Informative line

# Sign Rules for Addition of Integers

• The sign rule for addition of integers states:
• When we add two integers of the same sign, the sum will have the same sign of the integers.

Positive + Positive = Positive

Negative +Negative = Negative

• But when we add two integers with different signs, we need to find out which integer has a bigger absolute value.
• Suppose, we have a positive and a negative integer then,
• If the positive integer has a bigger absolute value, the sum will be a positive integer.

Example : $$-3+5=?$$

$$|-3|=3,\;|5|=5$$

Here, $$|5|$$ has a bigger absolute value than $$|-3|$$.

Since $$5$$ has a positive sign, so the sum will also have a positive sign.

$$-3+5=$$ a positive integer

• If the negative integer has a bigger absolute value, the sum will be a negative integer.

Example : $$7+(-9)=?$$

$$|7|=7$$ and $$|-9|=9$$

Here, $$|-9|$$ has a bigger absolute value than $$|7|$$.

Since $$-9$$ has a negative sign, so the sum will also have a negative sign.

$$7+(-9)=$$ a negative integer

#### Which one of the following expressions gives a negative integer as the answer?

A $$14+(-13)$$

B $$-12+10$$

C $$-10+12$$

D $$7+(-5)$$

×

Option (A): $$14+(-13)$$

$$|14|=14,\;|-13|=13$$

Here, $$|14|$$ has a bigger absolute value than $$|-13|$$.

Since  $$14$$ has a positive sign, so the sum will also have a positive sign.

$$14+(-13)=$$ a positive integer

Hence, option (A) is incorrect.

Option (B): $$-12+10$$

$$|-12|=12,\;|10|=10$$

Here, $$|-12|$$ has a bigger absolute value than $$|10|$$.

Since $$-12$$ has a negative sign, so the sum will also have a negative sign.

$$-12+10=$$ a negative integer

Hence, option (B) is correct.

Option (C): $$-10+12$$

$$|-10|=10,\;|12|=12$$

Here, $$|12|$$ has a bigger absolute value than $$|-10|$$.

Since $$12$$ has a positive sign,  so the sum will also have a positive sign.

$$-10+12=$$ a positive integer

Hence, option (C) is incorrect.

Option (D): $$7+(-5)$$

$$|7|=7,\;|-5|=5$$

Here, $$|7|$$ has a bigger absolute value than $$|-5|$$.

Since  $$7$$ has a positive sign, so the sum will also have a positive sign.

$$7+(-5)=$$ a positive integer

Hence, option (D) is incorrect.

### Which one of the following expressions gives a negative integer as the answer?

A

$$14+(-13)$$

.

B

$$-12+10$$

C

$$-10+12$$

D

$$7+(-5)$$

Option B is Correct

# Sign Rules for Subtraction of Integers

• The sign rule for subtraction of integers states:
• When we subtract two integers, then consider the following cases:

1. Positive – Positive

• If the first integer is greater than the second, we get a positive integer as the answer.

$$4-2=$$ Positive integer

• If the second integer is greater than the first, we get a negative integer as the answer.

$$2-4=$$ Negative integer

2. Negative – Positive

• If the first integer is negative and the second integer is positive then we get a negative integer as the answer.

$$-4-2=$$ Negative integer

3. Positive – Negative

• If the first integer is positive and the second integer is negative, we get a positive integer as the answer.

$$4-(-2)=$$ Positive integer

4. Negative – Negative

• If the absolute value of the first integer is greater than the absolute value of the second integer, we get a negative integer as the answer.

$$-4-(-2)=$$ Negative integer

• If the absolute value of the second integer is greater than the absolute value of the first integer, we get a positive integer as the answer.

$$-2-(-4)=$$ Positive integer

#### Which one of the following expressions gives a positive integer as the answer?

A $$-6-(-7)$$

B $$6-7$$

C $$-7-(-6)$$

D $$-6-7$$

×

Option (A):

$$-6-(-7)$$

Here, Negative – Negative

If the absolute value of the second integer is greater than the absolute value of the first integer, we get a positive integer as the answer.

$$\because\;|-6|=6,\;|-7|=7$$ and $$7>6$$

$$\therefore\;-6-(-7)=$$ Positive integer

Hence, option (A) is correct.

Option (B):

$$6-7$$

Here,  Positive – Positive

If the second integer is greater than the first, we get a negative integer as the answer.

$$\therefore\;6-7=$$ Negative integer

Hence, option (B) is incorrect.

