Question 47 of 47intermediate🔧 ApplyShort Answer2 marks

If 99×10099 \times 100 = 9900, without multiplication find 99×9999 \times 99.

Correct Answer

Step 1: Recognize that 99 = 100 - 1.

Step 2: Rewrite the multiplication: 99×9999 \times 99 = 99 × (100 - 1) 99×9999 \times 99 = 99×10099 \times 100 - 99

Step 3: Substitute the given value: 99×9999 \times 99 = 9900 - 99 99×9999 \times 99 = 9801

Reasoning: When one factor decreases by 1, the product decreases by the other factor.

Exercise: Let Us Think (Section 3) | Q: 6 | (Page Page 22)
For More Understanding

Explanation

Using the property that 99×9999 \times 99 = 99 × (100 - 1) = 99×10099 \times 100 - 99×199 \times 1 = 99×10099 \times 100 - 99. So we subtract 99 from 9900.

Solution Steps

  1. Step 1: Recognize that 99 = 100 - 1

  2. Step 2: 99×9999 \times 99 = 99 × (100 - 1) = 99×10099 \times 100 - 99

  3. Step 3: 99×9999 \times 99 = 9900 - 99 = 9801

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