Two volunteers split the sports day prize money between track and field events using the fraction \(\frac{6ab^2}{9a^2b}\), where \(a\) is the number of trac...
Question 1 Report
Two volunteers split the sports day prize money between track and field events using the fraction \(\frac{6ab^2}{9a^2b}\), where \(a\) is the number of track events and \(b\) is the number of field events held that day. Before announcing the split, the volunteers must write the fraction in its simplest possible form.
- Simplify this fraction fully. (3)
Answer Details
Simplifying an algebraic fraction means dividing the numerator and denominator by every factor they share, treating the numbers and each letter separately.
The numbers 6 and 9 share a common factor of 3, so dividing both by 3 gives \[\frac{6ab^2}{9a^2b}=\frac{2ab^2}{3a^2b}\] [1 mark]
Cancelling the common letter factors, one \(a\) from \(a^2\) and one \(b\) from \(b^2\), leaves \[\frac{2ab^2}{3a^2b}=\frac{2b}{3a}\] [1 mark]
No factor is now common to the top and bottom, so the fraction in its simplest form is \[\frac{2b}{3a}\] [1 mark]
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