A certain plant grows 1 2/5
inches every week. How long will it take the plant to grow 7 4/5
inches?
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Part 1
How long will it take the plant to grow 7 4/5
inches?
To solve this problem, we need to determine how many weeks it will take for the plant to grow 7 4/5 inches.
First, we need to convert the mixed number 7 4/5 into an improper fraction.
7 4/5 = (7 * 5 + 4)/5 = 39/5
Next, we can set up a proportion to find the number of weeks it will take for the plant to grow 39/5 inches.
1 2/5 inches/week = 39/5 inches/x weeks
Now, we can cross multiply and solve for x:
(1 2/5) * x = (39/5)
To simplify, we can convert the mixed number 1 2/5 into an improper fraction:
(7/5) * x = 39/5
To isolate x, we can multiply both sides of the equation by the reciprocal of 7/5, which is 5/7:
(7/5) * (5/7) * x = (39/5) * (5/7)
This simplifies to:
x = 39/7
Therefore, it will take the plant approximately 39/7 weeks to grow 7 4/5 inches.
To find out how long it will take the plant to grow 7 4/5 inches, we can set up a proportion.
Let "x" represent the number of weeks it will take for the plant to grow 7 4/5 inches.
The proportion can be set up as follows:
1 2/5 inches/week = 7 4/5 inches/x weeks
To solve the proportion, we first need to convert the mixed numbers to improper fractions:
1 2/5 = (5*1 + 2)/5 = 7/5
7 4/5 = (5*7 + 4)/5 = 39/5
The proportion can now be written as:
7/5 inches/week = 39/5 inches/x weeks
Next, we can cross-multiply:
(7/5)(x) = (39/5)(1)
Simplifying, we get:
7x = 39
Finally, we can solve for x by dividing both sides of the equation by 7:
x = 39/7
Therefore, it will take the plant approximately 5 and 4/7 weeks to grow 7 4/5 inches.
To find out how long it will take for the plant to grow 7 4/5 inches, we need to divide the total growth (7 4/5 inches) by the growth rate (1 2/5 inches per week).
First, let's convert 7 4/5 inches into an improper fraction.
To do this, we multiply the whole number (7) by the denominator (5) and add the numerator (4).
7 * 5 = 35
35 + 4 = 39
So, 7 4/5 inches can be written as 39/5 inches.
Now, let's convert 1 2/5 inches per week into an improper fraction.
1 * 5 = 5
5 + 2 = 7
So, 1 2/5 inches per week can be written as 7/5 inches per week.
To find out how long it will take for the plant to grow 39/5 inches at a rate of 7/5 inches per week, we divide the total growth (39/5 inches) by the growth rate (7/5 inches per week).
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
So, the calculation becomes:
(39/5) ÷ (7/5)
Multiplying by the reciprocal, this becomes:
(39/5) * (5/7)
The 5 in the numerator and denominator cancel out, leaving us with:
39/7
Therefore, it will take the plant approximately 39/7 weeks to grow 7 4/5 inches.