Question

A tree limb hangs 5 1/4 feet from a telephone wire. The city trims back the branch before it grows within 2 1/2 feet of the wire. Will the city allow the tree to grow 2 3/4 more feet?

Answer 1

the city will let it grow 2(3/4) more feet but it will be cut if it grows any further

Explanation:

Given A tree limb hangs 5(1/4) feet from a telephone wire

If the limb grows 2(3/4) more feet, then its distance from the wire will be:

distance = 5(1/4) - 2(3/4)

Distance = 21/4 - 11/4

Distance = 10/4 = 2(1/2)

Therefore, the city will let it grow 2(3/4) more feet but it will be cut if it grows any further.

Answer 2

Answer: The city won't allow the tree to grow
`2(3)/(4)` more feet.

Step-by-step explanation:

We need to make the conversion from mixed numbers to improper fractions:

• Multiply the whole number part by the denominator of the fraction.
• The sum of this product and the numerator of the fraction, will be the numerator of the improper fraction.
• The denominator does not change.

Then:

`5(1)/(4)\ ft=(((5*4)+1)/(4))\ ft=(21)/(4)\ ft\\\\2(1)/(2)\ ft=(((2*2)+1)/(2))\ ft=(5)/(2)\ ft`

We must subtract
`(21)/(4)` and
`(5)/(2)`.

Since the denominators are different, we must find the Least Common Denominator (LCD):

`4=2*2=2^2\\\\2=2\\\\LCD=2^2=4`

Finally, subtracting the fractions, we get:

`(21)/(4)-(5)/(2)=((21)(1)-(5)(2))/(4)=(11)/(4)\ ft`

To convert this result to mixed numbers:

• When we divide the numerator 11 by the denominator 4, we get a quotient of 2. This will be the whole number.
• We also get a remainder of 3. This will be the numerator of the fraction.
• The denominator does not change.

Then:

`(11)/(4)\ ft=2(3)/(4)\ ft`

If the tree grows
`2(3)/(4)` feet more, will be at the limit allowe. According to the exercise, the city trims back the branch before this limit.

Therefore, the city won't allow the tree to grow another
`2(3)/(4)` feet.