Giovanni went to Los Angeles, California for the summer to visit his cousins. He used a map of bus routes to get from the airport to his cousin’s house. The distance from the airport to his cousin’s house is 56 km. On his map, the distance was 4 cm. What is the scale factor as a fraction (like 1/20)?
(Recall: 1 km=100,000 cm, and scale factor is in the order of scale/actual).
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Nicole is running for school president. Her best friend designed her campaign poster, which measured 3 feet by 2 feet. Nicole liked the poster so much, she reproduced the artwork on rectangular buttons that measured 2 inches by
1 1/3 inches.
What is the scale factor (as a fraction)?
This is confusing can you tell me how to do it along with the answer please? Please don't do it just help me find the answer.
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Giovanni went to Los Angeles, California for the summer to visit his cousins. He used a map of bus routes to get from the airport to his cousin’s house. The distance from the airport to his cousin’s house is 56 km. On his map, the distance was 4 cm. What is the scale factor as a fraction
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To find the scale factor as a fraction, we need to compare the measurements on the map to the actual measurements in real life.
In Giovanni's case, the distance on the map is 4 cm and the actual distance is 56 km. We can convert the actual distance to cm by using the conversion factor 1 km = 100,000 cm. So, the actual distance in cm is 56 km * 100,000 cm/km = 5,600,000 cm.
Now we can calculate the scale factor. The scale factor is the ratio of the map distance to the actual distance. In this case, it is 4 cm / 5,600,000 cm. To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD), which in this case is 4. So, the scale factor is 1 cm / 1,400,000 cm or simplified as 1/1,400,000.
Now let's move on to Nicole's situation. Her campaign poster measures 3 feet by 2 feet, which means the actual measurements are 36 inches by 24 inches since 1 foot = 12 inches.
The rectangular buttons measure 2 inches by 1 1/3 inches. To compare these measurements, we need to convert the actual measurements to the same units as the button measurements, which is inches. So, the actual measurements are 36 inches by 24 inches.
To calculate the scale factor, we need to find the ratios of the corresponding sides. The scale factor is the ratio of the button length to the actual length and the ratio of the button width to the actual width.
For the length, the scale factor is 2 inches / 36 inches. To simplify this fraction, we divide both the numerator and denominator by their GCD, which is 2. So, the scale factor for the length is 1 inch / 18 inches or simplified as 1/18.
For the width, the scale factor is 1 1/3 inches / 24 inches. To simplify this fraction, we convert 1 1/3 to an improper fraction, which is 4/3. Then, we multiply the numerator and denominator by 3 to get rid of the fraction in the denominator. So, the scale factor for the width is (4/3) inches / (3 * 8) inches = 4 inches / 24 inches or simplified as 1/6.
Therefore, the scale factor for Nicole's campaign poster is 1/18 for the length and 1/6 for the width.