### 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.
1. 24
2. 25
3. 23
4. 243
5. 51
6. 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.
1. 14 / 20
2. 7 / 12
3. 24 / 36
4. 4 / 24
5. 24 / 4
6. 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.
1. 5 / 13 + 4 / 13
2. 5 / 8 - 3 / 8
3. 5 /8 - 1 / 2
4. 27 / 3 - 20 / 8
5. 3 / 5 + 5 / 3
6. 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.)
1. (3 / 5) * (4 / 7)
2. (3 / 5) * (5 / 3)
3. (14 / 5) * (4 / 21)
4. (1 / 2) * (2 / 3) * (3 / 4)
5. (3 / 5) * 5
6. 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.)
1. (3 / 5) / (4 / 7)
2. (3 / 5) / (5 / 3)
3. (14 / 5) / (4 / 21)
4. (3 / 5) / 4
5. 5 / (1 / 2)
6. 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.
1. 2 ^ (3 + 2)
2. (7 + 5) / (2 + 4)
3. 2 ^ 3 + 2
4. 7 / (2 + 4) + 5
5. -5 * 2^2 + 100
6. 5 * 8 - 4 * 7
7. (2 + 13) / (2 + 3)
8. 2 ^ (5 - 1)
9. sqrt(9 + 16)
10. (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.
1. 2 ^ (3 + 2)
2. 2 ^ 3 + 2
3. (7 + 5) / (2 + 4)
4. 7 + 5 / (2 + 4)
5. (7 + 5) / 2 + 4