Ordering
Which is greater:
−2.5−2.5 or −3.1−3.1?
Explain why.
-2.5-2.5 is greater.
-2.5-2.5=-5, and -3.1-3.1=-6.2, and -5>-6.2
Compute: −3+7.
4
Compute: (−4)×6.
-24
Maya owes $12. She pays back $5. Represent this as adding or subtracting signed numbers and find her remaining debt.
-12 + 5 = -7
Maya owes $7
Convert the mixed number 2 1/3 to an improper fraction.
7/3
Place these numbers in ascending order: 3/4, −0.9, 5/8, 0
-0.9, 0, 5/8, 3/4
Compute: 5.2+(−8.7).
Explain how you got your answer.
-3.5
Compute: (−2/3)×9/4. Simplify.
-18/12 = -3/2 or -1 1/2
A scuba diver is at −18 feet. She ascends 7 feet, then descends 12 feet. What is her final depth? Show as a computation with integers.
-23 feet
(-18 + 7 - 12 = -11 - 12 = -23)
Add: 1 1/4 + (-2/3). Give the result as a simplified fraction.
7/12
Which is farther from zero on the number line: −7 or 13/2? Show reasoning.
-7
-7 is 7 away from zero and 13/2=6.5, which is only 6.5 away from zero.
Evaluate: −5/6 − 1/3.
Show work (common denominators).
-7/6 or -1 1/6
(-5/6 - 2/6 = -7/6)
Evaluate: −5÷(2/5). Show steps and interpret the result.
-5÷(2/5)
-5/1 ÷ 2/5
-5/1 x 5/2
= -25/2 or -12 1/2
A recipe needs 3/4 cup of oil for one batch. You make −2 batches (i.e., remove two batches). Interpret and compute the total change in oil amount.
-3/2 cups or -1 1/2 cups.
(3/4 * -2 = 3/4 * -2/1 = -6/4 = -3/2 or -1 1/2)
Subtract: (-3 2/5) - (1 1/5)
-23/5 or -4 3/5
Compare using <, >, or = :
−2/3 ? −0.66.
Explain which is "bigger".
-2/3 < -0.66
-2/3 has a "bigger" value since it is further from zero, but -0.66 is "greater" because it is higher or more to the right on a number line.
A temperature model: If the temperature is −4oF and it drops 7oF, what is the new temperature? Write an expression using integers and then solve it.
-11oF
(-4 + -7 = -11 or -4 - 7 = -11)
Compute: (−3/7)×(−14/9) and explain why the product is positive or negative.
42/63 = 2/3
Positive. The signs match, -*- = +
A bank account has $45.50. A check for $72.25 is cashed. What is the account balance after the check? Show the operation using rational numbers and interpret the sign.
$117.75
45.50 + 72.25 = 117.75, positive because she has money, she is not in debt.
Multiply: (2 1/2) × (-4/5)
= (5/2) × (-4/5)
= -20/10
= -2
Between which two consecutive integers does −17/4 lie? Convert to a mixed number to justify.
Between -5 and -4, because
-17/4 = -4 1/4
Compute and explain using a number line: (-3/4) + (11/6). Show your work.
-3/4 + 11/6
-9/12 + 22/12
13/12 or 1 1/12
Explain why (−1)×(5/3)+(5/3)=0.
= -5/3 + 5/3
These are additive inverses, so they combine to equal 0.
A whale is swimming at 600 meters below sea level. Directly above the whale is a plane flying 1,400 meters above sea level. What is the difference in elevation between the whale and the plane?
2,000 meters.
(1,400 - -600 = 2,000 meters)
Divide: (-3 3/4) ÷ (2/5)
= (-15/4) ÷ (2/5)
= (-15/4) × (5/2)
= -75/8