Addition Algorithms

S. Matthews

Partial-Sums Method for Addition

Add from left to right and column by column.

The sum of each column is recorded on a separate line.

The value of each digit is determined by its place in the numeral.

Let’s practice the value of digits for Partial-Sums.

In the problem 23 + 45, we first

add the 2 and 4.

However, the 2 is worth 2 tens,

and the 4 is worth 4 tens. So we

say 20, not 2; and 40, not 4.

In the problem 23 + 45, we first

add the 2 and 4.

However, the 2 is worth 2 tens,

and the 4 is worth 4 tens. So we

say 20, not 2; and 40, not 4.

Let’s practice the value of digits for Partial-Sums.

Your turn.

What do we say when

adding the hundred’s

place for 376 + 832?

Your turn.

What do we say when

adding the hundred’s

place for 376 + 832?

You’ve got it!

We say 300, n

ot 3; a

nd

800, not 8

.

What is th

e sum of th

e

100’s place

?

You’ve got it!

We say 300, n

ot 3; a

nd

800, not 8

.

What is th

e sum of th

e

100’s place

?

Can’t fool you!

In 376 and 832, the 3 is

worth 300, and the 8 is worth

800.

300 + 800 is 1,100 or eleven

hundred.

Can’t fool you!

In 376 and 832, the 3 is

worth 300, and the 8 is worth

800.

300 + 800 is 1,100 or eleven

hundred.

Let’s practice the value of digits for Partial-Sums.

Let’s continue.

What do we say when

adding the tens place for

376 + 832?

Let’s continue.

What do we say when

adding the tens place for

376 + 832?

That’s rig

ht!

We say 70, n

ot 7; a

nd 30,

not 3.

What is th

e sum of th

e 10’s

place?

That’s rig

ht!

We say 70, n

ot 7; a

nd 30,

not 3.

What is th

e sum of th

e 10’s

place?

Can’t fool you!

In 376 and 832, the 7 is

worth 70, and the 3 is worth

30.

70 + 30 is 100 or ten tens.

Can’t fool you!

In 376 and 832, the 7 is

worth 70, and the 3 is worth

30.

70 + 30 is 100 or ten tens.

Take a look at the steps for

addition using the Partial-

Sums Method.Then we’ll practice the

method some more.

Take a look at the steps for

addition using the Partial-

Sums Method.Then we’ll practice the

method some more.

398 + 435

Add the 100’s: 300 + 400 =

+ 13

Add the 10’s: 90 + 30 =

Add the 1’s: 8 + 5 =

Find the total

120

700

833

Now, you try the Partial- sums method using the numbers we practiced.

Now, you try the Partial- sums method using the numbers we practiced.

376 + 832

Add the 100’s: 300 + 800 =

+ 8

Add the 10’s: 70 + 30 =

Add the 1’s: 6 + 2 =

Find the total

100

1100

1, 208

You are good!

Let’s try just one more.

You are good!

Let’s try just one more.

479 + 285

Add the 100’s: 400 + 200 =

+ 14

Add the 10’s: 70 + 80 =

Add the 1’s: 9 + 5 =

Find the total

150

600

764

Excellent! I know you’ve got the hang

of it.

Don’t forget, in the Partial-Sums method for

addition, you:

• add the 100’s,

• add the 10’s,

• add the 1’s.

• Then add the sums you just found.

(the partial sums)

Excellent! I know you’ve got the hang

of it.

Don’t forget, in the Partial-Sums method for

addition, you:

• add the 100’s,

• add the 10’s,

• add the 1’s.

• Then add the sums you just found.

(the partial sums)

Keep practicing.

Peace!

Keep practicing.

Peace!