Number Sense Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Without calculating exactly, determine which is greater: 3×993 \times 99 or 4×744 \times 74.

Solution

  1. 1
    Estimate each product: 3×99≈3×100=3003 \times 99 \approx 3 \times 100 = 300.
  2. 2
    Estimate the second: 4×74≈4×75=3004 \times 74 \approx 4 \times 75 = 300. These are very close.
  3. 3
    Refine: 3×99=2973 \times 99 = 297 and 4×74=2964 \times 74 = 296. So 3×99>4×743 \times 99 > 4 \times 74.

Answer

3×99>4×743 \times 99 > 4 \times 74
Number sense means using benchmark estimates to compare quantities before computing exactly. When estimates are close, a small refinement is needed. This strategy avoids unnecessary full computation.

About Number Sense

An intuitive understanding of numbers, their relative size, and how they relate to each other and to real quantities.

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More Number Sense Examples

Example 2 medium

A school has 483 students. Each classroom holds about 30 students. Approximately how many classrooms

Example 3 easy

Place the following numbers on a mental number line from smallest to largest: [formula], [formula],

Example 4 medium

Without a calculator, is [formula] closer to [formula] or to [formula]? Explain.

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