Solve the proportion.
[tex]\frac{r}{81}=\frac{1}{9}[/tex]
Answer (2)
To solve the proportion 81 r = 9 1 , multiply both sides by 81 to isolate r . This gives r = 9 81 , which simplifies to r = 9 . The final answer is 9 .
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Multiply both sides of the equation by 81: 81 r × 81 = 9 1 × 81 .
Simplify the equation: r = 9 81 .
Divide 81 by 9: r = 9 .
State the final answer: 9 .
Explanation
Understanding the Proportion We are given the proportion 81 r = 9 1 . Our goal is to find the value of r that makes this equation true.
Isolating the Variable To solve for r , we need to isolate it on one side of the equation. We can do this by multiplying both sides of the equation by 81. This will cancel out the 81 in the denominator on the left side.
Performing the Multiplication Multiplying both sides by 81, we get: 81 r × 81 = 9 1 × 81 r = 9 81
Simplifying the Fraction Now, we simplify the fraction 9 81 . Since 81 = 9 × 9 , we have: r = 9 9 × 9 = 9 So, the value of r that satisfies the proportion is 9.
Final Answer Therefore, the solution to the proportion is r = 9 .
Examples
Proportions are used in everyday life to scale recipes, convert currencies, and determine the size of objects in photographs. For example, if a recipe calls for 2 cups of flour for 1 cake, you can use a proportion to determine how much flour you need for 3 cakes. If cakes flour = 1 2 , then for 3 cakes, you would set up the proportion 1 2 = 3 x and solve for x to find that you need 6 cups of flour.
