3 Key excerpts on "Common Multiples"

• 

  eBook - ePub

  Math Intervention 3-5

  Building Number Power with Formative Assessments, Differentiation, and Games, Grades 3-5

  • Jennifer Taylor-Cox(Author)
  • 2016(Publication Date)
  • Routledge

    (Publisher)

  Multiples of a number are the product of multiplying that number by another whole number. For example, 18 is a multiple of 3 because 3 x 6 = 18. Three has other multiples, too: 3, 6, 9, 12, 15, 21, 24, 27, 30,. . . . Often the task is to find Common Multiples of two or more numbers. For example, 24 is a common multiple of 6 and 8 because 24 is a multiple of 6 and of 8. Every multiple of 24 is also a multiple of 6 and a multiple of 8. The Common Multiples of 6 and 8 follow an infinite pattern, 24, 48, 72, 96, 120,. . . . If the task is to find the least common multiple (LCM) of 6 and 8, the multiples of 6 and 8 are compared to find the smallest common multiple (other than zero), which is 24.

  CCSS

  Operations and Algebraic Thinking

  Formative Assessment

  To find out if a student understands the finding Common Multiples concept, ask the student to name at least five multiples of the following numbers:

  5

  7

  12

  Then ask the student to find at least two common multiple of the following pairs of numbers:

  5, 15

  4, 10

  24, 16

  Then ask the student to find the LCM of the following numbers:

  5, 6, 15

  50, 4, 20

  24, 6, 15

  Successful Strategies

  One of the most beneficial ways to help students find the LCM is to have students show the multiples of each number in a skip counting pattern. When students examine these patterns it is easier to find the Common Multiples and the LCM. Students may show the multiples with numbers, words, or models. The hundred chart serves as a valuable tool in helping students to find common and least Common Multiples.

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Maths from Scratch for Biologists

  • Alan J. Cann(Author)
  • 2013(Publication Date)
  • Wiley

    (Publisher)

  5. To factor an integer, break the integer down into a group of numbers whose product equals the original number. Factors are separated by multiplication signs. Note that the number 1 is the factor of every number. All factors of a number can be divided exactly into that number.

  2.6. Lowest common multiple and greatest common factor

  When manipulating fractions you frequently need to find these two terms – you will see examples of this below. To find the lowest common multiple (LCM) of two numbers, make a table of multiples (e.g. 2 and 3; see Table 2.2 ). To find the greatest common factor (GCF), meaning numbers or expressions by which a larger number can be divided exactly (‘factoring’), make a table of factors (e.g. 8 and 12; see Table 2.3 ).

  Table 2.2 Table of multiples

  Multiples of 2	Common Multiples	Multiples of 3
  246–	––6–	3–69

  Table 2.3 Table of factors

  Factors of 8	Common factors	Factors of 12
  12–48–	12–4––	1234612

  2.7. Adding and subtracting fractions

  To be able to add or subtract fractions to or from fractions, the denominators must be the same (‘common’): cannot be added, but can.

  To find a common denominator so you can add or subtract fractions, find the LCM of all the denominators involved. Then, make the denominators equal the LCM by multiplying both the denominator and numerator by the corresponding factor of the LCM. Whenever you manipulate fractions, the final step is to reduce the answer to the lowest terms:

  1. Factor the numerator. 2. Factor the denominator. 3. Find the fraction mix that equals 1.

  Example

  Add

  	The LCM of 3 and 5 (the denominators) is 15.
  	Both denominators must equal the LCM, so multiply 3 by 5, and 5 by 3. Now both denominators are the same (‘common’).
  	To avoid altering the problem, multiply the numerators by the same factor as their respective denominators. This is the same as multiplying each fraction by 15/15, i.e. by 1.
  	Now the denominators the same, add the fractions together.
  	You cannot reduce this fraction further, i.e. reduce numerator and denominator to their LCFs, so this is the final answer.

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  RtI in Math

  Evidence-Based Interventions

  • Linda Forbringer, Wendy Weber(Authors)
  • 2021(Publication Date)
  • Routledge

    (Publisher)

  Step one of this procedure is to rewrite the problem using a common denominator. The simplest, most straightforward way to find a common denominator is to multiply the denominators provided; the resulting product represents a common denominator. For example, to find a common denominator for 2/3 + 1/4, we multiply 3 × 4 to obtain the common denominator of 12. This process is identical to the process for crisscrossing fraction overlays to find equivalent fractions that we described previously. If we first model one fraction with vertical lines defining the pieces, and then place an overlay on top that uses horizontal lines to model the denominator of the other fraction, we have effectively created the common denominator. In other words, if we crisscross a clear overlay cut into fourths on top of a square that illustrates 2/3, we have shown that 2/3 = 8/12. If we repeat the process by crisscrossing a clear overlay cut into thirds on top of a square that illustrates 1/4, we have shown that 1/4 = 3/12, and have successfully rewritten the problem using common denominators.

  For some students, it may be best to continue to use the common denominator formed by multiplying denominators and not bother to introduce the idea of lowest common denominator. Math teachers often spend a great deal of time teaching students to find lowest common denominator, but students who have not mastered basic facts struggle with this process. Interventionists may consider omitting it, because while learning to find a common denominator is necessary, using the lowest common denominator is not an essential skill. Multiplying denominators produces a correct answer, and instructional time may be more effectively spent on other topics. However, when the denominators being multiplied contain multi-digit numbers, the resulting common denominator can be very large and unwieldy. For this reason, the interventionist may choose to introduce least common denominators. Instead of teaching students to use factor trees, we have found a shortcut method that is effective. Steps for the shortcut method are listed in Figure 11.12

  Sign up to read

  Learn more about book