In Grade 4 you made line plots of measurements in eighths. Now that you can add fractions with unlike denominators, a line plot can answer questions like “how much in all?” and “how much would each get if it were shared evenly?”
Idea clave
Each X is one measurement. To find a total, multiply each value by the number of X marks above it and add. To share the total equally, divide it by the number of measurements.
Por qué funciona
Three X marks above $\frac{3}{8}$ stand for $\frac{3}{8} + \frac{3}{8} + \frac{3}{8}$, which is $3 \times \frac{3}{8} = \frac{9}{8}$. Adding column by column is just grouping equal values. Sharing equally means pouring everything together and splitting it: total $\div$ number of beakers.
Worked examples
Ejemplo resuelto: The total
Use the line plot above. How much water is there in all?
- Column by column: $\frac{1}{8} + 2 \times \frac{1}{4} + 3 \times \frac{3}{8} + \frac{1}{2} + \frac{3}{4}$.
- In eighths: $\frac{1}{8} + \frac{4}{8} + \frac{9}{8} + \frac{4}{8} + \frac{6}{8} = \frac{24}{8}$.
- $\frac{24}{8} = 3$.
Respuesta: $3$ liters
Ejemplo resuelto: Share equally
If all of that water were poured back into the 8 beakers equally, how much would each hold?
- Divide the total by the number of beakers: $3 \div 8$.
- A fraction is a division: $3 \div 8 = \frac{3}{8}$.
Respuesta: $\frac{3}{8}$ liter
Ejemplo resuelto: Greatest minus least
How much more is in the fullest beaker than the emptiest?
- Greatest: $\frac{3}{4}$. Least: $\frac{1}{8}$.
- $\frac{3}{4} - \frac{1}{8} = \frac{6}{8} - \frac{1}{8} = \frac{5}{8}$.
Respuesta: $\frac{5}{8}$ liter
Error común
Adding only the values on the scale and ignoring how many X marks are stacked above each. Three marks at $\frac{3}{8}$ count three times. Check: count the X marks first; the total has to use every one.