Line Plots with Fractions

Real measurements rarely land exactly on a whole number.

The scale is marked in eighths

Between 0 and 1 there are eight equal steps, each one eighth.

Empty places still count

A value with no marks above it keeps its space, because the scale is a number line.

Reading a difference

The gap between the longest and shortest is a subtraction, counted in eighths.

A scale in eighths

Measuring to the nearest eighth of an inch means the line plot's scale must show all the eighths, evenly spaced. Every measurement then has a place to sit, whether or not any object actually landed there.

Questions the plot can answer

What is the longest? The shortest? What is the difference between them? How many are longer than 3 inches? Each needs a reading and often a fraction subtraction, which is why line plots appear after the fraction arithmetic.

Finding the range

If the longest is 4 3/8 and the shortest is 2 1/8, the difference is 2 2/8, which simplifies to 2 1/4. This is same-denominator subtraction with mixed numbers — the chapter's skills applied to real measurements.

Reading the shape of the data

A tall stack means many objects shared that measurement. A wide spread means they varied. One mark far from the rest is worth investigating — it might be a real outlier or a mismeasurement. Data displays exist so these things can be seen rather than computed.