# Khan/khan-exercises

Realign linear_equations exercises to tutorial

Summary:
one_step_equations is now only a+x=b
linear_equations_1 is now only ax=b and x/a=b

Test Plan: Tested locally

Reviewers: stephanie

Reviewed By: stephanie

Differential Revision: http://phabricator.khanacademy.org/D911
beneater committed Dec 4, 2012
1 parent 3a9c2f1 commit 3402466232b78d067e6c34bec336196152b975ec
Showing with 187 additions and 94 deletions.
1. +2 −2 css/khan-exercise.css
2. +89 −24 exercises/linear_equations_1.html
3. +96 −68 exercises/one_step_equations.html
 @@ -5,10 +5,10 @@ var { font-style: normal; } .hint_blue { color: #6495ED; } .hint_orange { color: #FFA500; } .hint_pink { color: #FF00AF; } -.hint_red { color: red; } +.hint_red { color: #DF0030; } .hint_green { color: #28AE7B; } .hint_gray { color: gray; } -.hint_purple{ color: purple; } +.hint_purple{ color: #9D38BD; } .final_answer { font-weight: bold; }
 @@ -8,42 +8,107 @@
- - randRange( 2, 10 ) - randRange( 2, 10 ) - fractionReduce( D, A ) - fractionReduce( 1, A ) + randFromArray("x") + randRange(2, 10) + randRange(2, 10) + fractionReduce(D, A) + fractionReduce(1, A)
-
-

Solve for x:

-
Ax = D
+
+

Solve for X:

+
AX = D
-

x = D / A

+

X = D / A

+
+
+

Divide both sides by A:

+

+ \red{\dfrac{\color{black}{AX}}{A}} = + \red{\dfrac{\color{black}{D}}{A}} +

+
+
+

Simplify:

+

\dfrac{\cancel{A}X}{\cancel{A}} = SOLUTION

+
+

X = SOLUTION

+
+
+ +
+

Solve for X:

+
D = AX
+
+

X = D / A

+
+
+
+

Divide both sides by A:

+

+ \red{\dfrac{\color{black}{D}}{A}} = + \red{\dfrac{\color{black}{AX}}{A}} +

+
+
+

Simplify:

+

SOLUTION = \dfrac{\cancel{A}X}{\cancel{A}}

+
+

X = SOLUTION

+
-
-
-
-

Multiply both sides by ONE_OVER_A.

-

(ONE_OVER_A) \cdot (Ax) = (ONE_OVER_A) \cdot (D)

+
+

Solve for X:

+
\dfrac{X}{A} = D
+ +
+

X = D * A

+
+
+
+

Multiply both sides by A:

+

+ \dfrac{X}{A} \red{\cdot A} = + D \red{\cdot A} +

+
+
+

Simplify:

+

\dfrac{X}{\cancel{A}} \cdot \cancel{A} = A * D

+
+

X = A * D

+
-
-

Simplify.

-

x = SOLUTION

+ +
+

Solve for X:

+
D = \dfrac{X}{A}
+ +
+

X = D * A

+
+
+
+

Multiply both sides by A:

+

+ D \red{\cdot A} = + \dfrac{X}{A} \red{\cdot A} +

+
+
+

Simplify:

+

A * D = \dfrac{X}{\cancel{A}} \cdot \cancel{A}

+
+

X = A * D

+
+
 @@ -7,108 +7,136 @@
-
- "abkmnpvx" - LETTERS.charAt( randRange( 0, LETTERS.length - 1 ) ) +
+

Solve equations in the forms:

+

\qquad x + 5 = 10

+

\qquad 5 + x = 10

+

\qquad 10 = x + 5

+

\qquad 10 = 5 + x

+
+ randFromArray("abkmnpvx") + randRangeNonZero(-30, 30) + randRangeNonZero(-30, 30) +
+

Solve for X:

+
+

X= B - A

+
+
-
-
- randRange( 0, 3 ) - randRangeNonZero( -30, 30 ) - randRangeNonZero( -30, 30 ) - Y > 0 ? "-" : "+" - [expr( ["+", X, Y] ), expr( ["+", Y, X] ), Z, Z][INDEX] - [Z, Z, expr( ["+", X, Y] ), expr( ["+", Y, X] )][INDEX] -
-

Solve for X.

-

\large{LEFT = RIGHT}

-
-
-

X= Z - Y

-
+
+

A + X = B

-

Add Y * -1 toSubtract Y from both sides.

