The image you provided is a worksheet titled "Percents from Fraction Models with Khan Academy." It appears to be designed to help students understand how to convert fractions and shaded areas into percents. Below, I will explain the solution for each question step by step.
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Worksheet Questions and Solutions
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Problem 1:
1.
Question 1: "In the first problem, how many 'bars' are in the entire square?"
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Solution: The first problem shows a square divided into 10 equal bars (or segments). Therefore, there are
10 bars in the entire square.
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Answer: 10
2.
Question 2: "What fraction of the bars are shaded? What is the fraction in reduced form?"
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Solution: In the first problem, 7 out of the 10 bars are shaded. This can be represented as the fraction \( \frac{7}{10} \). Since 7 and 10 have no common factors other than 1, the fraction is already in its simplest (reduced) form.
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Answer: \( \frac{7}{10} \)
3.
Question 3: "What decimal would represent the portion of the square that is shaded?"
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Solution: To convert the fraction \( \frac{7}{10} \) to a decimal, divide 7 by 10:
\[
\frac{7}{10} = 0.7
\]
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Answer: 0.7
4.
Question 4: "Show how Sal used the fraction to convert the representation into a percent."
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Solution: To convert the fraction \( \frac{7}{10} \) to a percent, multiply it by 100:
\[
\frac{7}{10} \times 100 = 70\%
\]
Alternatively, since the decimal form is 0.7, you can multiply 0.7 by 100 to get the same result:
\[
0.7 \times 100 = 70\%
\]
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Answer: 70%
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Problem 2:
5.
Question 5: "In the second problem, how many 'squares' are in the entire square? How many are shaded?"
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Solution: The second problem shows a square divided into 100 smaller squares (a 10x10 grid). Out of these 100 squares, 45 are shaded.
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Answer: 100 squares in total, 45 shaded
6.
Question 6: "What fraction of the square is shaded? Use that fraction to show what percent of the square is shaded."
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Solution: The fraction of the square that is shaded is \( \frac{45}{100} \). This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 5:
\[
\frac{45}{100} = \frac{45 \div 5}{100 \div 5} = \frac{9}{20}
\]
However, for converting to a percent, we typically use the unsimplified form \( \frac{45}{100} \).
To convert \( \frac{45}{100} \) to a percent, multiply by 100:
\[
\frac{45}{100} \times 100 = 45\%
\]
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Answer: \( \frac{45}{100} \) or \( \frac{9}{20} \) (in reduced form), and 45%
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Final Answers:
1. 10
2. \( \frac{7}{10} \)
3. 0.7
4. 70%
5. 100 squares in total, 45 shaded
6. \( \frac{45}{100} \) or \( \frac{9}{20} \), 45%
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Boxed Final Answer:
\[
\boxed{10, \frac{7}{10}, 0.7, 70\%, 100 \text{ squares in total, 45 shaded}, \frac{45}{100} \text{ or } \frac{9}{20}, 45\%}
\]
Parent Tip: Review the logic above to help your child master the concept of khan academy worksheets.
