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Design
Published in Wanda Grimsgaard, Design and Strategy, 2023
The aspect ratio in a format is the ratio of the width to the height of the format. The aspect ratio of a two-dimensional figure is the ratio between the longest and the shortest side, between width and the height (Rouse, 2005) when the rectangle has landscape orientation. In mathematics, the ratio is expressed as two numbers separated by a colon, x:y (pronounced: x to y). The values x and y do not represent the actual width and height, but the ‘ratio’ of width to height. For example, 8:5, 16:10, and 1.6: 1 have the same aspect ratio (‘Aspect Ratio,’ n.d.). Rational numbers: All rational numbers can be written as a ratio, a fraction, or a decimal number of a whole number (integer). Example: Ratio 1:2, fraction 1/2, recalculated 5/10 or decimal 0.5. In other words:1:2 = 1/2 = 5/10 = 0,5. Rational numbers are Q.
Rational Numbers
Published in Nita H. Shah, Vishnuprasad D. Thakkar, Journey from Natural Numbers to Complex Numbers, 2020
Nita H. Shah, Vishnuprasad D. Thakkar
One trivial representation of the rational number is as the ratio of integers, where the denominator is non-zero. There are some inherent difficulties in this representation. For example, adding or comparing 1725 and 4364 is not trivial. The process to compare is to have a common denominator.
Computer Number Systems
Published in Julio Sanchez, Maria P. Canton, Software Solutions for Engineers and Scientists, 2018
Julio Sanchez, Maria P. Canton
A number system also represents parts of a whole. For example, when a carpenter cuts one board into two boards of equal length we can represent the result with the fraction ½; the fraction ½ represents 1 of the two parts which make up the object. Rational numbers are those expressed as a ratio of two integers, for example, 1/2, 2/3, 5/248. Note that this use of the word rational is related to the mathematical concept of a ratio, not to reason.
Middle-school mathematics teachers’ provision of non-examples and explanations in rational number instruction
Published in International Journal of Mathematical Education in Science and Technology, 2022
C-7 requires teachers to use examples (as well as non-examples and counter-examples) and representations (e.g. tables, graphs, pictures, and diagrams) appropriately. To exemplify, T1 explained that 8, −2/3, 0, −7, −125, and −0.12 are examples of rational numbers. T2 explained that is a non-example of an irrational number. T4 first drew a circular shape, shaded 1/4 of this shape, and explained that the shaded region can be used to represent 1/4 of a cake. Thus, these explanations were coded as ‘establishment of C-7’.
On the density of ℚ in ℝ: Imaginary dialogues scripted by undergraduate students
Published in International Journal of Mathematical Education in Science and Technology, 2022
Ofer Marmur, Ion Moutinho, Rina Zazkis
Excerpt 8Pedro:Well, we’re looking at the distribution of rational numbers on the line. A rational number is one that can be written in the form of a fraction where . And and are integers.Maria:Yes, so far so good.[…]Pedro:In the Geogebra applet we have 2 controls called and .Maria:The shows in how many pieces I divide the unit and the second indicates how many jumps I take on the number line.Pedro:Correct, the can also be seen as the numerator of the fraction. And the as the denominator. Note that if I divide a unit into 2,3,4,5 parts and get one of them, ex. , , and so on … I’m dividing this unit into smaller and smaller parts but I’ll never get to zero. And as I can put any integer value, there will be infinite parts without reaching zero.Maria:I hadn't thought of it this way, but that does not mean that my statement is wrong.Pedro:Yes, I agree with you that we will always be able to find a point between and . But my demonstration goes further and shows that we can find infinite points between and . In Excerpt 8, the student correctly describes a rational number as a number that ‘can be written in the form of fraction where ’, and ‘ and are integers’. However, this definition is in practice exemplified only by positive proper fractions which can become ‘smaller and smaller’; thus, not attending to rational numbers in their general form as a quotient of any two integers, but only to specific familiar instances.