AC9M7N04

find equivalent representations of rational numbers and represent rational numbers on a number line

Elaborations

AC9M7N04_E1 - investigating equivalence of fractions using common multiples and a fraction wall, diagrams or a number line to show that a fraction such as \(\frac23\) is equivalent to \(\frac46\) and \(\frac69\) and therefore \(\frac23\leq\frac56\)
AC9M7N04_E2 - expressing a fraction in simplest form using common divisors
AC9M7N04_E3 - applying and explaining the equivalence between fraction, decimal and percentage representations of rational numbers; for example, \(16\%\), \(0.16\), \(\frac{16}{100}\) and \(\frac4{25}\), using manipulatives, number lines or diagrams
AC9M7N04_E4 - representing positive and negative fractions and mixed numerals on various intervals of the real number line, including intervals that are not symmetrical about zero

Achievement Standard Components

ASMAT705 - Students choose between equivalent representations of rational numbers and percentages to assist in calculations.
ASMAT706 - They use mathematical modelling to solve practical problems involving rational numbers, percentages and ratios, in financial and other applied contexts, justifying choices of representation.