Question

Match each fraction to a reasonable estimate

Answer 1

Answer:

• -3/13 ≈ -1/4
• -6/11 ≈ -1/2
• -7/9 ≈ -3/4

Step-by-step explanation:

We'll drop all the minus signs, since they don't contribute anything but distraction.

When numerators or denominators are relatively large, changing their value by 1 unit will have a relatively small effect on the value of the fraction. For example, ...

  3/13 ≈ 3/12 = 1/4

If we compare the decimal values of these fractions, we see that ...

  3/13 ≈ 0.230769... (6-digit repeating decimal)

The closest of the offered "reasonable estimate" fractions is 1/4 = 0.25.

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Likewise, 6/11 ≈ 6/12 = 1/2. In decimal, these fractions are ...

  6/11 = 0.54... (2-digit repeat)

  1/2 = 0.5

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We can also increase or decrease both numerator and denominator by the same amount to get a fraction with nearly the same value. This works best when the numbers are larger.

  7/9 ≈ 6/8 = 3/4 . . . . . . both numerator and denominator decreased by 1

In decimal, these are ...

  7/9 = 0.7... (1-digit repeat)

  3/4 = 0.75