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Basics
Published in William Bolton, Engineering Science, 2020
Fractions are a way of showing numbers that are part of a whole entity, e.g. that an area is half, i.e. 1/2, of the entire area. Equivalent fractions are fractions that are worth the same, even though they are written differently. For example, 1/2 is exactly the same as 2/4 because 2/4 can be simplified by dividing the numerator 2 and denominator 4 by a common factor of 2 to give 1/2. The numerator is the number on the top of the fraction and the denominator is the number on the bottom; e.g. for the fraction 3/4 the 3 is the numerator and the 4 is the denominator. Equivalent fractions are produced by multiplying or dividing the numerator and denominator of the fraction by the same number. For example, the fraction 1/3 where both the numerator and denominator are multiplied by 2: 13=1×23×2=26
Fractions
Published in James Kidd, Ian Bell, Maths for the Building Trades, 2014
Improper fractions can be turned into mixed numbers – that is, whole numbers and proper fractions – by dividing the denominator into the numerator and putting the remainder over the denominator. For example The fraction can be reduced further by dividing the numerator and the denominator by the highest factor that is common to them both (their HCF), in this case 5, giving the answer . If there is no obvious factor to divide by, this can be done gradually using a small number common to them both, for example When the denominator and numerator can no longer be divided by a number that is common to both of them, the fraction is said to be reduced to its lowest term.
Fractions
Published in Joanne Kirkpatrick Price, Basic Math Concepts, 2018
To convert from an improper fraction to a mixed number: Reduce the improper fraction, if possible.Divide the numerator by the denominator to obtain the whole number.Any remainder becomes the numerator of the mixed number. Use the same denominator as given for the improper fraction.Reduce the fraction part of the mixed number, if possible.
Comparing the development of the multiplication of fractions in Turkish and American textbooks
Published in International Journal of Mathematical Education in Science and Technology, 2018
Tuğrul Kar, Gürsel Güler, Ceylan Şen, Ercan Özdemir
Second, differences between the Turkish and American textbooks were also found in the development of procedural fluency. In the Turkish textbooks, procedural fluency and the conceptual meaning of multiplication with fractions was developed simultaneously. In the textbooks, word problems were modelled under the headings of the multiplication of a natural number with a fraction and the multiplication of two fractions. The algorithm of the operation used to multiply the fractions in each of the problems was presented as an alternative solution. After these activities, the algorithm was explained. For instance, in TB1, after modelling a word problem of the multiplication of a whole number with a fraction, the following was presented: . In this process, the number 3 was expressed as , following by the statement, ‘each whole number is a fraction, the denominator of which is 1.’ After similar activities were performed, the rule was summarized as follows: Indeed, multiplying a whole number with a fraction is the addition of fraction as much as the whole number. While a whole number is multiplied by a fraction, firstly the mixed fraction, if any, is converted to an improper fraction, then the numerators of the fractions are multiplied and written to the numerator of the result; denominators are multiplied and written to the denominator of the result. (TB1, [65], p.149)