Operations on numbers
Multiplication
Terms related to multiplication
Multiplication: Repeated addition is to add equal groups or the same number over and over. Multiplication is the repetitive addition.
Multiplicand: The number that is to be multiplied is called the multiplicand.
Multiplier: The number with which we multiply is called the multiplier.
Product: The number that is obtained as the result of multiplication is called the product.
Grid method of multiplication
- Grid method is the method to multiply the number by portioning it into simpler place value.
- It is also known as box method.
Multiplication of 3-digit and 1-digit numbers using the grid method
Step 1: Expand the first number as
hundreds, tens, and ones within the grid.
Step 2: Multiply each digit of the first
number by the second number. Write all the products within the grid.
Step 3: Add all the obtained product
outside the grid.
Example:
Multiply 346 by 6 using the grid method.
Solution:
Therefore, 346 × 6 = 2076.
Multiplication of 2-digit numbers using the grid method
Step 1: Expand the first number as tens
and ones within the grid.
Step 2: Expand the second number as tens
and ones within the grid.
Step 3: Multiply each digit of the first
number by each digit second number. Write all the products within the grid.
Step 4: Add all the obtained product
outside the grid.
Example:
Multiply 28 by 24 using the grid method.
Solution:
Therefore, 24 × 28 = 672.
Multiplication of 3 or 4-digit numbers by 1-digit number
Step 1: Write the multiplicand on the top
Step 2: Write the multiplier below it.
Step 3: Multiply each digit of the
multiplicand by the multiplier starting from the extreme right.
Step 4: Write the product below the
horizontal line. If the product is more than 9 then carry the ten digits to
the next column.
Example:
Multiply 354 by 7.
Solution:
Multiplication of 2 or 3-digit number by 2-digit number
Step 1: Write the multiplicand on the top.
Step 2: Write the multiplier below it.
Step 3: Multiply the unit digit of the
multiplier by each digit of the multiplicand. If the product is more than 9
then carry the ten digits to the next column.
Step 4: Write the product below the
horizontal line.
Step 5: Place a 0 below the last digit of
the obtained productMultiply the tens digit of the multiplier by each digit
of the multiplicand. If the product is more than 9 then carry the ten digits
to the next column.
Step 6: Multiply the tens digit of the
multiplier by each digit of the multiplicand. If the product is more than 9
then carry the ten digits to the next column.
Step 7: Add both the obtained products.
Example:
Multiply 213 by 27.
Solution:
Write 213 on the top and 27 below it.
Properties of Multiplication:
- If a number is multiplied by 0 then the product is 0.
Example:
-
If a number is multiplied by 1 then the product is the number itself.
Example:
-
If the number “a” is multiplied by the number “b” then the product is same
as the number “b” multiplied by the number “a”.
Example:
