Fractions, Unit Fractions and Measuring

A unit fraction has a numerator of 1: $\frac{1}{2},\frac{1}{3},\frac{1}{8},\frac{1}{16}$. The denominator says how many equal pieces the whole is cut into, so $\frac{1}{8}$ is one piece when the whole is cut into 8. Any positive fraction with whole-number parts is a count of unit fractions: $\frac{3}{8}$ means three pieces of size $\frac{1}{8}$. Because more cuts make smaller pieces, a larger denominator gives a smaller unit fraction: $\frac{1}{16}$ of an inch is half the size of $\frac{1}{8}$ of an inch.

Cut each of the pieces of $\frac{1}{2}$ into two, and you have $\frac{2}{4}$: twice as many pieces, each half as big, and exactly the same amount. That is the rule for equivalent fractions: multiply (or divide) the numerator and the denominator by the same number, as long as that number is not zero. Dividing both by a common factor is called simplifying; a fraction is in simplest form when the numerator and denominator have no common factor other than 1. To compare two fractions, rewrite them with the same denominator and compare the numerators.

Equivalent fractions | Fractions | Pre-Algebra | Khan Academy

A typical imperial ruler splits each inch in half, then halves the halves, and so on, until the smallest gap is $\frac{1}{16}$ inch (some precision rulers go on to $\frac{1}{32}$). The tick marks show this with their lengths: the longest ticks mark whole inches, the next longest the half inch, then quarters, eighths, and the shortest ticks are the sixteenths. So there are 16 equal gaps between inch marks. The reliable way to read a length is to count sixteenths from the last whole-inch mark, then simplify the fraction. If the count is odd (like 11 sixteenths) it cannot be simplified; if it is even, divide the top and bottom by 2 until you can't.

How to Read a Ruler or Tape Measure | Measuring to the Nearest 1/16 of an Inch | Math with Mr. J

A set of measuring cups is a set of unit fractions: usually 1 cup, $\frac{1}{2}$, $\frac{1}{3}$ and $\frac{1}{4}$ cup. To measure $\frac{3}{4}$ cup with only the $\frac{1}{4}$ cup scoop, fill it 3 times, because $\frac{3}{4}$ is three quarters. To measure $\frac{2}{3}$ cup, use the $\frac{1}{3}$ cup twice. Most Canadian recipes and measuring cups treat 1 cup as 250 mL (a US cup is a little smaller, about 237 mL). For length, the link between the two systems is exact: 1 inch is defined to be exactly 2.54 cm. To convert a fractional inch measurement, change the fraction to a decimal first, then multiply by 2.54.