Multiplication
Multiplication
 Multiplication is increasing the value of a number by adding in
equal sets.
 3 x 4 means add 3 together 4 times
3+3+3+3
 Multiplying larger numbers is the same
 22 x 14 means add 22 together 14 times
 This takes too long, so we have memorized the simple
multiplication facts to make this process easier.
3 x 9 = 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 27
3 x 9 = 27
Traditional Multiplication
3
45
X 16
270
450
720
Try It Out
 Use traditional multiplication on these problems
to solve for m.
2231 * 3 = m
24 * 46 = m
2342 * 14 = m
758 * 13 = m
24 * 12 = m
Try It Out
 Use traditional multiplication on these problems
to solve for m.
2231 * 3 = m
24 * 46 = m
2342 * 14 = m
758 * 13 = m
24 * 12 = m
M=6693
M=1536
M=32788
M=9854
M=288
Partial Products
 In the partial-products method, you must keep track of the
place value of each digit. It may help to label each place
value column.
100s 10s 1s
 3 * 197 = ?
Multiply each part of 197 by 3
100 * 3 = 3
0
0
90 * 3 = 2
7
0
7*3=
2
1
5
9
1
Partial Products
 64 * 72 =
100s
10s
42
1
2
0
2
8
45
46
10
0
1s
 60 + 4 * 70 +2 =
60 * 70 =
60 * 2 =
4 * 70 =
4* 2=
0
0
0
8
8
8
Try It Out
 Use partial products multiplication on these
problems to solve for m.
137 * 65 = m
625 * 30 = m
72 * 15 = m
420 * 31 = m
23 * 21 = m
Try It Out
 Use partial products multiplication on these
problems to solve for m.
137 * 65 = m
625 * 30 = m
72 * 15 = m
420 * 31 = m
23 * 21 = m
M = 8905
M =1875
M =1080
M =13020
M =483
Lattice Method
Try It Out
 Use lattice method of multiplication on these
problems to solve for m.
76 * 49 = m
53 * 83 = m
92 * 56 = m
63 * 15 = m
48 * 27 = m
M = 3724
M =4399
M = 5152
M =945
M =1296
Multiplying with Decimals
 When you are multiplying a whole number by a decimal, you are




going to find the value of that smaller amount of the big piece.
16 * .25 means what is .25 or 25% of the total of 16
We know .25 or 25% is 1 of 4 groups of the total.
If we break 16 into 4 equal groups, we get 4 in each group.
16
X .25
80
320
4 .0 0
We have multiplied, but we have gotten a smaller answer than
either one of the factors of the problem because we are looking at
the value of that smaller piece in the whole.
Multiplying with Decimals
 If you multiply a decimal by a decimal, you are still looking at
the problem in the same way.
 If the problem is .89 * .16, you are looking at what is .16 of
.89. In this case, .89 becomes the whole and .16 is the piece
you are trying to find the value of.
.89
X .16
534
890
.1424
But How Do You Place the Decimal?
 First count the numbers that sit in decimal place values.
.89
4
X .16
534
890
1424
 Next, start at the back of the number (right side) and count
toward the front the same number of place value spots.
.1 4 2 4
4 3 2 1
Try It Out
 Use lattice or partial-products method of multiplication
on these problems to solve for m. Be sure you show the
path you followed to place the decimal.
0.3 * 14 = m M = 4.2
6.8 * 4.5 = m M = 30.60 or 30.6
0.12 * 0.9 = m M = 0.108
0.3 * 0.919 = m M = 0.2754
2.7 * 5.6 = m
M = 15.12