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3 years ago

Show how Carly can work out 171/2% of 240 in her head

Mathematics

1 answer:

KATRIN_1 [288]3 years ago

5 0

17 ½ % of 240

First option

Change the fraction ½ to a decimal. It would be 0.5 ( 1 divided by 2)

½=0.5

You will add the whole number 17 to the result.

17 + 05 = 17.5

Now you will divide by 100 (percent)

17.5 /100 To divide a decimal by 100, move the decimal point two places to the left.

17.5 /100 = 0.175 times 240

0.175 x 240 = 42

Second option

Change the percent to an improper fraction

17 ½= 35/2 (you have to multiply (2 x 17) plus 1 equals 35 over 2 ( keep the denominator). It will be 35/2. Put the other number (240) over 100 and multiply.

35/2 x 240/100 = 42

There is another way . You can simplify

Cancel all the zeros that you have and start to reduce.

7 12

35 x 24 0 = 42

2 10 0

1 5

17 ½ % of 240 = 42

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3 years ago

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3 years ago

Segment AB has endpoints at A(-7,2) and b(9,-6). Point P lies on AB such that AP:BP=3:1

bekas [8.4K]

The coordinates of the point P which divides the line segment AB made by the points A(-7,2) and B(9,-6) is (x,y) = (5,-4)

<h3>What is the coordinate of the point which divides a line segment in a specified ratio?</h3>

Suppose that there is a line segment $\overline{AB}$ such that a point P(x,y) lying on that line segment $\overline{AB}$ divides the line segment $\overline{AB}$ in m:n, then, the coordinates of the point P is given by:

$(x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)$

where we have:

the coordinate of A is $(x_1, y_1)$
and the coordinate of B is $(x_2, y_2)$

We're given that:

Coordinate of A is $(x_1, y_1)$ = (-7,2)
Coordinate of B is $(x_2, y_2)$ = (9.-6)
The point P lies on AB such that AP:BP=3:1 (so m = 3, and n = 1)

Let the coordinate of P be (x,y), then we get the values of x and y as:

$(x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)\\\\(x,y) = \left( \dfrac{3(9) + 1(-7)}{3+1} , \dfrac{3(-6) + 1(2)}{3+1} \right)\\\\(x,y) = \left( \dfrac{20}{4} , \dfrac{-16}{4} \right) = (5,-4)$

Thus, the coordinates of the point P which divides the line segment AB made by the points A(-7,2) and B(9,-6) is (x,y) = (5,-4)

Learn more about a point dividing a line segment in a ratio here:

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ale4655 [162]

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3 years ago