What are scales? In a mathematical term, scales measure (typically) length and width. They are, simply, a representation of a full scale model/object based on a ratio and a proportion. A scale model can be one-half, one third, one tenth or even a thousandth the size of the actual. A scale model can also be larger that the actual object, two times, three times and even five times. Determining which number represents what model is the first step to solving a scale-type mathematical question.
Now here we have a little dilemma, let’s say, your friend has a strange desire to find out how much one centimeter of her teddy bear would stand up to a real wild grizzly bear. Now if the stuffed animal was around 40cm tall, and a real bear (if you got close enough to count) is about 182 cm tall; a scale would easily show you how many centimeters long are equivalent to your huggable toy. To find the answer, take the first two numbers (40cm and 182cm) and turn it into a fraction with 40cm as the numerator and 182cm as the denominator. Now with that fraction, make a proportion with the second fraction as 1cm as the numerator over x as the denom
inator (when you make a scale, the first number has to equal 1). Then cross-multiply 1cm by 182cm and divide by 40cm. Therefore, x equals 4.55; the ratio now becomes 1:4.55. Make sure you tell your friend that ‘for every 1cm of her stuffed animal, a real bear would be 4.55 cm’.
Now here we have a little dilemma, let’s say, your friend has a strange desire to find out how much one centimeter of her teddy bear would stand up to a real wild grizzly bear. Now if the stuffed animal was around 40cm tall, and a real bear (if you got close enough to count) is about 182 cm tall; a scale would easily show you how many centimeters long are equivalent to your huggable toy. To find the answer, take the first two numbers (40cm and 182cm) and turn it into a fraction with 40cm as the numerator and 182cm as the denominator. Now with that fraction, make a proportion with the second fraction as 1cm as the numerator over x as the denom
inator (when you make a scale, the first number has to equal 1). Then cross-multiply 1cm by 182cm and divide by 40cm. Therefore, x equals 4.55; the ratio now becomes 1:4.55. Make sure you tell your friend that ‘for every 1cm of her stuffed animal, a real bear would be 4.55 cm’. Once you measure an objects size, you can upsize or downsize by an appropriate number to compare the scale model to the full size.
You do this by taking the number of mm/cm/m (or any other means of measuring) of the full scale model or the actual item and turn it into a fraction. Then with that fraction, turn the equation into a proportion and with that proportion, comes the result of a ratio. So, to sum up; a scale is a ratio showing the differences between a length in a drawing/model and an actual length.
You do this by taking the number of mm/cm/m (or any other means of measuring) of the full scale model or the actual item and turn it into a fraction. Then with that fraction, turn the equation into a proportion and with that proportion, comes the result of a ratio. So, to sum up; a scale is a ratio showing the differences between a length in a drawing/model and an actual length.
3 comments:
Great post! You really put quite a bit of thought into this. I liked the way you used the "bear" idea for your example. Way to go!! (Who is our next blogger from 8Z?)
WOW really good!! I liked that it was easy to read!!
GO BEARS IN WINTER!!!!
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