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How Do You Solve a Word Problem That Compares Two Fractions?

Brad and Ariel have been playing the stock market. Last week Ariel's stock went up four and a half points, then down two and a third points two days in a row, then up three quarters of a point. In the same week Brad's stock went up a total of four sevenths of a point. Whose stock did better overall?

Summary

  1. Lets make an equation form of Ariel's overall change in stock
  2. Brad's equation is just four sevenths!
  3. We can't yet compare the two equations with an inequality
  4. Let's change the mixed fractions into improper fractions
  5. Give each fraction a common denominator and add them
  6. Compare the fractions by taking a cross product
  7. Ariel did better than Brad in the stock exchange!

Notes

    1. 'Increased' means that 4 and a half is a positive number
    1. 'Decreased' means that 2 and one third is a negative number
    1. Three fourths is a positive number because of the verb 'increased'
    1. Four sevenths is a positive number because of the verb 'increased'
    1. 2•4 + 1 = 9
    1. 3•2 + 1 = 7
    1. 2•7 = 14
    1. We can't add the fractions as they are, so let's find a common denominator!
    1. LCD is an abbreviation for Least Common Denominator
    1. We have to multiply the denominator by 6 to make it equal to the LCD, 12
    2. We don't want the value of the fraction to change
    3. So multiply the numerator by 6 also
    4. 9•6 = 54
    1. We have to multiply the denominator by 4 to make it equal to the LCD, 12
    2. We don't want the value of the fraction to change
    3. So multiply the numerator by 4 also
    4. 14•4 = 56
    1. We have to multiply the denominator by 3 to make it equal to the LCD, 12
    2. We don't want the value of the fraction to change
    3. So multiply the numerator by 3 also
    4. 3•3 = 9
    1. The signs of each number must stay the same
    2. The first and last term were positive, so they stay positive
    3. The middle term was negative, so it stays negative
    4. Working with just the numerators:
    5. 54 - 56 + 9 = -2 + 9 = 7
    1. Multiply cross terms together, denominator time numerator
    2. 7•7 = 49
    3. 12•4 = 48
    1. The inequality for 49 and 48 is the same inequality that applies to Ariel's and Brad's stocks!
    2. So Ariel did better at the stock market than Brad!