Last Sync: 2022-05-02 08:30:04

Mathematics/Prealgebra/Mixed_and_improper_fractions.md

@@ -72,6 +72,40 @@ Calculate $-2\frac{1}{12} \cdot 2 \frac{4}{5}$:
     \begin{split}
     -2\frac{1}{12} = -2 \cdot -12  \\
     = 24 + 1 \\
-  = \frac{24}{12}
+    = - \frac{25}{12}
     \end{split} 
   $$
+
+  $$
+  \begin{split}
+    2 \frac{4}{5} =2 \cdot 5 \\
+    = 10 + 4 \\ 
+    = \frac{14}{5}
+  \end{split} 
+  $$
+
+2. Then carry out the multiplication [using factorization](./Multiplying_fractions.md#prime-factorisation-in-place):
+  $$
+    \begin{split}
+    - \frac{25}{12} \cdot \frac{14}{5} = \\
+   - \frac{(5 \cdot 5) \cdot (7 \cdot 2)}{(3 \cdot 2 \cdot 2) \cdot (5)} = - \frac{5 \cdot 7 }{2 \cdot 3} \\
+    \end{split} 
+  $$
+
+3. Then simplify:
+  $$
+    - \frac{35}{6}
+  $$
+
+4. Finally, convert back into a mixed fraction:
+  
+  $$
+    \begin{split}
+    - \frac{35}{6} = -35 \div 6 \\
+    -  5 r 5 = \\ 
+    - 5 \frac{5}{6}
+    \end{split} 
+  $$
+
+  ## Adding and subtracting mixed fractions
+