Option (C):

$$-7-(-6)$$

Here,  Negative – Negative

If the absolute value of the first integer is greater than the absolute value of the second integer, we get a negative integer as the answer.

$$\because\;|-7|=7,\;|-6|=6$$ and $$7>6$$

$$\therefore\;-7-(-6)=$$ Negative integer

Hence, option (C) is incorrect.

Option (D):

$$-6-7$$

Here,  Negative – Positive

If the first integer is negative and the second integer is positive, we get a negative integer as the answer.

$$-6-7=$$ Negative integer

Hence, option (D) is incorrect.

### Which one of the following expressions gives a positive integer as the answer?

A

$$-6-(-7)$$

.

B

$$6-7$$

C

$$-7-(-6)$$

D

$$-6-7$$

Option A is Correct

# Sign Rules for Multiplication of Integers

• The sign rule for multiplication of integers states:
• When we multiply two integers of the same sign, we get a positive integer as the answer.

Positive × Positive = Positive

Negative × Negative = Positive

• But when we multiply two integers with different signs, we get a negative integer as the answer.

Positive × Negative = Negative

Negative × Positive = Negative

#### Which one of the following expressions gives a negative integer as the answer?

A $$-3×4$$

B $$-3×(-4)$$

C $$3×4$$

D $$5×20$$

×

Option (A): $$-3×4$$

Here, $$-3$$ is a negative integer and $$4$$ is a positive integer.

When we multiply two integers with different signs, we get a negative integer as the answer.

Thus, $$-3×4=$$ a negative integer

Hence, option (A) is correct.

Option (B): $$-3×(-4)$$

Here, $$-3$$ is a negative integer and $$-4$$ is also a negative integer.

When we multiply two integers with the same sign, we get a positive integer as the answer.

Thus, $$-3×(-4)=$$ a positive integer

Hence, option (B) is incorrect.

Option (C): $$3×4$$

Here, $$3$$ is a positive integer and $$4$$ is also a positive integer.

When we multiply two integers with the same sign, we get a positive integer as the answer.

Thus, $$3×4=$$ a positive integer

Hence, option (C) is incorrect.

Option (D): $$5×20$$

Here, $$5$$ is a positive integer and $$20$$ is also a positive integer.

When we multiply two integers with the same sign, we get a positive integer as the answer.

Thus, $$5×20=$$ a positive integer

Hence, option (D) is incorrect.

### Which one of the following expressions gives a negative integer as the answer?

A

$$-3×4$$

.

B

$$-3×(-4)$$

C

$$3×4$$

D

$$5×20$$

Option A is Correct

# Sign Rules for Division of Integers

• The sign rule for division of integers states:
•  When dividend and divisor are of the same sign, we get a positive integer as the answer.

Positive ÷ Positive = Positive

Negative ÷ Negative = Positive

• But when dividend and divisor are of different signs, we get a negative integer as the answer.

Positive ÷ Negative = Negative

Negative ÷ Positive = Negative

#### Which one of the following expressions gives a positive integer as the answer?

A $$12\div(-4)$$

B $$-15\div5$$

C $$-12\div(-4)$$

D $$-12\div4$$

×

Option (A): $$12\div(-4)$$

Here, $$12$$ is a positive integer and $$-4$$ is a negative integer.

When dividend and divisor are of different signs, we get a negative integer as the answer.

Thus, $$12\div(-4)=$$ a negative integer

Hence, option (A) is incorrect.

Option (B): $$-15\div5$$

Here, $$-15$$ is a negative integer and $$5$$ is a positive integer.

When dividend and divisor are of different signs, we get a negative integer as the answer.

Thus, $$-15\div5=$$ a negative integer

Hence, option (B) is incorrect.

Option (C): $$-12\div(-4)$$

Here, $$-12$$ is a negative integer and $$-4$$ is also a negative integer.

When dividend and divisor are of the same sign, we get a positive integer as the answer.

Thus, $$-12\div(-4)=$$ a positive integer

Hence, option (C) is correct.

Option (D): $$-12\div4$$

Here, $$-12$$ is a negative integer and $$4$$ is a positive integer.

When dividend and divisor are of different signs, we get a negative integer as the answer.

Thus, $$-12\div4=$$ a negative integer

Hence, option (D) is incorrect.

### Which one of the following expressions gives a positive integer as the answer?

A

$$12\div(-4)$$

.

B

$$-15\div5$$

C

$$-12\div(-4)$$

D

$$-12\div4$$

Option C is Correct