Place both fractions on a number line with the same zero and one. The point farther to the right is the larger fraction. Mark equal intervals before plotting either value.
Draw a shared scale
Draw a line from 0 to 1 and divide it into eight equal intervals. A ruler can make this easier. On a 16 cm line, each interval is 2 cm long. Count spaces between tick marks. Eight intervals require nine marks when you include both endpoints.
Locate three quarters and five eighths
Three quarters is six eighths because each quarter occupies two eighth-size intervals. Put three quarters at the sixth interval from zero. Put five eighths at the fifth. The marks are 12 cm and 10 cm from zero on the sample line, so three quarters is larger.
Diagnose a mixed scale
If you drew quarters on one line and eighths on another, check that both lines use the same distance from zero to one before comparing the points. If you put three quarters at the third tick of the eighths scale, mark one quarter first and count three jumps of that size.
Practice a pair that lands together
Plot one half and four eighths. Both land at the fourth interval. Then plot seven eighths and three quarters. How many eighth-size steps separate them?
Read the denominator as a number of spaces
The denominator tells you how many equal parts make up one whole. To plot three quarters, divide the stretch from zero to one into four equal spaces and count three spaces from zero. The zero tick is where you start counting. If you count zero as the first space, your point will land too far left.
Find a common scale for an unfamiliar pair
Compare two thirds with three quarters. Draw a line from zero to one with twelve equal spaces because twelve can be divided into both thirds and quarters. Two thirds occupies eight of the twelve spaces and three quarters occupies nine. Draw both marks on the same line. Three quarters is greater by one twelfth, the distance between those adjacent marks.
Use a halfway check
Plot three eighths and five eighths on the eight-space line. Four eighths is the halfway mark, so three eighths should fall just before it and five eighths just after it. If both marks appear on the same side of halfway, count the spaces again. Try the same check with two sixths and four sixths. What fraction names the midpoint on that scale?
