Multiplication Rules
What is the product of (-3) x (-4)?
12
Multiplying two negative numbers results in a positive product.
If the temperature drops 3 degrees every hour for 4 hours, what is the total change in temperature?
-12 degrees.
(-3) × 4 = -12.
What is 6 ÷ (-3)?
-2
Dividing a positive by a negative results in a negative quotient.
Covert 1/4
0.25
Divide 1 by 4
A bank account decreases by $20 each day for 3 days. What is the total change?
-$60
(-20) × 3 = -60.
What property explains why (-2)(3 + 4) = (-2)(3) + (-2)(4)?
The Distributive Property
This property ensures multiplication applies to each term inside the parentheses.
A hiker descends 5 meters per minute. After 6 minutes, how far has the hiker descended?
-30 meters.
(-5) × 6 = -30.
If -12 ÷ 4 = x, what is x?
-3.
Dividing a negative by a positive results in a negative.
Convert 2/3 to a decimal.
0.6666666666........(repeating)
Divide 2 by 3; the result repeats
A runner completes 3/4 of a lap in 0.25 hours. What is their spped in laps per hour?
3 laps/hour
3/4 divided by 0.25 = 3
Is (-5)(0) positive, negative, or zero?
0
Any number multiplied by 0 equals 0.
A company loses $50 each day for 7 days. What is the total loss?
-$350.
Simplify (-20) ÷ (-4).
5
Dividing two negatives results in a positive.
is -7/8 a rational number?
Yes, Rational numbers can be expressed as fractions.
A container holds 2.5 gallons. If used evenly over 5 days, how much is used per day?
0.5 gallons
What is the product of (-1)(-1)(-1)?
-1
Multiplying three negatives results in a negative because there is an odd number of negative factors.
A submarine rises 15 feet per minute for 3 minutes. What is its change in depth?
45 feet
(-15)(-3) = 45, since both the rate and time are negative.
If p = -24 and q = -6, what is p ÷ q?
4
(-24) ÷ (-6) = 4, since both are negative.
Write -1.25 as a fraction.
-5/4, Convert the decimal to a fraction by placing it over 100 and simplifying.
A cyclist rides -20 miles west, then -10 miles east. What is their total distance?
-30 miles.
(-20) + (-10) = -30.
Why does (-1)(-x) = x for any rational number x?
Multiplying two negatives results in a positive, so -1 times -x equals x.
A car's speed decreases by 8 mph every hour. After 5 hours, what is the total decrease in speed?
-40 mph.
(-8) × 5 = -40.
Why does (-p) ÷ q = p ÷ (-q)?
The placement of the negative does not change the result.
Division rules ensure a single negative in any position results in a negative quotient.
Convert -0.4 to a fraction
-2/5, Write it as -4/10 and simplify.
A recipe calls for 2/3 cup of sugar, but only 1/2 the reciepe is being made. How much sugar is needed?
1/3 cup
2/3 x 1/2 = 1/3