Appreciating product
We already know the following about the product of multiplication:
- It is the outcome of a multiplication process – we multiply to get the product of the numbers being multiplied; this product summaries the required information or action.
- Quantitatively, it is the same as the sum of repeatedly added numbers.
- It has the same unit as the sum of the multiplicands (assuming multipliers are numerals).
- It can be more, less, or equal to the multiplicand (it all depends on the multiplier).
- It is one quantity, one number.
- From the product, we cannot figure out the multiplier and multiplicand that resulted in the product.
- Various combinations of multiplier and multiplicand can give us the same product.
- There is a loss of information when a multiplication expression is reduced to its product. For example, the expression 3 x 7 books tell us that there are 3 sets of 7 books. The product – 21 books – does not contain the information of ‘3 sets of 7 books’. 21 books could also be 7 sets of 3 books.
While this list of characteristics is longer than those we discussed for multiplicand and multiplier, the product is a simpler idea. Here are a few examples of product:
1. 68 students
(Product of students of 2 sections)
2. 1 Km
(Product of ‘1 hour x 1 km/hour’)
3. 120 chairs
(10 rows of 12 chairs in every column)
The number of chairs (put in a rectangular arrangement) in a cinema hall is the product of the number of rows and the number of columns.
4. INR 8400
(Product of ‘7 nights of hotel room rent at the rate of INR 1200/night)
The amount of money you pay the hotelier after staying for a week is the product of room charges per day and the number of days stayed (1 week)
5. 30 Rooms
(Product of ‘10 flats and 3 rooms/flats’)
The number of rooms in a building of 10 flats is the product of rooms per flat and the number of flats (10 flats).
6. 150 teachers
(Product of ‘5 schools and 30 teachers/school’)
The number of teachers in 5 different schools is the product of teachers per school and the number of schools.
7. 80 square metres
(8m x 10m)
The area of a rectangle of dimensions 8m and 10m is the product of 8m and 10m
8. 100 balloons
(10 x 10 balloons)
The product of 10 sets and 10 balloons in each set is 100 balloons.
9. 1200 families
(3 localities x 400 families/locality)
The product of 400 families/locality and 3 localities is 1200 families.
10. 1000 litres
(1m x 1m2)
The volume of a tank whose base area is 1m2 and height is 1m is 1000 litres.
Evidently, product is a quantity of a certain specific thing – a number.
Summary
Product is the outcome of a multiplication process – we multiply to get the product of the numbers being multiplied; product summaries the needed information, or action. It has the same unit as the sum of the multiplicands (assuming multipliers are numerals)
Excerpted from the book ‘Foundations of Multiplication (Mathematics as a language)’ by Sandeep Srivastava and Saloni Srivastava