Every division

About this video

The number family grew because people kept asking questions their numbers couldn't answer. With only the counting numbers, 7 - 9 has no answer: you can't take nine away from seven. Negative numbers fix that, and 7 - 9 = -2. With only whole numbers, 3 ÷ 4 has no answer either: four people can't share three bars and each get a whole one. Fractions fix that, and 3 ÷ 4 = 3/4.

This short animation draws the family as boxes inside boxes. The counting numbers 1, 2, 3 sit inside the whole numbers, which add 0. Those sit inside the integers, which add the negatives, and all of them sit inside the rational numbers, which add the fractions. A rational number is any number you can write as a fraction a/b, where a and b are integers and b is not zero, because nothing can be divided by zero. Written as decimals, rational numbers either end, like 1/4 = 0.25, or repeat forever, like 1/3 = 0.333... This video goes with The Number Family lesson of Numbers Level 1 on Knaph.

Transcript

1. 0:00Does every division have an answer?
2. 0:04With counting numbers, seven take away nine has no answer. Negatives fix it.
3. 0:10Three divided by four has no whole answer. Fractions fix it.
4. 0:15Each family of numbers holds the one before.
5. 0:21A rational number is one integer over another, never over zero.
6. 0:27As decimals, they end, or they repeat.
7. 0:31Rational means a fraction of integers.