Solve for $r$ in the proportion: [tex]$\frac{r}{56}=\frac{33}{22}$[/tex]
Answer (2)
Multiply both sides of the equation by 56 to isolate r : r = 22 33 × 56 .
Simplify the fraction 22 33 to 2 3 .
Calculate r = 2 3 × 56 .
Simplify to find the value of r : 84 .
Explanation
Isolating r We are given the proportion 56 r = 22 33 . Our goal is to solve for r . To isolate r , we need to multiply both sides of the equation by 56.
Multiplying by 56 Multiplying both sides by 56, we get: 56 r × 56 = 22 33 × 56
Simplifying the equation This simplifies to: r = 22 33 × 56
Simplifying the fraction We can simplify the fraction 22 33 by dividing both the numerator and the denominator by their greatest common divisor, which is 11. So, 22 33 = 22 ÷ 11 33 ÷ 11 = 2 3 .
Substituting the simplified fraction Now we have: r = 2 3 × 56
Calculating r To calculate r , we multiply 2 3 by 56: r = 2 3 × 56 = 2 168 = 84
Final Answer Therefore, the value of r is 84.
Examples
Proportions are useful in everyday life. For example, if you know that 3 apples cost 2 , yo u c an u se a p ro p or t i o n t o f in d t h ecos t o f 15 a ppl es . S e tt in gu pt h e p ro p or t i o n \frac{3}{2} = \frac{15}{x} , w h ere x i s t h ecos t o f 15 a ppl es , a ll o w syo u t oso l v e f or x$ and find the cost. Proportions are also used in cooking, scaling recipes, and converting units.
To solve for r in the proportion 56 r = 22 33 , we isolate r by multiplying both sides by 56. After simplifying the fraction to 2 3 , we multiply it by 56 to find that r = 84 . Therefore, the value of r is 84.
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