diff --git a/src/9_crystal_structure.md b/src/9_crystal_structure.md
index a1d53cca6fb65e15a7323f6e5c8aee86ae3dd4f5..72a760ca395c559c7ced0e7b217138bca94b5559 100644
--- a/src/9_crystal_structure.md
+++ b/src/9_crystal_structure.md
@@ -225,7 +225,7 @@ Does the choice of a lattice need to coincide with the centre of our arbitrary $
 > The description of objects with respect to the reference lattice point is known as a **basis**.
 
 The reference lattice point is the chosen lattice point to which we apply the lattice vectors in order to reconstruct the lattice.
-In the 'Lattice A' case, the basis is trivial $\star = (0,0)$ since each lattice points corresponds with the $\star$ object. In 'Lattice B', each object is shifted half a $a_1$ away from the lattice point. Therefore, its basis is $\star = (1/2,0)$ in fractional coordinates. The basis is especially important when a crystal has many different types of atoms (for example manny salts like NaCl)
+In the 'Lattice A' case, the basis is trivial $\star = (0,0)$ since each lattice points corresponds with the $\star$ object. In 'Lattice B', each object is shifted half a $a_1$ away from the lattice point. Therefore, its basis is $\star = (1/2,0)$ in fractional coordinates. The basis is especially important when a crystal has many different types of atoms (for example many salts like NaCl)
 
 Rather than work with the whole space of the crystal, it is practical to use the smallest possible 'building block' of the crystal - a **unit cell**: 
 
diff --git a/src/9_crystal_structure_solutions.md b/src/9_crystal_structure_solutions.md
index 57fac21fa8559b6c641c2fa29697d75dfa25fc30..3be699613d613d29df2d7db9192c148842380058 100644
--- a/src/9_crystal_structure_solutions.md
+++ b/src/9_crystal_structure_solutions.md
@@ -116,7 +116,7 @@ $V = a^3$
 ## Exercise 3: Directions and Spacings of Miller planes
 ### Subquestion 1
 
-Miller plane - plane that intersects and infinite number of lattice points
+Miller plane - plane that intersects an infinite number of lattice points
 
 Miller index - Set of 3 integers which specify a set of parallel planes
 
@@ -124,7 +124,7 @@ Miller index - Set of 3 integers which specify a set of parallel planes
 
 ??? hint "Small hint"
 
-    The $(hkl)$ plane intersects lattice at position vectors of \frac{\mathbf{a_1}}{h}, \frac{\mathbf{a_2}}{k}, \frac{\mathbf{a_1}}{l}. Can you define a general vector inside the $(hkl)$ plane? 
+    The $(hkl)$ plane intersects lattice at position vectors of $\frac{\mathbf{a_1}}{h}, \frac{\mathbf{a_2}}{k}, \frac{\mathbf{a_1}}{l}$. Can you define a general vector inside the $(hkl)$ plane? 
     
 ??? hint "Anoter small hint"