The four basic operations are as follows:
(a) Positive integers are the same as natural numbers and so the previous definition applies. The product of two positive numbers is a positive number.
(b) The product of one positive number with another negative gives us a negative number.
(c) The product of a negative number with a positive number is negative.
(d) The product of a negative number with another negative number would give a positive number.
In brief: Sign of product absolute value
Positive $\times$ positive gives + multiplied
Positive $\times$ negative gives - multiplied
Negative $\times$ positive gives - multiplied
Negative $\times$ negative gives + multiplied
Negative 1 times a number gives opposite sign to the number.
Example: (-1) $\times$ number = (- number) i.e, (-1) $\times$ 3 = (-3)
Let us take an example elementary methods:
3 $\times$ 5 means 3 rows and 5 columns of an object. We take stars to show this problem.
* * * * *
* * * * *
* * * * *
Each row has 5 stars.
3 $\times$ 5 = 5 + 5 + 5 = 15
Or
Each column has 3 stars.
3 $\times$ 5 = 3 + 3 + 3 + 3 + 3 = 5
This can also be represented as:
* * *
* * *
* * *
* * *
* * *
3 $\times$ 5 is also 5 rows and 3 columns.
Multiplication of single digits is written as 3 $\times$ 5 and read as “3 times 5”
This means adding “3” to itself “5” times.
Multiplication of single digits is same as adding the first digit repeatedly second digit times.
3 $\times$ 5 = 5 $\times$ 3
Multiplication is adding the number repeatedly.
Let us do some problems.
- (2 $\times$ 4) = 2 + 2 + 2 + 2 = 8
- (9 $\times$ 8) = 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 = 72
- (7 $\times$ 5) = 7 + 7 + 7 + 7 + 7 = 35
- (3 $\times$ 9) = 3 + 3 + 3+ 3 + 3 + 3 + 3 + 3 + 3 = 27
- (8 $\times$ 7) = 8 + 8 + 8 + 8 + 8 + 8 + 8 = 56
- (1 $\times$ 1) = 1
- (5 $\times$ 0) = 0
- (2 $\times$ 2 $\times$ 2) = (2 + 2 ) $\times$ 2 = (2 +2) + (2 + 2) = 4 + 4 = 8
- (5 $\times$ 5) = 5 + 5 + 5 + 5 = 25
- (4 $\times$ 5) $\times$ 2 = (4 + 4 + 4 + 4 + 4) $\times$ 2 = 20 $\times$ 2 = 20 + 20 = 40
- 3 $\times$ 2 $\times$ 5 = (3 $\times$ 2) $\times$ 5 = (3 + 3) $\times$ 5 = 6 $\times$ 5 = 6 + 6 + 6 + 6 + 6 = 30
- 5 $\times$ 5 $\times$ 5 = ( 5 $\times$ 5 ) $\times$ 5 = (5 + 5 + 5 + 5 + 5) $\times$ 5 = 25 $\times$ 5 = 25 +25 +25 +25 +25 = 125
Multiplication of single digit numbers can be done on a number line also.
Example: 2 $\times$ 4
We start from (0) zero and go 2 numbers at a time. We repeat this process 4 times.
We reach number 8.
We use the fingers of our hands which correspond to numbers 6, 7, 8, 9,10.
We ask the kids to correspond 6, 7, 8, 9, 10 on both the hands.
This is used for multiplying 6, 7, 8, 9,10 by 6, 7, and 8, 9,10.
(6 $\times$ 6) to (6 $\times$ 10), (7 $\times$ 6) to (7 $\times$ 10), (8 $\times$ 6) to (8 $\times$ 10), (9 $\times$ 6) to (9 $\times$ 10)
Lets see how to multiply 8 times 6.
We ask the kids to join the finger pointing number 6 (thumb) of one hand with the finger pointing number 8 (middle finger) on the other hand.
The fingers towards our side from the joining point of the thumb and middle fingers are – two thumbs, one middle finger, and one index finger – 4 fingers.
Now, 4 becomes the tens place of the product of 6 $\times$ 8.
The remaining fingers are four fingers on one hand and two fingers on the other hand. 4 $\times$ 2 = 4 + 4 = 8.
8 is the units place.
6 $\times$ 8 = 48
Below you could see single digit multiplication word problems
Solved Examples
Question 1: In a play ground, four children are playing tennis together. All of them have seven balls. How many of the balls, four children having?
Solution:
Four children’s are playing tennis.
Each of them has seven balls.
Total number balls are denoted by A.
A = Number of children’s $\times$ Number of balls for each
= 4 $\times$ 7
Using multiplication operation,Multiply the above values
= 28 balls
The total number of balls are 28.
Question 2: In a restaurant, Williams’s family orders five pizzas to eat. Each pizza is divided into four equal pieces. How many of the total pieces do Williams’s family got?
Solution:
In Williams’s family, there are five members,
Each pizza is divided into four equal parts.
Total number of pieces of pizzas is denoted by A.
A = Number of pieces $\times$ Number of pieces ordered in the restaurant
= 4 $\times$ 5
Using multiplication operation, Multiply the above values
= 20
Solution to the total number of pieces of Williams’s family got is 20.