TAILIEUCHUNG - New SAT Math Workbook Episode 1 part 3

Tham khảo tài liệu 'new sat math workbook episode 1 part 3', ngoại ngữ, ngữ pháp tiếng anh phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Operations with Fractions 25 3. SIMPLIFYING FRACTIONS All fractional answers should be left in simplest form. There should be no factor that can still be divided into numerator and denominator. In simplifying fractions involving very large numbers it is helpful to tell at a glance whether or not a given number will divide evenly into both numerator and denominator. Certain tests for divisibility assist with this. If a number is divisible by Then 2 its last digit is 0 2 4 6 or 8 3 the sum of the digits is divisible by 3 4 the number formed by the last 2 digits is divisible by 4 5 the last digit is 5 or 0 6 the number meets the tests for divisibility by 2 and 3 8 the number formed by the last 3 digits is divisible by 8 9 the sum of the digits is divisible by 9 Example By what single digit number should we simplify 428 376 Solution Since both numbers are even they are at least divisible by 2. The sum of the digits in the numerator is 24. The sum of the digits in the denominator is 30. Since these sums are both divisible by 3 each number is divisible by 3. Since these numbers meet the divisibility tests for 2 and 3 they are each divisible by 6. Example 43 672 Simplify to simplest form 52 832 Solution Since both numbers are even they are at least divisible by 2. However to save time we would like to divide by a larger number. The sum of the digits in the numerator is 22 so it is not divisible by 3. The number formed by the last two digits of each number is divisible by 4 making the entire number divisible by 4. The numbers formed by the last three digits of each number is divisible by 8. Therefore each number is divisible by 8. Dividing by 8 we have 7777. Since these numbers are no 6604 longer even and divisibility by 3 was ruled out earlier there is no longer a single digit factor common to numerator and denominator. It is unlikely at the level of this examination that you will be called on to divide by a two-digit number. 26 Chapter 2 Exercise 3 Work

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