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Problem Solving Involving Algebraic Fractions

Problem Solving Involving Algebraic Fractions. Algebraic Method. Let the unknown be denoted by a variable. Form an equation involving the variable. Solve the equation. Check the solution.

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Problem Solving Involving Algebraic Fractions

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  1. Problem Solving Involving Algebraic Fractions

  2. Algebraic Method • Let the unknown be denoted by a variable. • Form an equation involving the variable. • Solve the equation. • Check the solution.

  3. When a number is subtracted from 52 and the result is divided by 6, the answer obtained is twice the original number. What is the number? Let x = the number How do we represent the number subtracted from 52? How do we write the result divided by 6? What is twice the original number?

  4. TRY THIS IN YOUR NOTEBOOKS When 18 is added to ¼ of a number, the result is 2 ½ times the original number. What is the number?

  5. TRY THIS 5 is subtracted from 4 times a number and the result is then doubled. If the answer is 6, what is the original number?

  6. How can the number 39 be divided into two parts in order that the sum of 2/3 of one part and ¾ of the other part is 28? x 39 – x 39

  7. TRY THIS Meiling and Meimei divide $69 into 2 shares. ¾ of Meiling’s share is equal to 2/5 of Meimei’s share. How much does each get?

  8. The sum of the reciprocals of two consecutive integers is 11. Find these integers. 30 1/n = reciprocal of smaller integer 1 . n + 1 = reciprocal of larger integer Let n = smaller integer n + 1 = larger integer

  9. TRY THIS If the same number is added to both the numerator and denominator of the fraction 3 5 the result is 4. Find the number. 5

  10. TRY THIS • page 137 numbers 11, 16 • page 150 numbers 4, 5, 6

  11. TRY THIS If a piece of wood 5 cm longer than a second piece, and ¾ of the second piece is equal to 3/5 of the first, what is the length of the second piece?

  12. TRY THIS A certain number of matches are needed to fill 24 boxes, with each box containing the same number of matches. When 4 less matches are put into each box, there are enough for 28 boxes. Find the total number of matches.

  13. TRY THIS What is the number which when multiplied by 2 and added to 8 gives the same result as when it is divided by 2 and has 32 added to it?

  14. TRY THIS When a number is divided by 4 and has 28 added to it, the result is equal to twice the number. Find the number.

  15. TRY THIS The difference between the reciprocal of two consecutive positive even numbers is 1/12. Find the two numbers.

  16. Mary’s age is 2/3 that of Peter’s. Two years ago Mary’s age was ½ of what Peter’s age will be in 5 years’ time. How old is Peter now?

  17. TRY THIS John’s father is 5 times older than John and John is twice as old as his sister Alice. In two years time, the sum of their ages will be 58. How old is John now?

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