Phone Plans: Check the Quotients

Use signed division to compare plan adjustments.

Quotient Checks

Find each missing number or choose the correct statement. Write noninteger answers as simplified fractions or decimals.

−35 ÷ 7 =

13 ÷ (−4) =

(−21)/(−10) =

Find the missing integer divisor.

28 ÷ = −7

Which statement correctly describes (−17)/6?

A. It is rational because it is a ratio of integers with a nonzero denominator.B. It is undefined because its numerator is a negative integer.C. It is an integer because both starting numbers are integers.D. It is irrational because the division has a nonzero remainder.

Signs and Zero

Check where the negative sign belongs and when division is defined.

Select every expression equal to −(8/15).

Which statement about zero is correct?

A. 0 ÷ (−9) is undefined, but (−9) ÷ 0 equals 0.B. 0 ÷ (−9) equals 0, but (−9) ÷ 0 is undefined.C. 0 ÷ (−9) and (−9) ÷ 0 are both undefined.D. 0 ÷ (−9) and (−9) ÷ 0 both equal 0.

For integers p and q, which restriction makes all three expressions in this equation defined?
−(p/q) = (−p)/q = p/(−q)

A. The integer p must not equal 0.B. The integer q must not equal 0.C. The integers p and q must both be positive.D. The integers p and q must have opposite signs.

A phone plan comparison uses negative dollar amounts for reductions in a bill. Each adjustment below is spread equally over the listed months.

Bill Adjustments
Plan	Total adjustment ($)	Months
Flex	−9	6
Connect	−14	8

What is Flex's signed adjustment per month? dollars per month

10.

Use the Bill Adjustments table in question 9. Which comparison of the signed monthly adjustments is correct?

A. Connect's is more negative: −1.75 dollars versus −1.50 dollars.B. The adjustments are equal: each is −0.50 dollars per month.C. Connect's is more negative: −14 dollars versus −9 dollars.D. Flex's is more negative: −1.50 dollars versus −1.75 dollars.

Plan Decisions

Apply division to each plan situation. Use a signed number when the question asks for a signed adjustment.

11.

A provider corrects an overcount of data use. The total signed correction is −5 GB, spread equally across 4 days.

What is the signed correction per day? GB per day

12.

A family pays a total activation fee of $0 for 3 phone lines. Which calculation correctly gives the activation fee per line?

A. 3 ÷ 0 gives a fee of $0 per line.B. 3 ÷ 0 gives a fee of $3 per line.C. 0 ÷ 3 gives a fee of $0 per line.D. 0 ÷ 3 gives an undefined fee per line.

13.

Noor rewrites a signed monthly bill adjustment as −(19/8) = (−19)/(−8). Which correction preserves the original value?

A. Use (−19)/(−8) because a negative quotient needs two negative signs.B. Use 19/8 because two negative signs cancel.C. Use 8/(−19) because moving a negative sign reverses the fraction.D. Use 19/(−8) because one negative sign makes the quotient negative.

14.

A plan spreads an $11 bill reduction equally over 4 months. Eli says, “The signed monthly adjustment must be a whole number because −11 and 4 are integers.” Find the signed monthly adjustment. Explain why Eli's conclusion is wrong and why the result is rational.