Algebra Properties and Proportions Flashcards

Questions and Answers

A proportion is an equation that states two _____ are equal.

ratios

The extremes in the proportion 3/4=15/20 are?

3 and 20

All of the following proportions are equivalent except?

a+c/b+d

a/b = d/c

a/d = c/b (correct)

a/b = c/d

1:2 = 4:8. The product of both the means and the extremes is?

8 Signup and view all the answers

10/7 = x/5. Which of the following equations could be used to solve for the value of x?

7x = 50 Signup and view all the answers

If 9 : x = x:4, then x = _____.

6 Signup and view all the answers

Find the value of x in this proportion: (x+3)/6 = 5/4.

9/2 Signup and view all the answers

Two complementary angles have measures in the ratio of 1 to 5. Find the measure of each angle.

15 and 75 Signup and view all the answers

A 30-inch segment is cut into two parts whose lengths have the ratio 3 to 5. Find the length of the shortest part.

11.25 Signup and view all the answers

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.

20 Signup and view all the answers

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.

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.