Verified Answer :

  • Simplify the first term \(\frac{10}{5}\) to 2.
  • Express 2 as \(\frac{4}{2}\) to have a common denominator with \(\frac{3}{2}\).
  • Subtract the fractions: \(\frac{4}{2} - \frac{3}{2} = \frac{1}{2}\).
  • The final result is \(\boxed{\frac{1}{2}}\).

Explanation

  1. Simplifying the first term

We need to simplify the expression \(\frac{10}{5} - \frac{3}{2}\). The first step is to simplify the fraction \(\frac{10}{5}\). Since 10 divided by 5 is 2, we can write the expression as \(2 - \frac{3}{2}\).

  1. Finding a common denominator

To subtract \(\frac{3}{2}\) from 2, we need to express 2 as a fraction with a denominator of 2. Since \(2 = \frac{2}{1} = \frac{2 \times 2}{1 \times 2} = \frac{4}{2}\), the expression becomes \(\frac{4}{2} - \frac{3}{2}\).

  1. Performing the subtraction

Now that both terms have the same denominator, we can subtract the numerators: \(\frac{4-3}{2} = \frac{1}{2}\). This fraction is already in its simplest form. Thus, \(\frac{10}{5} - \frac{3}{2} = \frac{1}{2}\).

Examples

Imagine you have two large pizzas. If you have already eaten 10 out of 5 portions (which is actually just 2 whole pizzas) and then you give away 3 out of 2 portions (or 1 and a half pizzas), you can easily calculate how much pizza you have left. By using common denominators, you can see that you are left with exactly half a pizza. This simple arithmetic helps in everyday situations like cooking, sharing items, or managing time.

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