Lesson 39: Reading an Inch Scale to the Nearest Fourth, Activity Make a Ruler and Measure

New Concept

To measure lengths in inches, we use an inch scale. These scales let us read to the nearest half inch, quarter inch, or eighth inch.

What’s next

Next, you’ll practice reading an inch scale to the nearest quarter inch and see how equivalent fractions like $\frac{2}{4}$ and $\frac{1}{2}$ are used.

Property

Inch scales have tick marks between the inch marks that let us read the scale to the nearest quarter inch. Remember that one quarter inch is the same as one fourth inch, which can be written as $\frac{1}{4}$ in.

Example

A paperclip measures past the 1-inch mark to the first small tick.
Its length is $\tfrac{1}{4}$ inches.

A crayon stops at the third tick mark after the 3-inch line.
Its length is $3\tfrac{3}{4}$ inches.

Property

When reading inch scales, keep in mind that $\frac{2}{4}$ equals $\frac{1}{2}$.

Example

A toothpick measures $2\tfrac{2}{4}$ inches.
We simplify this to its proper form: $2\tfrac{1}{2}$ inches.

An arrow points to $\tfrac{2}{4}$ on a ruler.
The correct way to name this point is $\tfrac{1}{2}$ inch.

Property

To find the combined thickness of stacked objects, add their individual thicknesses. First, add the whole numbers, then add the fractions. If the fractions add up to a whole number or more, simplify and add it to the whole number total.

Example

A $1\tfrac{1}{2}$ inch board on a 2 inch board:
$1 + 2 = 3$, so the total is $3\tfrac{1}{2}$ inches.

A $1\tfrac{1}{2}$ inch block on a $2\tfrac{1}{2}$ inch block:
$(1+2) + (\tfrac{1}{2} + \tfrac{1}{2}) = 3 + 1 = 4$ inches.