Integers

Operations & Rules

100

Divide: What is 24 ÷ 6?

4

200

Divide: What is -42 ÷ 7?

-6

300

Divide: What is 5 ÷ -2? Give your answer as a rational number (fraction or decimal).

-5/2 or -2.5

400

Evaluate: What is (-3/4) ÷ (1/2)?

(-3/4) ÷ (1/2) = (-3/4) × 2 = -3/2 or -1 1/2

Signs & Patterns

100

True or False: A negative ÷ negative = negative. (Answer and correct the statement if false.)

False. Negative ÷ negative = positive.

200

Pattern: If you divide a positive integer by a negative integer, what is the sign of the quotient?

Negative

300

Compute: What is (-36) ÷ (-4)? Then explain how you determined which sign was correct.

9; negative ÷ negative = positive.

400

Predict: Without calculating fully, determine the sign of (-7) ÷ (2) ÷ (-1). Then explain the rules that you used to figure it out.

• Sign positive; because -7 divided by positive 2 would be negative and then that negative divided by -1 would be positive. 

Rational Results

100

Convert: What is 3 ÷ 4 written as a decimal?

0.75

200

Simplify: What is 6 ÷ 8 as a simplified fraction?

3/4

300

Compute: What is (-5) ÷ 2 as a mixed number or fraction?

-5/2  or  - 2  1/2

400

Long division: Divide 7 by 3 and tell whether the decimal terminates (ends) or repeats.

2.3333... repeats

Algebra with Divsion

100

Variable evaluation: If x = -12, what is x ÷ 3?

-4

200

Solve for x: x ÷ 4 = -6

x = -24

300

Solve for x: -24 ÷ x = 6

x = -4

400

Expression: Write an expression (math problem) for "divide y by -5" and when y = 15.  Then solve.

y ÷ (-5); when y=15: 15 ÷ (-5) = -3

Multi-Step Problems

100

Compute: What is (−8) ÷ 2 + 5?

(-8) ÷ 2 + 5 = -4 + 5 = 1

200

Order of operations: Calculate: 6 + (−12 ÷ 3)

6 + (−12 ÷ 3) = 6 + (−4) = 2

300

Combine operations: What is (−3) × (−4) ÷ 2 ?

(-3) × (-4) ÷ 2 = 12 ÷ 2 = 6

400

Multi-step with fractions: Compute: (1/2) ÷ (−1/4) + 3

• (1/2) ÷ (−1/4) + 3 = (1/2 × -4) + 3 = -2 + 3 = 1