Multiplication

MultiplicationMultiplication is increasing the value of a number

by adding in equal sets.3 x 4 means add 3 together 4 times

3 + 3 + 3 + 3Multiplying larger numbers is the same22 x 14 means add 22 together 14 timesThis 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

270450720

Try It OutUse traditional multiplication on

these problems to solve for m.

2231 * 3 = m24 * 46 = m

2342 * 14 = m758 * 13 = m24 * 12 = m

Try It OutUse traditional multiplication on

these problems to solve for m.

2231 * 3 = m 24 * 46 = m

2342 * 14 = m758 * 13 = m24 * 12 = m

M=6693

M=1536M=32788M=9854M=288

Partial ProductsIn 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 1s3 * 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 Products64 * 72 = 100s 10s 1s60 + 4 * 70 +2 =

60 * 70 = 42 0 060 * 2 = 1 2 0

4 * 70 = 2 8 0 4 * 2 = 8

45 10 8 46 0 8

Try It OutUse partial products multiplication

on these problems to solve for m.

137 * 65 = m625 * 30 = m72 * 15 = m

420 * 31 = m23 * 21 = m

Try It OutUse partial products multiplication

on these problems to solve for m.

137 * 65 = m625 * 30 = m72 * 15 = m

420 * 31 = m23 * 21 = m

M = 8905M =1875 M =1080 M =13020 M =483

Lattice Method

Try It OutUse lattice method of

multiplication on these problems to solve for m.

76 * 49 = m53 * 83 = m92 * 56 = m63 * 15 = m48 * 27 = m

M = 3724M =4399 M = 5152M =945 M =1296

Multiplying with DecimalsWhen 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 16We 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 8 0 3 2 0 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 DecimalsIf 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

5 3 4 8 9 0 .1424

.4 3 2 1

But How Do You Place the Decimal?First count the numbers that sit in decimal

place values. .89

X .16 5 3 4

8 9 0 1 4 2 4

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

Try It OutUse 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 = m6.8 * 4.5 = m0.12 * 0.9 = m0.3 * 0.919 = m2.7 * 5.6 = m

M = 4.2M = 30.60 or 30.6M = 0.108

M = 0.2754M = 15.12