Negative Fractions and Decimals on a Number Line

0:00Which is smaller, negative three quarters or negative two thirds?

0:05It is tempting to say negative two thirds, as three quarters is bigger than two thirds.

0:12Both are rational numbers: they can be written as one integer over another, with a bottom that is not zero.

0:20An integer is a whole number or its negative, like negative 3, 0 or 4.

0:28The minus sign of a fraction can go in front, on the top, or on the bottom.

0:34Each one equals negative 0.75: 3 divided by 4 is 0.75, and one minus sign makes it negative.

0:44So all three are the same number.

0:49To compare, write each as a decimal. Negative three quarters is negative 0.75.

0:572 divided by 3 is 0.666 and so on, so negative two thirds is about negative 0.67.

1:07Add two more: negative 0.6, which is negative 6 tenths, and one half, which is 0.5.

1:15On a number line, numbers get smaller to the left and bigger to the right.

1:21Mark negative three quarters, negative two thirds, negative 0.6 and one half.

1:29Negative 0.75 is further left than negative 0.67, so negative three quarters is smaller.

1:37Three quarters is bigger than two thirds, so negative three quarters is further from zero.

1:44Below zero, further from zero means further left, so smaller.

1:50From smallest to biggest: negative three quarters, negative two thirds, negative 0.6, one half.

2:00Further left on the number line means smaller, so negative three quarters is less than negative two thirds.