The quotient of two numbers with different signs is negative.
G
What is the least common multiple of 21 and 7?
H
The product of two positive numbers and one negative number is negative.
A
5/24
B
10/3 or 3 13
C
77/16 or 4 1316
D
- 60/7 or - 8 47
E
0.15
F
- 3.375
G
- 1/21
H
- 0.42
Practice makes perfect
We want to find the common denominator to to simplify the expression.
3/4-1/3+(- 5/24)
In this exercise, we have three fractions with different denominators. We can find a common denominator by finding the least common multiple (LCM) of the denominators. Since 24 is a multiple of both 4 and 3, we can start by multiplying both the numerator and denominator of 34 by 6 and both the numerator and denominator of 13 by 8 to create a common denominator.
When dividing real numbers, the quotient will be positive if the signs are the same and it will be negative if the signs are different.
cc
Same Sign & Different Signs
(+)(+)=(+) & (+)(-)=(-)
(-)(-)=(+) & (-)(+)=(-)
In our case both numbers are positive, so the quotient will be positive.
When multiplying real numbers, the product will be positive if the signs are the same and it will be negative if the signs are different.
cc
Same Sign & Different Signs
(+)(+)=(+) & (+)(-)=(-)
(-)(-)=(+) & (-)(+)=(-)
In our case both numbers are positive, so the product will be positive. Now, we can start by rewriting each mixed number as a fraction.
When dividing real numbers, the quotient will be positive if the signs are the same and it will be negative if the signs are different.
cc
Same Sign & Different Signs
(+)(+)=(+) & (+)(-)=(-)
(-)(-)=(+) & (-)(+)=(-)
In our case one number is negative and one number is positive, so the quotient will be negative.
When multiplying real numbers, the product will be positive if the signs are the same and it will be negative if the signs are different.
cc
Same Sign & Different Signs
(+)(+)=(+) & (+)(-)=(-)
(-)(-)=(+) & (-)(+)=(-)
In our case both numbers are negative, so the product will be negative.
When dividing real numbers, the quotient will be positive if the signs are the same and it will be negative if the signs are different.
cc
Same Sign & Different Signs
(+)(+)=(+) & (+)(-)=(-)
(-)(-)=(+) & (-)(+)=(-)
In our case one number is negative and one number is positive, so the quotient will be negative.
We want to find the common denominator to to simplify the expression.
8/21+(- 3/7)
In this case, we have two fractions with different denominators. Since 24 is a multiple of both 7, we can start by multiplying both the numerator and denominator of - 37 by 3 to create a common denominator.
When multiplying real numbers, the product will be positive if the signs are the same and it will be negative if the signs are different.
cc
Same Sign & Different Signs
(+)(+)=(+) & (+)(-)=(-)
(-)(-)=(+) & (-)(+)=(-)
In our case two numbers are positive and one number is negative. This means that our product will be negative.
