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Rajesh’s plant grew 3cm last week. Sabrina’s plant grew \[2\dfrac{1}{2}\] times as fast as Rajesh’s plant. How many centimeters did Sabrina’s plant grow last week?

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Last updated date: 13th Jun 2024
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Answer
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Hint: Use the one person’s given plant’s length after growth and multiply the number of times the other person’s plant’s growth rate. Convert the mixed fraction into proper fraction by multiplying the whole number by denominator and add the numerator to form a new numerator and keep the denominator the same.
* General form of a mixed fraction is \[a\dfrac{b}{c}\] and it can be converted into proper fraction as \[a\dfrac{b}{c} = \dfrac{{a \times c + b}}{c}\]

Complete step-by-step answer:
We are given that Rajesh’s plant grew 3cm last week
\[ \Rightarrow \]Length that Rajesh’s plant grew after a week\[ = 3\]cm
We are given that Sabrina’s plant grew\[2\dfrac{1}{2}\]times as fast as Rajesh’s plant.
We convert the mixed fraction into a proper fraction.
We know mixed fraction \[a\dfrac{b}{c} = \dfrac{{a \times c + b}}{c}\]
Substitute the value of a as 2, b as 1 and c as 2 in the formula
\[ \Rightarrow 2\dfrac{1}{2} = \dfrac{{2 \times 2 + 1}}{2}\]
Add the terms in the numerator
\[ \Rightarrow 2\dfrac{1}{2} = \dfrac{5}{2}\]
Now we can find the length that Sabrina’s plant grew by multiplying the rate at which Sabrina’s plant grows with the length of Rajesh’s plant after growth.
\[ \Rightarrow \]Length that Sabrina’s plant grew after a week\[ = \dfrac{5}{2} \times 3\]cm
Multiply the whole number to the numerator.
\[ \Rightarrow \]Length that Sabrina’s plant grew after a week\[ = \dfrac{{15}}{2}\]cm
Divide the numerator by denominator
\[ \Rightarrow \]Length that Sabrina’s plant grew after a week\[ = 7.5\]cm

So, Sabrina’s plant grew 7.5 centimeters last week.

Note: Students might make mistakes while converting mixed fraction to proper fraction as they tend to multiply the whole number with numerator and then add the denominator. Keep in mind we multiply the whole number to number in denominator and then add the number in numerator which becomes our new numerator.