-

\large{X = RIGHT\color{blue}{Y_SIGNabs( Y )}}

-

\large{LEFT\color{blue}{Y_SIGNabs( Y )} = X}

+

+ Add abs(A) to both sides: + Subtract abs(A) from both sides: +

\qquad + \begin{eqnarray} \\ + A + X &=& B \\ \\ + \red{A < 0 ? "+" : "-"abs(A)} && \red{A < 0 ? "+" : "-"abs(A)} + \end{eqnarray} +

+
+
+

\qquad + \begin{eqnarray} + \hphantom{A + X} &\hphantom{=}& \hphantom{B} \\ + X &=& B \red{- A} \\ + \end{eqnarray} +

Simplify.

-

\large{X = Z - Y}

+

\qquad X = B - A

-
-
- randRange( 0, 1 ) - randRange( 2, 20 ) * randRangeNonZero( -1, 1 ) - randRange( 2, 20 - abs( Y ) + 5 ) * randRangeNonZero( -1, 1 ) * Y - Y * Z > 0 ? "" : "-" - [expr( ["*", Y, X] ), Z][INDEX] - [Z, expr( ["*", Y, X] )][INDEX] -
-

Solve for X.

-

\large{LEFT = RIGHT}

-
-

X= Z / Y

-
- +
+

X + A = B

-
-

Divide both sides by Y.

-

\large{X = \dfrac{Z}{\color{blue}{Y}}}

-

\large{X = \color{blue}{Y_SIGN}Y_SIGN\dfrac{abs( Z )}{\color{blue}{abs( Y )}}}

+
+

+ Add abs(A) to both sides: + Subtract abs(A) from both sides: +

\qquad + \begin{eqnarray} \\ + X + A &=& B \\ \\ + \red{A < 0 ? "+" : "-"abs(A)} && \red{A < 0 ? "+" : "-"abs(A)} + \end{eqnarray} +

-
-

Divide both sides by Y.

-

\large{\dfrac{Z}{\color{blue}{Y}} = X}

-

\large{\color{blue}{Y_SIGN}Y_SIGN\dfrac{abs( Z )}{\color{blue}{abs( Y )}} = X}

+
+

\qquad + \begin{eqnarray} + \hphantom{A + X} &\hphantom{=}& \hphantom{B} \\ + X &=& B \red{- A} \\ + \end{eqnarray} +

Simplify.

-

\large{X = Z / Y}

+

\qquad X = B - A

-
-
- randRange( 0, 1 ) - randRange( 2, 20 ) - randRange( 2, 20 - abs( Y ) + 5 ) * randRangeNonZero( -1, 1 ) -
-

Solve for X.

-

\large{\dfrac{X}{Y} = Z}

- -
-

X= Z * Y

-
- +
+

B = A + X

-

Multiply both sides by Y.

-

\large{X = Z \cdot {\color{blue}{Y}}}

+

+ Add abs(A) to both sides: + Subtract abs(A) from both sides: +

\qquad + \begin{eqnarray} \\ + \hphantom{B \red{- A}} &\hphantom{=}& \hphantom{X} \\ + B &=& A + X \\ \\ + \red{A < 0 ? "+" : "-"abs(A)} && \red{A < 0 ? "+" : "-"abs(A)} \\ + \end{eqnarray} +

+
+
+

\qquad + \begin{eqnarray} \\ + B \red{- A} &=& X \\ + \end{eqnarray} +

Simplify.

-

\large{X = Z * Y}

+

\qquad X = B - A

-
-

\large{Z = \dfrac{X}{Y}}

+
+

B = X + A

-

Multiply both sides by Y.

-

\large{Z \cdot {\color{blue}{Y}} = X}

+

+ Add abs(A) to both sides: + Subtract abs(A) from both sides: +

\qquad + \begin{eqnarray} \\ + \hphantom{B \red{- A}} &\hphantom{=}& \hphantom{X} \\ + B &=& X + A \\ \\ + \red{A < 0 ? "+" : "-"abs(A)} && \red{A < 0 ? "+" : "-"abs(A)} \\ + \end{eqnarray} +

+
+
+

\qquad + \begin{eqnarray} \\ + B \red{- A} &=& X \\ + \end{eqnarray} +

Simplify.

-

\large{X = Z * Y}

+

\qquad X = B - A

-