2. Operations (N)
  3. Lesson 5: Adding Rational Numbers

Exercises


  1. Evaluate, showing all steps.
    1. \(\dfrac{1}{4}+\dfrac{3}{8}\)
    2. \(\dfrac{5}{14}+\dfrac{1}{2}\)
    3. \(\dfrac{3}{5}+\dfrac{3}{10}\)
    4. \(\dfrac{7}{32}+\dfrac{3}{4}\)
    5. \(\dfrac{1}{3}+\dfrac{3}{2}\)
  2. Evaluate, showing all steps.
    1. \(\dfrac{1}{2} + \dfrac{3}{5} \)
    2. \( \dfrac{4}{7} + \dfrac{3}{10} \)
    3. \(\dfrac{3}{2} + \dfrac{5}{7} \)
    4. \( \dfrac{2}{3} + \dfrac{11}{7} \)
    5. \( \dfrac{4}{3} + \dfrac{13}{8} \)
    1. How would you estimate the sum \(\dfrac{31}{40} + \dfrac{9}{10}+\dfrac{11}{25}+\dfrac{15}{16}\)?
    2. What is your estimation?
    1. Find the perimeter of a rectangle with length \(4\) cm and a width of \(7\) cm.
    2. Find the perimeter of a rectangle with length \(12\dfrac{3}{4}\) cm and a width of \(8\dfrac{2}{5}\) cm.
  5. To find the sum of three fractions, we can simply use our method for adding two fractions twice in succession.  Consider the following sum: \(\dfrac{1}{4}+\dfrac{1}{2}+\dfrac{5}{8}\)
    1. First, compute \(\dfrac{1}{4}+\dfrac{1}{2}\); let's call your answer \(\boxed{\phantom{\square}}\).
    2. Now evaluate \(\boxed{\phantom\square}+\dfrac{5}{8}\).
  6. As we showed in the previous question, the sum of three fractions can be computed using techniques for summing two fractions twice in succession.  Now, try to compute the sum \(\dfrac{2}{5}+\dfrac{1}{2}+\dfrac{4}{3}\) simultaneously.
    1. Examine the three denominators in the sum.  What value do you predict you will need to use as a common denominator for all three fractions?
    2. Express each term in the sum as an equivalent fraction using your predicted common denominator.
    3. Compute the sum of the three equivalent fractions from part b.
  7. If the pattern \(1\dfrac{2}{3} + ~4\dfrac{5}{6} + ~7\dfrac{8}{9} + ~10\dfrac{11}{12} + \cdots \) continues, how many numbers does it take to get a sum just over \(100\)?
  8. Consider the following images, each of which is composed of squares with given side lengths.
    A square with side length 1.The first square has a side length of 1, the second square has a side length of one-half.The first square has a side length of 1, the second square has a side length of one-half, and the last square has a side length of one-fourth.
    1. Find the perimeter of each image.
    2. What is the perimeter of the next image, which is composed of four squares?