Proportions Lesson Assessment
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Questions and Answers

Which of the following situations represents a proportion?

  • A student reads 20 pages of a book in 30 minutes, and then reads 40 pages in 60 minutes. (correct)
  • A car travels 100 kilometers in 2 hours, and then travels 200 kilometers in 4 hours.
  • A worker earns 50 LE for 4 hours of work, and then earns 75 LE for 6 hours of work.
  • A recipe calls for 2 cups of flour for 12 cookies, and then calls for 3 cups of flour for 18 cookies.

    • Magdy can run 75 meters in 25 seconds. If he maintains his speed, what proportion can be used to find the time (X) he needs to run 300 meters?

  • $\frac{75}{25}=\frac{X}{300}$
  • $\frac{75}{300}=\frac{25}{X}$
  • $\frac{75}{25}=\frac{300}{X}$ (correct)
  • $\frac{25}{75}=\frac{X}{300}$

    • Which of the following graphs represents a proportional relationship?

  • A graph of a curve going upward, but not straight.
  • A graph of a line going upward, but not straight.
  • A graph of a line going downward at a constant rate.
  • A graph of a line going upward at a constant rate. (correct)

    • Are the quantities 5, 8, 15, and 24 proportional? If yes, what is the proportion?

    <p>Yes, (\frac{5}{8} = \frac{15}{24}) (C)</p> Signup and view all the answers

    Which of the following represents a proportion?

    <p>$\frac{5}{4} = \frac{?}{7.5}$ (A), $\frac{2}{5} = \frac{?}{10}$ (D)</p> Signup and view all the answers

    Solve the proportion (\frac{3}{4} = \frac{X}{20}). What is the value of X?

    <p>X = 15 (A)</p> Signup and view all the answers

    Complete the proportion (\frac{6}{8} = \frac{}{}) with the simplest possible fractions.

    <p>$\frac{6}{8} = \frac{3}{4}$ (C)</p> Signup and view all the answers

    The table shows Ibrahim's savings over several months. Are the amounts saved proportional to the number of months?| Amount (LE) | Number of Months |---|---| | 300 | 2 | | 600 | 4 | | 900 | 6 | | 1200 | 8 |

    <p>Yes, the amounts saved are proportional to the number of months because the ratio between amount saved and the number of months is constant. (D)</p> Signup and view all the answers

    Flashcards

    Proportion

    An equation stating that two ratios are equal.

    Identifying Proportion

    Determining if two quantities are in proportion using ratios.

    Graph of Proportion

    A straight line graph indicates a proportional relationship.

    Using Proportions to Solve

    Setting up an equation with known and unknown values to find missing quantities.

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    Solving Proportions

    The process of finding the value of a variable in a proportion.

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    Partial Proportion Example

    An example: if 2/5 = ?/10, solve for the missing part.

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    Proportional Savings

    Savings that increase steadily over equal time periods show proportionality.

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    Ratio Comparison

    The relationship between two quantities, showing how many times one value contains another.

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    Study Notes

    Lesson Assessment: Proportions

    • Conceptual Understanding:

      • Proportions: A proportion is an equation stating that two ratios are equal.
      • Example 1: If the price of 3 kg of bananas is 54 LE, and 5 kg is 80 LE, this demonstrates a proportion (the price per kg remains constant).
      • Example 2: If someone can run 75 meters in 25 seconds, to run 300 meters they would need a proportional amount of time (the speed remains constant). Correct proportion setup: 75/25 = 300/x
      • Example 3: Reading 3 books in 2 months, and 9 books in 6 months shows a proportion (the rate of reading books per month remains constant).
      • Example 4: 144 pulses in 2 minutes and 210 pulses in 3 minutes. (checking proportionality, pulse rate per minute remains constant.)

    • Proportional Graphs:

      • Proportional relationships are shown with straight lines passing through the origin (0,0) in a graph
      • Graphs showing curves depict non-proportional relationships

    • Applying Scientific Concepts:

      • Solving Proportions: Finding unknown values in a proportion is done using proportional relationships and cross-multiplication.
      • Example: Solving 4/x = 20/5, x = 1.
      • Example: Solving a:16 = 5:4
      • Proportional quantities are quantities that maintain a fixed ratio or rate (constant).

    • Proportion Exercises:

      • Identifying proportions: Exercises test the understanding of whether the given relationships are proportional by checking if the ratios are equivalent or if rates are constant.
      • Writing proportions: Exercises provided to write the proportion using given quantities.
      • Completing proportions: Exercises are given to complete the proportion with missing values by finding the missing quantity.

    Saving Amounts and Proportionality

    • Saving amounts: Example data demonstrates how much someone saves over time.
    • Proportionality check: The provided data can be used to determine if the amount saved is proportional to the number of months. (Checking if the ratio of amount saved per month is constant using the example data).

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    Description

    Test your understanding of proportions with this lesson assessment. Learn key concepts such as proportional relationships, ratio equations, and linear graphs. This quiz includes real-world examples to demonstrate how proportions apply in various scenarios.

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