5th Grade Integers Worksheet | Addition and Subtraction of Integers - Free Printable

Let's solve the problems step by step.

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Problem 1: Find the given integers

#### (i) Opposite of 71
The opposite of a number is its additive inverse. For any integer \( x \), the opposite is \( -x \).

- The opposite of 71 is \( -71 \).

Answer: \(\boxed{-71}\)

#### (ii) Opposite of -42
Similarly, the opposite of \(-42\) is \( -(-42) \), which simplifies to \( 42 \).

Answer: \(\boxed{42}\)

#### (iii) \( |-71| \)
The absolute value of a number is its distance from zero on the number line, so it is always non-negative. For any integer \( x \), \( |x| = x \) if \( x \geq 0 \), and \( |x| = -x \) if \( x < 0 \).

- The absolute value of \(-71\) is \( 71 \).

Answer: \(\boxed{71}\)

#### (iv) 4 more than -7
To find "4 more than \(-7\)", we add 4 to \(-7\):

\[
-7 + 4 = -3
\]

Answer: \(\boxed{-3}\)

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Problem 2: Find the value of the following

#### (i) \( 81 + 16 \)
Add the two positive integers:

\[
81 + 16 = 97
\]

Answer: \(\boxed{97}\)

#### (ii) \( -20 - 12 \)
Subtracting a positive number is the same as adding its opposite. So, \(-20 - 12\) is the same as \(-20 + (-12)\):

\[
-20 - 12 = -32
\]

Answer: \(\boxed{-32}\)

#### (iii) \( 20 - 55 \)
Subtracting a larger positive number from a smaller one results in a negative number. Here, \( 20 - 55 \) is the same as \( 20 + (-55) \):

\[
20 - 55 = -35
\]

Answer: \(\boxed{-35}\)

#### (iv) \( -6 - 3 \)
Subtracting a positive number is the same as adding its opposite. So, \(-6 - 3\) is the same as \(-6 + (-3)\):

\[
-6 - 3 = -9
\]

Answer: \(\boxed{-9}\)

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Problem 3: Write true or false for the given statements

#### (i) Zero is the smallest integer.
This statement is false. Integers extend infinitely in both the positive and negative directions. There is no smallest integer because negative integers can be arbitrarily large in magnitude (e.g., \(-1, -2, -3, \ldots\)).

Answer: \(\boxed{\text{False}}\)

#### (ii) The smallest negative integer is -1.
This statement is true. Among all negative integers, \(-1\) is the closest to zero and thus the "smallest" in the sense of being the least negative.

Answer: \(\boxed{\text{True}}\)

#### (iii) 0 is greater than -4.
This statement is true. On the number line, 0 is to the right of \(-4\), meaning 0 is greater than \(-4\).

Answer: \(\boxed{\text{True}}\)

#### (iv) -16 is greater than -26.
This statement is true. On the number line, \(-16\) is to the right of \(-26\), meaning \(-16\) is greater than \(-26\).

Answer: \(\boxed{\text{True}}\)

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Final Answers

1. (i) \(\boxed{-71}\)
(ii) \(\boxed{42}\)
(iii) \(\boxed{71}\)
(iv) \(\boxed{-3}\)

2. (i) \(\boxed{97}\)
(ii) \(\boxed{-32}\)
(iii) \(\boxed{-35}\)
(iv) \(\boxed{-9}\)

3. (i) \(\boxed{\text{False}}\)
(ii) \(\boxed{\text{True}}\)
(iii) \(\boxed{\text{True}}\)
(iv) \(\boxed{\text{True}}\)