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Vladimir [108]
3 years ago
9

Jake’s measures the height of a tree to be 74 3/8

Mathematics
1 answer:
goblinko [34]3 years ago
7 0

I'm assuming the question is asking how tall the tree is if it has grown 2 3/4 inches.

The initial height of the tree is 74 3/8 inches and it grows 2 3/4 inches after six months. We can add these two numbers together to calculate the height of the tree now.

74\frac{3}{8} + 2\frac{3}{4}

Since these are both mixed numbers, we must find a common denominator to add our fractions. 8 is the lowest common denominator for 4 and 8. So:

74\frac{3}{8} + 2\frac{6}{8}

We can now add our whole numbers up (74 + 2) and add the numerators of the fractions together to get a single fraction (\frac{3}{8} + \frac{6}{8}).

74 + 2 = 76

\frac{3}{8} + \frac{6}{8} = \frac{9}{8}

Putting these two together, we get 76 \frac{9}{8}, which is equal to 77\frac{1}{8}.

We can also turn this answer into an improper fraction. This is done by multiplying the whole number by the denominator and adding the numerator. So in this case:

77 x 8 = 616

616 + 1 = 617

The denominator stays the same, so our answer as an improper fraction would be \frac{617}{8}.

So the tree is 77\frac{1}{8} inches tall, or \frac{617}{8} inches tall.

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\huge \boxed{\mathbb{QUESTION} \downarrow}

  • How do you simplify this?
  • x²y+xy² / y²+2/5 × xy

\large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}

\sf\frac{  { x  }^{ 2  }  y+x { y  }^{ 2  }    }{  { y  }^{ 2  }  + \frac{ 2  }{ 5  }   \times  xy  } \\

Factor the expressions that are not already factored.

_____

<u>How </u><u>to</u><u> factorise</u><u> </u><u>:</u><u>-</u>

<u>NUMERATOR</u> \downarrow

\sf \: x ^ { 2 } y + x y ^ { 2 }

Factor out xy.

\sf \: xy\left(x+y\right)

<u>DENOMINATOR</u> \downarrow

\sf{ y  }^{ 2  }  + \frac{ 2  }{ 5  }   \times  xy \\

Factor out 1/5.

\sf \: {\frac{1}{5}y\left(2x+5y\right)}  \\

_____

Continuing...

\sf\frac{xy\left(x+y\right)}{\frac{1}{5}y\left(2x+5y\right)}  \\

Cancel out y in both the numerator and denominator.

\sf\frac{x\left(x+y\right)}{\frac{1}{5}\left(2x+5y\right)}  \\

Expand the expression.

\sf\frac{x^{2}+xy}{\frac{2}{5}x+y}  \\

This can further simplified to as \downarrow

=    \boxed{\boxed{\bf\frac{5x\left(x  +y\right)}{2x+5y}}}

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