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Sign Rules For Integers

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

Illustration Questions

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

Illustration Questions

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

Illustration Questions

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

Illustration Questions

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

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