Question

assume that each circle shown below represents one unit. express the shaded amount as an improper fraction and as a mixed number.

answer attempt 1 out of 2
fraction:

mixed number:

Explanation:

Step1: Analyze the circles

Each circle is divided into 10 equal parts. The first circle is fully shaded (10/10), and the second circle has 6 shaded parts (6/10).

Step2: Calculate total shaded as improper fraction

Total shaded parts: \(10 + 6 = 16\), so improper fraction is \(\frac{16}{10}\) (simplify to \(\frac{8}{5}\) if needed, but original division is 10 parts, so initially \(\frac{16}{10}\) or reduced \(\frac{8}{5}\)). Wait, wait, first circle is 10/10 (1 whole), second circle: total parts 10, shaded 6. So total shaded is \(1 + \frac{6}{10}\) as mixed, or \(\frac{10 + 6}{10}=\frac{16}{10}=\frac{8}{5}\) (simplified) or \(\frac{16}{10}\) (original). Wait, maybe the circles are divided into 10? Wait the first circle has 10 shaded, second: let's count. First circle: 10 segments, all shaded. Second circle: 10 segments, 6 shaded (since 4 are white). So total shaded: 10 + 6 = 16, over 10. So improper fraction: \(\frac{16}{10}\) (or simplify to \(\frac{8}{5}\)). Mixed number: \(1\frac{6}{10}\) (or \(1\frac{3}{5}\)). Wait, maybe the denominator is 10? Let's check again.

Wait, first circle: 10 equal parts, all shaded (1 unit). Second circle: 10 equal parts, 6 shaded. So total shaded: 1 (from first) + 6/10 (from second) = 16/10 (improper) or 1 6/10 (mixed). Simplifying: 16/10 = 8/5, 1 6/10 = 1 3/5. But maybe the problem uses denominator 10. Let's confirm.

So step1: each circle is 1 unit, divided into 10 parts. First circle: 10/10 shaded. Second circle: 6/10 shaded. Total shaded: 10/10 + 6/10 = 16/10 (improper fraction). Mixed number: 1 (from 10/10) + 6/10 = 1 6/10.

Step3: Write improper and mixed

Improper fraction: \(\frac{16}{10}\) (or \(\frac{8}{5}\) if simplified). Mixed number: \(1\frac{6}{10}\) (or \(1\frac{3}{5}\)). But let's see the original division. The circles have 10 parts each. So first circle: 10/10, second: 6/10. So total: 16/10 (improper) and 1 6/10 (mixed).

Wait, maybe I miscounted. Let's look at the second circle: how many white? 4. So shaded: 10 - 4 = 6. So yes, 6. So improper fraction: (10 + 6)/10 = 16/10 = 8/5 (simplified). Mixed number: 1 + 6/10 = 1 3/5 (simplified) or 1 6/10.

So the answer:

Improper fraction: \(\frac{16}{10}\) (or \(\frac{8}{5}\))

Mixed number: \(1\frac{6}{10}\) (or \(1\frac{3}{5}\))

But let's check the problem again. The question says "each circle shown below represents one unit. Express the shaded amount as an improper fraction and as a mixed number."

So first circle: 1 unit (10/10). Second circle: 6/10 shaded. So total shaded: 1 + 6/10 = 16/10 (improper) or 1 6/10 (mixed). Simplifying 16/10 to 8/5 and 6/10 to 3/5, so 1 3/5.

So:

Fraction (improper): \(\frac{16}{10}\) (or \(\frac{8}{5}\))

Mixed Number: \(1\frac{6}{10}\) (or \(1\frac{3}{5}\))

But maybe the circles are divided into 10, so initial is 16/10 and 1 6/10.

Answer:

Fraction: \(\frac{16}{10}\) (or \(\frac{8}{5}\))
Mixed Number: \(1\frac{6}{10}\) (or \(1\frac{3}{5}\))

(Note: If simplifying, \(\frac{8}{5}\) and \(1\frac{3}{5}\) are simplified forms. If keeping original denominator, \(\frac{16}{10}\) and \(1\frac{6}{10}\).)