Stories about rain, rope, juice and distance often use fractions with the same denominator. Use the skills from adding and subtracting mixed numbers; the story tells you which one.
Key idea
Decide what the story does. Putting amounts together (in all, total, altogether) means add. Taking away, finding what is left, or comparing (how much more, how much farther) means subtract. Then keep the denominator and work with the numerators.
Why it works
A fraction story is a whole-number story with fraction-sized pieces. "It rained 3 eighths of an inch, then 4 eighths more" is the same as "3 drops, then 4 more drops," only the drops are eighths. A tape diagram shows the parts and the whole.
Worked example: Put together
It rained $\dfrac{3}{8}$ inch on Monday and $\dfrac{4}{8}$ inch on Tuesday. How much rain fell in all?
- "In all" means add.
- $\dfrac{3}{8} + \dfrac{4}{8} = \dfrac{7}{8}$.
Answer: $\dfrac{7}{8}$ inch
Worked example: What is left
A rope is $5\dfrac{1}{4}$ feet long. Sam cuts off $2\dfrac{3}{4}$ feet. How much rope is left?
- "Left" means subtract: $5\dfrac{1}{4} - 2\dfrac{3}{4}$.
- $\dfrac{1}{4} < \dfrac{3}{4}$, so trade a whole: $5\dfrac{1}{4} = 4\dfrac{5}{4}$.
- $4\dfrac{5}{4} - 2\dfrac{3}{4} = 2\dfrac{2}{4}$.
Answer: $2\dfrac{2}{4}$ feet (or $2\dfrac{1}{2}$ feet)
Write the unit with your answer. "$2\dfrac{2}{4}$" alone does not say whether it is feet, miles or cups.