Ways to Multiply and Divide Class 5 Notes Maths Chapter 13

Multiplication 

• Multiplication is a method to find result of addition of repeated numbers.
• Symbol used for multiplication is ×.
• Think addition of the same number, say 5, 2 times 5+5=10 but you can do multiplication as 5×2=10. 
• But if you need to add 5 for 13 times then will you add them 13 times? No. Now you will prefer an alternative of addition that is nothing but multiplication. For Example, 5 + 5 + 5+ 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 65 but when we multiply we have 5 × 13 = 65 (from the table 13).
• In multiplication, the multiplication table is very important to multiply 2 or more digits with another 2 or more digits number.

Multiplication table

• 1 to 10
  
• 11 to 20
  

Example 1: Ram is earning ₹245 per day, how much will he earn in a week?

Here given that Ram is earning ₹245 in a day.
To find total earning in a week means in 7 days.
245 = 200 + 40 + 5

245 × 7 =  1400 + 280 + 35 = 1715
So, Ram will earn ₹1715 in a week.

Multiplication of Higher Numbers by Two methods
Method 1: To multiply 485 by 46, we will follow the following steps, 485=400+80+5 and 46=40+6

485 × 46 = 18400 + 3680 + 230 = 22310

Method 2: To multiply 485 by 46, we will follow the following steps,

Example: Multiply 698 by 25.

Here the given numbers are 698 and 25.

To multiply 698 by 25, we will follow the following steps, 698 = 600 + 90 + 8 and 25 = 20 + 5

698 × 25 = 15000 + 2250 + 200 = 17450
Or, To multiply 698 by 25, we will follow the following steps,

Multiplication Creates Pattern

Example: Multiply 111 by 111.

Given numbers are 111 and 111

Isn’t it interesting?

Division

• Division is a method to find a number equal parts of a number.
• Symbol used for division is ÷.

• Think of a number, let 36 and to divide it into 4 equal parts you will do it as 36 = 9 + 9+ 9 + 9 = 4 × 9. Now we have 36 ÷ 4 = 9. Each equal part is 9.
• Now to divide 9786 by 6
  
  Here we can rewrite 9786 as 1631×6+0=9786 
• Divisor)Dividend(Quotient
  −XXXXX/Remainder

Example: Sonam has ₹500, she wants to purchase notebooks whose rate is ₹43 each. How many notebooks can she purchase? 

Given that Sonam has ₹500. Rate of the notebook is ₹43 each.
To find 500÷43.

Here, 11 notebooks she can purchase. 

• In the above example you observe that at the end there is 27 instead of 0. It is called remainder. 
• Again rewrite 500 as 11 × 43 + 27 = 473 + 27 = 500

Multiplication and Division are related

• Multiplication and division are related to each other.
• If a × b=c then c ÷ a = b or c ÷ b = a, where a, b, c ≠ 0.
• Multiple 951 by 14 then 951 × 14 = 13314.
  
  Now divide 13314 by 14 then 13314 ÷ 14 = 951.