WHY DO THIS?

•

_{DASHES REMIND YOU HOW MANY}

DIGITS YOUR ANSWER SHOULD HAVE

•

_{PEOPLE OFTEN FORGET THE ZEROS}

X

5 does not go

into 2

5 does go into 20, so place dashes over all remaining

digits

The dashes tell us that this will be a 3 digit

answer

STEP 2 - DIVIDE

X

Using the 1

dash,

think “5 goes into

20 how many

times?” or think “5

times what = 20?”

Answer – 4

4

STEP 3 - MULTIPLY

X

Multiply by the

divisor & place this

under the dividend.

5 x 4 = 20

4

2

0

STEP 4 - SUBTRACT

X

20 – 20 = 0

4

- 2 0

0

STEP 5 - CHECK

X

Check – “Is zero

less than 5?”

Answer – Yes so

you may

continue

4

- 2 0

0

If the answer is “no” you made a division error

Check to make sure the answer from the subtraction is less

than the divisor

STEP 6 – BRING DOWN

X

Bring down the

# under the

next dash

4

- 2 0

0

1

If you have any other dashes, bring down the next digit in

the dividend

STEP 7 – REPEAT

X

5 does not go

into zero. Don’t

forget to put a

zero in the next

dash

4

- 2 0

0

1

After bringing down a digit, always return to step 2 (divide)

and proceed through the steps until there are no other

digits to bring down

D D M S C B R

0

Check – Is 1 less

than 5?

Answer – Yes so it’s

okay to continue

STEP 7 – CONTINUED

X

5 x 0 = 0

4

- 0

1

0

After bringing down a digit, always return to step 2 (divide)

and proceed through the steps until there are no other

digits to bring down

D D M S C B R

0

- 2 0

0

1

2

- 1 0

0

Division has stopped and

there is no remainder.

ADDITIONAL SINGLE DIGIT DIVISOR

EXAMPLES

X

X

2 DIGIT DIVISORS

1. ROUND THE DIVISOR, TO ESTIMATE THE QUOTIENT

2. FOLLOW THE REST OF THE LONG DIVISION STEPS (DDMSCBR)

Round the divisor to 25 because this # is easy to work with

using mental math

X

Since you rounded the divisor to 25, use

this to help estimate the first

division 25 x 2 = 50 which is close to

47.

Now try 2 x the actual divisor (23

x 2 = 46)

https://www.youtube.com/watch?v=HdU_rf7eMTI

EXAMPLE 1

70 because this # is easier to work with.

Use 70 to help estimate. 70 x 8 = 560, so try multiplying the actual divisor by 8.

73 x 8 = 584 (that’s too much, so now try

7)

73 x 7 = 511 (this is as close as we can get so

use 7)

Use the rounded divisor of 70 to help estimate. Since 70 x 9 = 630, try the actual divisor with 9 (73 x 9 = 657). That’s too much,

so use 8 (73 x 8 = 584)

r44

EXAMPLE 2

1. ROUND THE DIVISOR, TO ESTIMATE THE QUOTIENT

2. FOLLOW THE REST OF THE LONG DIVISION STEPS (DDMSCBR)

Round the divisor to 20, since this is

easier to use with mental math. 20 x

2 = 40, since this is close to 36 try the actual divisor x

2

21 x 2 = 42 (that’s too much, so use

1)

20 x 1 = 20

X

1

-2 0

1 8 2

-1 6 8

1 4

2

- 1 2

6

1

6

8

Check “Is 18 smaller than 21?” Answer – Yes (okay to continue)

Use the rounded divisor of 20 to help estimate. Since 20 x 9 = 180, try the actual divisor with

9 (21 x 9 = 189). That’s too much, so use 8 (21 x 8 = 168) Use the rounded divisor of 20 to

help estimate. Since 20 x 7 = 140, try 7 (21 x 7 = 147). That’s

too much to use 6

6 r16