Question 42 of 42intermediate🔍 AnalyzeShort Answer4 marks

Observe the following multiplications. The answers have been provided.

12×13=15612 \times 13 = 156 11×14=15411 \times 14 = 154 13×14=18213 \times 14 = 182 11×12=13211 \times 12 = 132

In each case, do you see any pattern in the two numbers and their product? (Hint: Look at the coloured digits!) For what other multiplication problems will this pattern hold? Find 5 such examples.

Correct Answer

Pattern: For two consecutive numbers (like 11 and 12, 12 and 13, etc.), the product can be found using a special method.

Example: 12×1312 \times 13: Take the smaller number (12) Add the unit digit of the larger number: 12+3=1512 + 3 = 15 Multiply the unit digits: 2×3=62 \times 3 = 6 Giving 156

Five other examples:

14×15=21014 \times 15 = 210 15×16=24015 \times 16 = 240 16×17=27216 \times 17 = 272 17×18=30617 \times 18 = 306 18×19=34218 \times 19 = 342
Exercise: Chinnu's Coins | Q: 47 | (Page Page 18)
For More Understanding

Explanation

The chapter shows a pattern for multiplying consecutive numbers. For n×(n+1)n \times (n+1): Write n(n+1)n(n+1) as a two-digit result where the tens digit comes from n+(n+1)′sn + (n+1)'s unit digit manipulation, and units digit is the product of unit digits.

Solution Steps

  1. Step 1: Identify the pattern for consecutive number multiplication

  2. Step 2: Apply to find 5 new examples

  3. Step 3: Verify each multiplication

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