Algebra Worksheet featuring two activities: completing number sentences and solving equations with variables.

Problem Explanation and Solution

The worksheet provided involves basic algebraic concepts, focusing on solving equations and substituting values into expressions. Let's solve each part step by step.

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#### Activity A: Complete each number sentence

We need to find the missing numbers in each equation.

1. a) \( 56 + \square = 60 \)
To find the missing number, subtract 56 from 60:
\[
60 - 56 = 4
\]
So, the answer is:
\[
\boxed{4}
\]

2. b) \( \square + 90 = 100 \)
To find the missing number, subtract 90 from 100:
\[
100 - 90 = 10
\]
So, the answer is:
\[
\boxed{10}
\]

3. c) \( 35 + \square = 46 \)
To find the missing number, subtract 35 from 46:
\[
46 - 35 = 11
\]
So, the answer is:
\[
\boxed{11}
\]

4. d) \( \square + 14 = 20 \)
To find the missing number, subtract 14 from 20:
\[
20 - 14 = 6
\]
So, the answer is:
\[
\boxed{6}
\]

5. e) \( 125 + \square = 130 \)
To find the missing number, subtract 125 from 130:
\[
130 - 125 = 5
\]
So, the answer is:
\[
\boxed{5}
\]

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#### Activity B: Write a number sentence to show each of the following

We need to substitute the given values into the expressions and simplify them.

1. f) If \( \triangle = 8 \), what is \( 6 + \triangle \)?
Substitute \( \triangle = 8 \) into the expression:
\[
6 + \triangle = 6 + 8 = 14
\]
So, the answer is:
\[
\boxed{14}
\]

2. g) When \( X = 4 \), find \( X + X + 3 \).
Substitute \( X = 4 \) into the expression:
\[
X + X + 3 = 4 + 4 + 3 = 8 + 3 = 11
\]
So, the answer is:
\[
\boxed{11}
\]

3. h) What is \( b + 2 \) when \( b = 7 \)?
Substitute \( b = 7 \) into the expression:
\[
b + 2 = 7 + 2 = 9
\]
So, the answer is:
\[
\boxed{9}
\]

4. i) If \( y = 5 \), what is \( 10 + y \)?
Substitute \( y = 5 \) into the expression:
\[
10 + y = 10 + 5 = 15
\]
So, the answer is:
\[
\boxed{15}
\]

5. j) When \( n = 13 \), what is \( n + n \)?
Substitute \( n = 13 \) into the expression:
\[
n + n = 13 + 13 = 26
\]
So, the answer is:
\[
\boxed{26}
\]

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Final Answers:

- Activity A:
a) \( \boxed{4} \)
b) \( \boxed{10} \)
c) \( \boxed{11} \)
d) \( \boxed{6} \)
e) \( \boxed{5} \)

- Activity B:
f) \( \boxed{14} \)
g) \( \boxed{11} \)
h) \( \boxed{9} \)
i) \( \boxed{15} \)
j) \( \boxed{26} \)

Boxed Final Answer:
\[
\boxed{4, 10, 11, 6, 5, 14, 11, 9, 15, 26}
\]