Math, Chapter 8: Multiply and Divide Signed Rational Numbers.

Let a and b be non-zero integers. Which of the following is NOT true?

(-a/b) = (-a/-b)

The steps to simplify the expression 5 ÷ 100 × (-0.7) × (-20) are shown below, with one step missing. 5 ÷ 1/100 x (-0.7) x (-20) = 5 x 100 x (-0.7) x (-20) =? = -100 x (-70) =7000 Which is the missing step?

(5 x (-20)) x (100 x (-0.7))

For every 240 days of milking, cow's milk production decreases by 2 gallons. Which shows the average change in cow's production?

-(1/120) gallons per day

Howard is rock climbing. He descended 300 meters in 5 hours. Which is NOT equivalent to Howard's average change in location per hour?

-(300/5) meters per hour

In the following expression, 𝘯 is a rational number: -0.7(𝘯 + (-𝘯)) Which expression below is equivalent to this expression?

-0.7 x 𝘯 + (-0.7) x (-𝘯)

Which is equivalent to -36/3?

-12

Apply the distributive property to simplify -1/2(12+30).

-14

Which expression is equivalent to -3.5 (4x - 3)?

-14x - 10.5

A fish descended 3 feet each minute. Which expression should be used to find the total depth of descent in 5 minutes?

5(-3)

Evaluate the expression using properties of operations. -1.2 ÷ 1/6 × 5 × (-2)

72

Marie was trying to show her friend why -3x-8 equals a positive product. This is what she wrote: -3x0=0 -3x -3(8)+-3(-8)= 0 -24+24=0 What should Marie write in place of the question mark?

8 + (-8)

A grizzly bear's top speed is about 36 mph. This speed makes the bear about 1 1/2 times as fast as an African elephant. What is the top speed of an African elephant?

An African elephant can reach a top speed of about 24 mph because 36÷ 3/2 = 24.

Quiz:

Applying Properties to Multiply and Divide Rational Numbers

Quiz:

Dividing Integers

Sarah used properties of operations to write the following three equivalent expressions to 1/2 [-4+8+(-6)]. Expression 1: 1/2 (-4) + 1/2 (8) + 1/2 (-6) Expression 2: 11-4+(-6) +4 Expression 3: -2+4+3 Which of the expressions is not equivalent and what was Sarah's error?

Expression 3. Sarah applied the Distributive Property but incorrectly multiplied 1/2 (-6).

Quiz:

Interpreting Products of Rational Numbers

Quiz:

Interpreting Quotients of Rational Numbers

Quiz:

Multiplying Signed Rational Numbers

Miranda wrote the following incorrect equation while attempting to simplify the expression 8 × 10 1/4. 8 x (10 1/4) = (8 + 10) x (8 + 1/4) How can Miranda correct her mistake in the right hand side of the equation?

She should switch addition to multiplication and multiplication to addition.

A submarine started at sea level and was 400 meters below sea level in 10 minutes. Which statement correctly explains the submarine's rate of movement?

Since -400/10= -40, you find that the submarine descended at a rate of 40 meters per minute.

The steps to simplify the expression -100 ÷ 3 × (-0.6) are shown. -100 ÷ 3 × (-0.6) = -100 × 1⁄3 × (-0.6) Step 1 =-100 x (-0.6) x 1/3 Step 2 = 60 × 1/2 Step 3 =20 Step 4 Which step is justified by the commutative property of multiplication?

Step 2

To make the perfect purple hue, the artist used 1/2 cup of blue paint per batch and 3/4 cup of red paint per batch. He wanted to make 17 batches of purple paint. What does 1/2 (17) represent?

The amount of blue paint he will need.

At the hot dog stand, 1/3 of all hot dogs served had sesame 3 buns, 2/5 of all hot dogs had ketchup, and 1/10 to of all hot dogs were plain. What does the product of 1/3(2/5) stand for?

The amount of hot dogs with sesame buns and ketchup.

Marcus is filling a pool with water. The pool had 18 gallons of water and 25 minutes later had 428 gallons of water. What does the quotient of 16.4 mean?

The pool is being filled at a rate of 16.4 gallons per minute.

Which of the following is true if Tom walks his dog 13.5 blocks each day and Margo walks her dog 12.5 blocks each day?

The product of 4(13.5) means that Tom walked his dog 54 blocks in 4 days.

Brenna writes a product of six negative factors. She uses the following steps to determine that the product of the six numbers will be positive. Step 3 is missing. 1. Group the factors into pairs. 2. The numbers in each pair have the same sign. 3.___________________________________________ 4. The product of three positive numbers is positive. 5. Therefore, the product of the original six factors is positive. What is step 3?

The product of two numbers with the same sign is positive.

There were 512 cups of water in a cooler before a soccer game. After the soccer game there were 384 cups of water in the cooler. There are 16 cups in a gallon. Which one of the following statements is true?

The quotient 128/16 = 8 means that 8 gallons of water were used during the soccer game.

Earth has 24 time zones spread over its 360° circumference. Each time zone is 15° wide. Boston is close to longitude 71° W; Honolulu is close to longitude 158° W. How many time zones apart are Boston and Honolulu?

They are 6 time zones apart because 87/15 = 6.

Tracey's dog weighed 38.5 pounds. Tracey weighed her dog and found that the dog lost 1/2 pound each month for three months. Tracey used the expression 38.5+ 3(0.5) to find her dog's weight at the end of the 3 months. What is the error in Tracey's expression?

Tracey's dog is losing weight so she should have used -0.5 instead of 0.5 in the expression.

Let a and b be non-zero integers. Done Which of the following is always true about the ratio -a/b?

c) It is always a rational number. You cannot determine its sign without knowing the values of a and b.