Multiplying numbers near 100 – Part 2

In the section, “Multiplying numbers near 100 – Part 1“, we discussed how to  multiply 2 numbers which are near base 100.

But there are some additional cases which need special attention. When we multiply 2 figures on right, the result can be of 3 digits, i.e. it will become carry if number is positive and borrow if number is negative. For example, say we have to find 123 x 105; The figures on right are 23 and 5, and resultant product of 23 and 5 is 115. Here we have carry as 1.

There can be 3 special cases:
Case 4: Multiplying numbers just above 100, which gives carry on right part
Let us understand this method with an example.
116 x 112
116 is 16 above 100
112 is 12 above 100
Since 100 has 2 zeroes, so there will be 2 digits in the right part.
To get right part, we multiply 2 figures on right vertically, i.e. 16 x 12 = 192. Right part will become 92 and 1 will be carried to left part.
To get left part, we perform crosswise addition of 1st number with 2nd figure on right (116 + 12) or 2nd number with 1st figure on right (112 + 16) and further add carry 1.

Case 5: Multiplying numbers just below 100, which gives carry on right part
Let us understand this method with an example.
84 x 92
84 is 16 below 100
92 is 8 below 100
Since 100 has 2 zeroes, so there will be 2 digits in the right part.
To get right part, we multiply 2 figures on right vertically, i.e. (-16) x (-8) = 128. Right part will become 28 and 1 will be carried to left part.
To get left part, we perform crosswise addition of 1st number with 2nd figure on right (84 + (-8)) or 2nd number with 1st figure on right (92 + (-16)) and further add carry 1.

Case 6: Multiplying numbers on either side of 100, which gives carry on right part
Let us understand this method with an example.
115 x 91
115 is 15 above 100
91 is 9 below 100
Since 100 has 2 zeroes, so there will be 2 digits in the right part.
To get right part, we multiply 2 figures on right vertically, i.e. 15 x (-9) = (-135). To make Right part positive, we borrow 2 from Left part, i.e. 200 + (-135) = 65.
To get left part, we perform crosswise addition of 1st number with 2nd figure on right (115 + (-9)) or 2nd number with 1st figure on right (91 + 15)) and further subtract 2 as 2 was borrowed in previous step, i.e. 115 + (-9) – 2 = 104 or 91 + 15 – 2 = 104.

With this method, we can multiply any pair of numbers which are close to base 100 and produce carry; For example: 112 x 115, 113 x 117, 121 x 84, 92 x 83, 83 x 89 etc.

 

⇐ Practice Test: Day 2

Practice Test: Day 1 ⇒