Podcast
Questions and Answers
A proportion is an equation that states two _____ are equal.
A proportion is an equation that states two _____ are equal.
ratios
The extremes in the proportion 3/4=15/20 are?
The extremes in the proportion 3/4=15/20 are?
3 and 20
All of the following proportions are equivalent except?
All of the following proportions are equivalent except?
1:2 = 4:8. The product of both the means and the extremes is?
1:2 = 4:8. The product of both the means and the extremes is?
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10/7 = x/5. Which of the following equations could be used to solve for the value of x?
10/7 = x/5. Which of the following equations could be used to solve for the value of x?
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If 9 : x = x:4, then x = _____.
If 9 : x = x:4, then x = _____.
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Find the value of x in this proportion: (x+3)/6 = 5/4.
Find the value of x in this proportion: (x+3)/6 = 5/4.
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Two complementary angles have measures in the ratio of 1 to 5. Find the measure of each angle.
Two complementary angles have measures in the ratio of 1 to 5. Find the measure of each angle.
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A 30-inch segment is cut into two parts whose lengths have the ratio 3 to 5. Find the length of the shortest part.
A 30-inch segment is cut into two parts whose lengths have the ratio 3 to 5. Find the length of the shortest part.
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The perimeter of a triangle is 48 inches and the sides are in the ratio of 3:4:5. Find the length of the longest side.
The perimeter of a triangle is 48 inches and the sides are in the ratio of 3:4:5. Find the length of the longest side.
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Study Notes
Proportions and Ratios
- A proportion is an equation that states two ratios are equal.
- Extremes in a proportion are the first and last terms; for example, in 3/4 = 15/20, the extremes are 3 and 20.
Equivalence of Proportions
- All proportions can be expressed in equivalent forms, but not all variations are equivalent; for example, a/d ≠ c/b is not equivalent to other forms.
Product of Means and Extremes
- For the proportion 1:2 = 4:8, calculating the product of the means (24) and extremes (18) gives a result of 8.
Solving for Unknowns
- The equation 10/7 = x/5 can be rewritten to solve for x as 7x = 50.
- For the proportion 9 : x = x : 4, the value of x is determined to be 6.
Finding Values in Proportions
- To find x in the proportion (x+3)/6 = 5/4, the solution yields x = 9/2.
- Two complementary angles in the ratio of 1 to 5 measure 15 degrees and 75 degrees respectively.
Ratio and Lengths
- A segment of 30 inches cut in a ratio of 3 to 5 results in the shortest part measuring 11.25 inches.
- In a triangle with a perimeter of 48 inches and sides in a ratio of 3:4:5, the longest side measures 20 inches.
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Description
Test your knowledge on algebraic properties and proportions with these flashcards. Each card provides a key term related to ratios and proportions, along with its definition. This quiz is suitable for students aiming to strengthen their understanding of algebra concepts.
