Fractions and Rational Numbers

This course is about fractions. It starts with a cake cut into equal pieces, and it ends with multiplying and dividing. Every idea is shown with cakes, chocolate bars or a number line before any rule is written down.

The lessons build up in order. The first cuts a whole into equal parts, and separates proper fractions from improper ones. The second gives the two numbers their names, numerator and denominator, and shows mixed fractions such as $\displaystyle 1\frac{1}{4}$. It also sorts like fractions from unlike ones. The third widens fractions into rational numbers, written $\displaystyle \frac{p}{q}$ with integers above and below the line. It shows why that bottom number can never be zero. The fourth is about simplest form, and about telling which of two fractions is bigger. The fifth places fractions on a number line, going past one and to the left of zero. The last two lessons do the arithmetic: adding and taking away first, then multiplying and dividing.

By the end you will be able to:

• Tell a proper fraction from an improper one by comparing the top and bottom numbers.
• Name the numerator and the denominator, and change $\displaystyle \frac{9}{4}$ into $\displaystyle 2\frac{1}{4}$ and back again.
• Write a whole number as a rational number, and say why zero cannot sit below the line.
• Show that $\displaystyle \frac{1}{2}$, $\displaystyle \frac{2}{4}$ and $\displaystyle \frac{3}{6}$ are the same amount.
• Put a number into simplest form by cancelling with the H.C.F, and tidy the minus sign.
• Put fractions in ascending or descending order, including ones below zero.
• Mark a fraction on a number line, to the right past one and to the left of zero.
• Add and take away fractions, using the L.C.M when the bottom numbers do not match.
• Multiply two fractions, and divide by turning the second one over.