Question Find the scale factor of Andy's scale drawing of a swimming pool, where 3 millimeters $=1$ meter. Express the scale factor as a simplified fraction.

Studdy Solution

STEP 1

Assumptions
1. The scale used in the drawing is 3 millimeters for every 1 meter in real life.
2. The scale factor is the ratio of the drawing's units to the real-life units.

STEP 2

To find the scale factor, we need to express both the drawing's units and the real-life units in the same type of units. Since the scale is given in millimeters per meter, we will convert meters to millimeters.
$1\, meter = 1000\, millimeters$

STEP 3

Now we can write the scale as a ratio of millimeters in the drawing to millimeters in real life.
$Scale\, factor = \frac{Drawing\, millimeters}{Real-life\, millimeters}$

STEP 4

Substitute the given scale into the ratio.
$Scale\, factor = \frac{3\, millimeters}{1000\, millimeters}$

STEP 5

Simplify the ratio by dividing both the numerator and the denominator by the greatest common divisor, which in this case is 1, since 3 is a prime number.
$Scale\, factor = \frac{3}{1000}$

STEP 6

The scale factor of the drawing is thus $\frac{3}{1000}$ , which is already in its simplest form as a fraction.
The scale factor of Andy's drawing is $\frac{3}{1000}$ .

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Question Find the scale factor of Andy's scale drawing of a swimming pool, where 3 millimeters $=1$ meter. Express the scale factor as a simplified fraction.

Studdy Solution

STEP 1

Assumptions
1. The scale used in the drawing is 3 millimeters for every 1 meter in real life.
2. The scale factor is the ratio of the drawing's units to the real-life units.

STEP 2

To find the scale factor, we need to express both the drawing's units and the real-life units in the same type of units. Since the scale is given in millimeters per meter, we will convert meters to millimeters.
$1\, meter = 1000\, millimeters$

STEP 3

Now we can write the scale as a ratio of millimeters in the drawing to millimeters in real life.
$Scale\, factor = \frac{Drawing\, millimeters}{Real-life\, millimeters}$

STEP 4

Substitute the given scale into the ratio.
$Scale\, factor = \frac{3\, millimeters}{1000\, millimeters}$

STEP 5

Simplify the ratio by dividing both the numerator and the denominator by the greatest common divisor, which in this case is 1, since 3 is a prime number.
$Scale\, factor = \frac{3}{1000}$

STEP 6

The scale factor of the drawing is thus $\frac{3}{1000}$ , which is already in its simplest form as a fraction.
The scale factor of Andy's drawing is $\frac{3}{1000}$ .

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Question Find the scale factor of Andy's scale drawing of a swimming pool, where 3 millimeters =1=1=1 meter. Express the scale factor as a simplified fraction.

Studdy Solution

STEP 1

Assumptions1. The scale used in the drawing is 3 millimeters for every 1 meter in real life.2. The scale factor is the ratio of the drawing's units to the real-life units.

STEP 2

To find the scale factor, we need to express both the drawing's units and the real-life units in the same type of units. Since the scale is given in millimeters per meter, we will convert meters to millimeters.1 meter=1000 millimeters1\, meter = 1000\, millimeters1meter=1000millimeters

STEP 3

Now we can write the scale as a ratio of millimeters in the drawing to millimeters in real life.Scale factor=Drawing millimetersReal−life millimetersScale\, factor = \frac{Drawing\, millimeters}{Real-life\, millimeters}Scalefactor=Real−lifemillimetersDrawingmillimeters​

STEP 4

Substitute the given scale into the ratio.Scale factor=3 millimeters1000 millimetersScale\, factor = \frac{3\, millimeters}{1000\, millimeters}Scalefactor=1000millimeters3millimeters​

STEP 5

Simplify the ratio by dividing both the numerator and the denominator by the greatest common divisor, which in this case is 1, since 3 is a prime number.Scale factor=31000Scale\, factor = \frac{3}{1000}Scalefactor=10003​

STEP 6

The scale factor of the drawing is thus 31000\frac{3}{1000}10003​, which is already in its simplest form as a fraction.The scale factor of Andy's drawing is 31000\frac{3}{1000}10003​.

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Question Find the scale factor of Andy's scale drawing of a swimming pool, where 3 millimeters $=1$ meter. Express the scale factor as a simplified fraction.

Assumptions
1. The scale used in the drawing is 3 millimeters for every 1 meter in real life.
2. The scale factor is the ratio of the drawing's units to the real-life units.

To find the scale factor, we need to express both the drawing's units and the real-life units in the same type of units. Since the scale is given in millimeters per meter, we will convert meters to millimeters.
$1\, meter = 1000\, millimeters$

Now we can write the scale as a ratio of millimeters in the drawing to millimeters in real life.
$Scale\, factor = \frac{Drawing\, millimeters}{Real-life\, millimeters}$

Substitute the given scale into the ratio.
$Scale\, factor = \frac{3\, millimeters}{1000\, millimeters}$

Simplify the ratio by dividing both the numerator and the denominator by the greatest common divisor, which in this case is 1, since 3 is a prime number.
$Scale\, factor = \frac{3}{1000}$

The scale factor of the drawing is thus $\frac{3}{1000}$ , which is already in its simplest form as a fraction.
The scale factor of Andy's drawing is $\frac{3}{1000}$ .