Determine whether each of the following numbers is an integer: 71, 56/8, 64/8, 15/2, 70.28.

Question image

Understand the Problem

The question is asking whether each of the given values, which include both whole numbers and fractions, are integers. To address this, we will evaluate each value by calculating the results of the fractions and then determining if each result is a whole number.

Answer

Yes for 71, $ \frac{56}{8} $, and $ -\frac{64}{8} $; No for $ -\frac{15}{2} $ and 70.28.
Answer for screen readers
  • Yes for 71, $ \frac{56}{8} $, and $ -\frac{64}{8} $.
  • No for $ -\frac{15}{2} $ and 70.28.

Steps to Solve

  1. Evaluate the Whole Number

The first value is 71. Since this is a whole number, we classify it as an integer.

  1. Calculate the Fraction

For the next value, we need to evaluate $ \frac{56}{8} $.

Calculating this gives:

$$ \frac{56}{8} = 7 $$

Since 7 is a whole number, it is an integer.

  1. Evaluate the Subtraction of the Fraction

Next, we evaluate $ -\frac{64}{8} $.

Calculating this gives:

$$ -\frac{64}{8} = -8 $$

Since -8 is a whole number, it is also an integer.

  1. Calculate Another Fraction

Now we calculate $ -\frac{15}{2} $.

Calculating this gives:

$$ -\frac{15}{2} = -7.5 $$

Since -7.5 is not a whole number, it is not an integer.

  1. Evaluate the Decimal

Finally, we examine 70.28. Since this is a decimal, it is not a whole number, so it is also not an integer.

  • Yes for 71, $ \frac{56}{8} $, and $ -\frac{64}{8} $.
  • No for $ -\frac{15}{2} $ and 70.28.

More Information

An integer is a whole number that can be positive, negative, or zero, but it cannot be a fraction or a decimal. In this case, 71, 7 ($ \frac{56}{8} $), and -8 ($ -\frac{64}{8} $) fit this definition, while -7.5 and 70.28 do not.

Tips

  • Misinterpreting fractions and assuming they are integers without calculating them.
  • Confusing decimals with integers; it’s important to recognize that decimals with non-zero figures after the point are not considered integers.
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