diff options
Diffstat (limited to 'ratios.tex')
-rw-r--r-- | ratios.tex | 215 |
1 files changed, 215 insertions, 0 deletions
diff --git a/ratios.tex b/ratios.tex new file mode 100644 index 0000000..a9a9ec0 --- /dev/null +++ b/ratios.tex @@ -0,0 +1,215 @@ +\documentclass[12pt,a4paper,twocolumn,landscape]{exam} + +\usepackage{xparse} +\usepackage{tikz} + \usetikzlibrary{arrows,calc,fit} +\usepackage{mathtools} +\usepackage{fullpage} +\usepackage{todonotes} +\usepackage{float} +\usepackage[compact,explicit]{titlesec}% http://ctan.org/pkg/titlesec +\usepackage[utf8]{inputenc} +\usepackage{titling} +\usepackage{boxedminipage} +\usepackage{wrapfig} +\usepackage{parskip} % Don't indent paragraphs + +\usepackage{fib} +\usepackage{common} + +\pagestyle{headandfoot} + +\firstpageheadrule +\firstpageheader{Ratios} + {Level 5-6} + {\today} + +\runningheadrule +\runningheader{Ratios} + {Ratios, Page \thepage\ of \numpages} + {\today} + +\firstpagefooter{}{}{} +\runningfooter{}{}{} + +\begin{document} +\section*{Ratios - Level 5-6} + +\begin{wrapfigure}{R}{0.3\linewidth} + \centering + \begin{boxedminipage}{\linewidth} + Keywords: + \begin{itemize} + \item Ratio + \item Comparison + \end{itemize} + \end{boxedminipage} +\end{wrapfigure} + +\textbf{Ratios} are used to show how much of one thing there is compared to +another thing. + +Ratios will be written in two ways, either in words "2 to 1" or as "2:1". Both +are read the same way. + +A question involving \textbf{ratios} will often ask you to find out how many of +one thing there is. + +\subsection*{Worked Example} + +\begin{questions} + +\question + +20 sweets are shared between James and Sasha in the ration 1:3, how many sweets +do James and Sasha each receive? + +The first step is to look at what the ratio means for each sweet that James +gets, Sasha gets three so we can expect Sasha to have more sweets than James in +our answer. + +The ratio 1:3 means that 4 parts are shared between the boys. + +To find out how many sweets are in 1 part, we divide 20 by 4. $20 \div 4 = 5$ +sweets are in 1 part. + +Since James gets one part, we now know that he receives 5 sweets. + +Sasha gets 3 parts, so we times the number of sweets in 1 part by 3. $3 \times +5 = 15$ sweets in 3 parts. + +Sasha gets 15 sweets. + +\textbf{Check} + +We can write this back in ration form as the number of sweets James has to +Sasha is. 5:15 We know there has to be 20 sweets in total so we can check that +we have shared all 20 sweets out by adding the numbers of sweets that James and +Sasha have. $5 + 15 = 20$, so this supports our answer. + +\end{questions} + +\subsection*{Questions} + +\begin{questions} + +\question +What is the simplest form of the following ratios? + +\begin{parts} +\part +6:15 + +\begin{solution}[0.2in] +2:5 +\end{solution} + +\part +2:8 + +\begin{solution}[0.2in] +1:4 +\end{solution} + +\part +4:12 + +\begin{solution}[0.2in] +1:3 +\end{solution} + +\part +9:3 + +\begin{solution}[0.2in] +3:1 +\end{solution} + +\part +4:2 + +\begin{solution}[0.2in] +2:1 +\end{solution} + +\part +10:14 + +\begin{solution}[0.2in] +5:7 +\end{solution} + +\end{parts} + +\newpage + +\question + +John and Sam stand on a pair of scales, together the weigh 200kg, if the ratio +of John and Sam's weights is 2:3, how heavy is Sam? + +\begin{solution}[2in] + +Sum the sides of the ratio, to convert the ratio in to two fractions. + +$2 + 3 = 5$ + +Therefore, Sam weighs $3 \div 5$'s of 200kg. + +Sam weighs 120kg. + +\end{solution} + +\question + +A recipe for a cake requires 200g of flour, 100g of butter, 50g of sugar and 2 +eggs. The cake recipe indicates that the cake will serve 4. How much of each +ingredient is necessary for the cake to serve 8? + +\begin{boxedminipage}{\linewidth} + Hint: What is the ratio of cake servings? +\end{boxedminipage} + +\begin{solution}[2in] + + Create a ratio between the people that the recipe serves (4) and the people to + serve (8). + + 4:8 + + Simplify the ratio. + + 1:2 + + So it takes 2 lots of each ingredient, for every 1 in the recipe. + + This means: + \begin{itemize} + \item 400g of flour + \item 200g of butter + \item 100g of sugar + \item 4 eggs + \end{itemize} + +\end{solution} + +\question + +John and Sam run a race, in total the race takes them 1 hour, however John is +twice as fast as Sam. How long does Sam take to finish the race? + +\begin{solution}[2in] + + Create a ratio between John's time, and Sam's. + + 1:2 + + Therefore, Sam took twice (2 times) as long as John. + + $2 \times 1hour = 2hours$ + +\end{solution} + +\end{questions} + +\end{document} |