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Math Study guide for Fractions Directions: This study guide is intended for an adult to review key terms, skills, and activities with your 4 th grader. Students WILL receive extra credit only if an adult reviews and practices the following information with his or her child. Return signed ON Friday March 20, 2015 for extra credit. Extra credit will not be given after March 20th. Strategies taught at school are meant to be used for homework, classwork, quizzes, tests, and other assessments. Your child should be able to explain the following strategies to you. All of these have been reviewed and practiced in detail. SOL 4.5a – The student will determine common multiples and factors, including least common multiple and greatest common factor. This is where knowing the multiplication facts are a MUST. Students have been taught to write fractions in the simplest form and to do this they write out the factors for the numerator and the denominator. They look for the greatest common factor that both the numerator and the denominator share. Factors are the numbers multiplied together. To write 10/12 is in its simplest form. 1. On their paper the students write 10=1, 10, 2, 5 – they get this by saying 1x10=10 and 2x5=10 12=1, 12, 2,6,3,4 – these factors are from 1x12=12, 2x6=12, 3x4=12 2. 2 is the greatest common factor for both the numerator and the denominator (GCF) 3. Divide 10 – the numerator by 2 4. Divide 12 – the denominator by 2 5. 10/12 = 5/6 A fraction is in its simplest form when the numerator and the denominator have no common factors other than one. The following fractions are consecutive and are in their simplest form: ½, 2/3, ¾, 4/5, 5/6, 6/7, 7/8, 8/9, 9/10, 10/11, 11/12 SOL 4.5b– The students will add fractions with like and unlike denominators and simplify fractions when necessary. Adding fractions with like or same denominators: 1. Add the numerator 2. Use the same denominator 3. Simplify fraction when necessary SOL 4.5b – The students will add and subtract fractions having like and unlike denominators that are limited to 2,3,4,5,6,7,8,9,10,11,12 and simplify the resulting fractions, using common multiples and factors. If the denominators are different then: 1. Look at the denominators to determine the least common multiple. Students need to know all of the multiples from 2 through 12. A list of multiples is provided For example: 4/8 -1/4 Multiples of 4=4, 8, 12 Multiples of 8=8, 16 2. Once the denominator is determined a new numerator or numerators will need to be solved. The least common multiple 4 and 8 have in common is 8. The denominator for this subtraction problem is 8. 3. A new subtraction (or addition) problem needs to be written: 4/8 - 1/4 4/8 - 2/8 The new numerator is determined by multiplying 4 from the numerator x what = 8? We know that 4x2=8. When you multiply the denominator by 2 to make it an 8, then you also multiply the numerator by 2. 2x1=2. 4. Now that the denominators are the same, you can subtract or add in addition problems. 5. 4/8 -2/8 2/8 6. Since fractions must be written in their simplest form. Usually, but not always, if the fraction has 2 even numbers and the denominator is 10 or less, we divide the numerator and the denominator by 2, unless the fraction is 4/8. If this is not the case, then you need to write out the factors to determine the greatest common factor. Divide the numerator by 2 and the denominator by 2. 7. 2/8 =1/4 *A mixed number is a whole number and a fraction part such as 1 1/3. *5/3 is an improper fraction because its numerator is greater than its denominator. *A fraction where the numerator is equal to the denominator such as 3/3 is also an improper fraction. * A factor of a number is the divisor of the number. * A multiple of a number is the product (answer) of the number and any natural number. * A common factor of 2 or more numbers is a divisor that all the numbers share or that they have the same. * The least common multiple of 2 numbers is the smallest common multiple of those 2 numbers. For example, the least common multiple of 6/12 and 3/6 is 12. Multiples of 6 are 6, 12, 18. Multiples of 12 are 12, 24. * The greatest common factor of 2 numbers is the largest factor that both numbers share or have in common. For example, the greatest common factor (GCF) of 4/12 is 4. The factors of 4 are 1, 4, 2, 2. The factors of 12 are 1, 12, 2, 6, 3, 4 * Fractions should always be written in their simplest form. All students need to be able to write the following multiples from memory: Practice this at home until it is memorized 2=2, 4,6,8,10,12 3=3, 6,9,12 4=4, 8, 12 5=5, 10 6=6, 12 7=7, 14 8=8, 16 9=9, 18 10=10, 20 11=11, 22 12=12, 24 These skills have been used at school and should be used at home as well. When completing homework assignments, students must show all of their work. My child and I have read, reviewed, and discussed the study guide. Further review will be done at home _____________________________________________________________________________ (guardian signature) My child has reviewed and studied this guide. _____________________________________________________________