From 65aafc8e77e5bf531990dac90abbd73548b129a1 Mon Sep 17 00:00:00 2001
From: thomasabishop <tactonbishop@gmail.com>
Date: Mon, 2 May 2022 08:00:04 +0100
Subject: [PATCH] Last Sync: 2022-05-02 08:00:04

---
 .../Mixed_and_improper_fractions.md           | 31 ++++++++++++++++++-
 1 file changed, 30 insertions(+), 1 deletion(-)

diff --git a/Mathematics/Prealgebra/Mixed_and_improper_fractions.md b/Mathematics/Prealgebra/Mixed_and_improper_fractions.md
index 885d04a..dd5f977 100644
--- a/Mathematics/Prealgebra/Mixed_and_improper_fractions.md
+++ b/Mathematics/Prealgebra/Mixed_and_improper_fractions.md
@@ -45,4 +45,33 @@ The procedure is as follows:
 Thus:
 $$
     4 \frac{7}{8} = \frac{(4 \cdot 8) + 7 }{8}
-$$
\ No newline at end of file
+$$
+
+## Converting improper fractions into mixed fractions 
+It is quite obvious how to reverse the process and turn an improper fraction into a mixed fraction. 
+
+Take $\frac{27}{5}$. We work out how many times the numerator is divisible by the denominator and make that the whole number. The remainder is then left as the fractional part.
+
+$$
+\begin{split}
+\frac{27}{5} = 27 \div 5  \\
+= 5 r 2 \\
+= 5 \frac{2}{5}
+\end{split}
+$$
+
+##  Multiplying and dividing by mixed fractions
+Now that we know how to convert mixed fractions into improper fractions, it is straight forward to multiply and divide with them. We convert the mixed fraction into an improper fraction and then divide and multiply as we would with a proper fraction. 
+
+### Demonstration
+
+Calculate $-2\frac{1}{12} \cdot 2 \frac{4}{5}$:
+
+1. First convert each mixed fraction into an improper fraction:
+  $$
+  \begin{split}
+  -2\frac{1}{12} = -2 \cdot -12  \\
+  = 24 + 1 \\
+  = \frac{24}{12}
+  \end{split} 
+  $$
\ No newline at end of file