25 ## WORD PROBLEMSTHAT LEAD TO ## EQUATIONS WITH FRACTIONSHERE ARE SOME WORD PROBLEMS that lead to equations with fractions. Example 1. Half of a number, added to a fifth of three less than the number, is equal to two thirds the number. What is the number?
Here is the equation:
The LCM of denominators is 30. And upon clearing of fractions, we have
Example 2. The whole is equal to the sum of the parts. This problem is from a classical Hindu text on algebra from the 9th century. During an amorous struggle, the lady's pearls broke. Half of the pearls fell onto the floor; a fourth rolled under a chair; a sixth fell into her lap; and three pearls remained on the strand. How many were there originally on the strand?
First, we will clear the equation of fractions. The LCM of 2, 4, and 6 is 12. We will multiply every term by 12, and cancel the denominators:
There were originally 36 pearls on the strand. Example 3. One number is three times another. The sum of their reciprocals is 4. What are the two numbers?
(Note that the sum of their reciprocals -- 3 + 1 -- does equal 4.) Problem 1. Half of a number added to its third part, is eight less than the number. What is the number? To see the equation, pass your mouse over the colored area. The equation is:
Problem 2. Three fifths of a number, plus 8, is equal to the number. What is the number? Here is the equation:
Problem 3. Half of a number, plus a fifth of two less than the number, is four less than the number. What is the number? Here is the equation:
Problem 4. Melissa went shopping and spent half of her money on shoes, a third on a blouse, a tenth to take her boyfriend to lunch, and she came home with $12. How much did she start out with? Here is the equation:
Problem 5. One number is four times another. The sum of their
Let
These are the two numbers. Problem 6 If the same number is added to the numerator and
Here is the equation:
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