Algebra: Cancellation Of Indices Term Practice 2
In this practice set of 4 questions, students will focus specifically on applying the cancellation technique in algebraic fractions. They will work on spotting common numerical and algebraic factors and simplifying expressions by cancelling these factors correctly.
Related Lessons:
Practice 2 - Question 1
Simplify the expression \(\frac{3x}{6xy}\times\frac{\left(2y\right)^2}{5}\) as a single fraction in its simplest form.
Solution:
\[
\begin{align*}
\frac{3x}{6xy}\times\frac{\left(2y\right)^2}{5}&=\frac{3x}{6xy}\times\frac{2y\times2y}{5}\\
&=\frac{2y}{5}
\end{align*}
\]
Practice 2 - Question 2
Taking the positive square root, simplify, as a single fraction, the expression
\(\sqrt{\frac{16x^4y^2}{25z^4}}\div\frac{12x+12y}{2x^2z^3}\times\left(\frac{3\left(x+y\right)}{-2xz}\right)^3\)
Solution:
\(\sqrt{\frac{16x^4y^2}{25z^4}}\div\frac{12x+12y}{2x^2z^3}\times\left(\frac{3\left(x+y\right)}{-2xz}\right)^3\)
\(=\frac{\sqrt{16}x^\frac{4}{2}y^\frac{2}{2}}{\sqrt{25}z^\frac{4}{2}}\times\frac{2x^2z^3}{12\left(x+y\right)}\times\frac{3^3\left(x+y\right)^3}{\left(-2\right)^3x^3z^3}\)
\(=\frac{-9xy\left(x+y\right)^2}{20z^2}\)
Practice 2 - Question 3
Express \(\frac{3xy}{2m}\times\frac{\left(2m\right)^2}{6xy^2}\) as a single fraction in its simplest form.
Solution:
\[
\begin{align*}
\frac{3xy}{2m}\times\frac{\left(2m\right)^2}{6xy^2}&=\frac{3xy}{2m}\times\frac{2m\times2m}{6xy^2}\\
&=\frac{m}{y}\\
\end{align*}
\]
Practice 2 - Question 4
Simplify \(\frac{a^4}{b^3}\times\left(\frac{b}{2a}\right)^2\div b^0\) as a single fraction in its simplest form.
Solution:
\[
\begin{align*}
\frac{a^4}{b^3}\times\left(\frac{b}{2a}\right)^2\div b^0&=\frac{a^{4\ 2}}{b^3}\times\frac{b}{2a}\times\frac{b}{2a}\div1\\
&=\frac{a^2}{4b}\\
\end{align*}
\]
Step By Step Full Solution
For students who found the above questions challenging or would like to strengthen their understanding and technique, below is the complete step-by-step working for Algebra Cancellation Practice 2.