### Chapter 1 - Algebra Coach Exercises

**Algebra Coach Exercise on factoring numbers.**

Factor the following numbers.
To do this drag-and-drop each number into the
Algebra Coach and then click the Factor button.
- 24
- 25
- 23
- 243
- 51
- 47250

**Algebra Coach Exercise on simplest equivalent fractions.**

Reduce each of the following fractions to its
simplest equivalent fraction.
To do this drag-and-drop each fraction into the
Algebra Coach and then click the Simplify a Fraction button.
- 14 / 20
- 7 / 12
- 24 / 36
- 4 / 24
- 24 / 4
- 126 / 72

**Algebra Coach Exercise on adding and subtracting fractions.**

For each question add or subtract the fractions.
To do this drag-and-drop each question into the
Algebra Coach and then click the Add 2 Fractions button.
- 5 / 13 + 4 / 13
- 5 / 8 - 3 / 8
- 5 /8 - 1 / 2
- 27 / 3 - 20 / 8
- 3 / 5 + 5 / 3
- 27 / 3 - 36 / 4

**Algebra Coach Exercise on multiplying fractions.**

For each question multiply the fractions.
To do this drag-and-drop each question into the
Algebra Coach and then click the Simplify button twice.

(Required Options setting: the *exact or floating point* option must be set to *keep exact*.)
- (3 / 5) * (4 / 7)
- (3 / 5) * (5 / 3)
- (14 / 5) * (4 / 21)
- (1 / 2) * (2 / 3) * (3 / 4)
- (3 / 5) * 5
- 10 * (3 / 5)

**Algebra Coach Exercise on dividing fractions.**

For each question divide the fractions.
To do this drag-and-drop each question into the
Algebra Coach and then click the Simplify button repeatedly.

(Required Options setting: the *exact or floating point* option must be set to *keep exact*.)
- (3 / 5) / (4 / 7)
- (3 / 5) / (5 / 3)
- (14 / 5) / (4 / 21)
- (3 / 5) / 4
- 5 / (1 / 2)
- 3 / (3 / 5)

**Algebra Coach Exercise on order of operations.**

Simplify each of the following expressions as much as possible, paying attention
to the order of operations.
To do this drag-and-drop each expression into the
Algebra Coach and click the Simplify button repeatedly.
- 2 ^ (3 + 2)
- (7 + 5) / (2 + 4)
- 2 ^ 3 + 2
- 7 / (2 + 4) + 5
- -5 * 2^2 + 100
- 5 * 8 - 4 * 7
- (2 + 13) / (2 + 3)
- 2 ^ (5 - 1)
- sqrt(9 + 16)
- (sqrt(4 + 5) + 2) / (5 + 2)

**Algebra Coach Exercise on invisible brackets.**

Simplify each of the following expressions as much as possible.
To do this drag-and-drop each expression into the
Algebra Coach and click the Simplify button repeatedly.
Notice how the invisible brackets affect the order of operations.
- 2 ^ (3 + 2)
- 2 ^ 3 + 2
- (7 + 5) / (2 + 4)
- 7 + 5 / (2 + 4)
- (7 + 5) / 2 + 4