Let's solve each part step-by-step.
### Part (a): [tex]\( 8 + (6 + 5) = (6 + 8) + \_ \)[/tex]
1. Start by simplifying both sides of the equation.
- Left side: [tex]\( 8 + (6 + 5) \)[/tex]
- First, calculate the innermost parentheses [tex]\( 6 + 5 \)[/tex]:
[tex]\[ 6 + 5 = 11 \][/tex]
- Then add 8 to the result:
[tex]\[ 8 + 11 = 19 \][/tex]
- Right side: [tex]\( (6 + 8) + \_ \)[/tex]
- First, calculate the parentheses [tex]\( 6 + 8 \)[/tex]:
[tex]\[ 6 + 8 = 14 \][/tex]
2. To balance the equation, the right side should also equal 19:
[tex]\[ 14 + \_ = 19 \][/tex]
3. Solve for the missing number:
[tex]\[ \_ = 19 - 14 \][/tex]
[tex]\[ \_ = 5 \][/tex]
So, the missing number is 5.
### Part (c): [tex]\( (4 + \_) + 2 = (2 + 5) + 4 \)[/tex]
1. Start by simplifying the right side:
- Right side: [tex]\( (2 + 5) + 4 \)[/tex]
- Calculate [tex]\( 2 + 5 \)[/tex]:
[tex]\[ 2 + 5 = 7 \][/tex]
- Then add 4 to the result:
[tex]\[ 7 + 4 = 11 \][/tex]
2. To balance the equation, the left side should also equal 11:
[tex]\[ (4 + \_) + 2 = 11 \][/tex]
3. Simplify the left side:
- [tex]\( 4 + \_ = x \)[/tex]:
4. Solve for [tex]\( x \)[/tex]:
[tex]\[ x + 2 = 11 \][/tex]
[tex]\[ x = 11 - 2 \][/tex]
[tex]\[ x = 9 \][/tex]
- So, [tex]\( 4 + \_ = 9 \)[/tex]
5. Solve for the missing number:
[tex]\[ \_ = 9 - 4 \][/tex]
[tex]\[ \_ = 5 + 4 \][/tex]
[tex]\[ \_ = 4 \][/tex]
So, the missing number is 4.
### Part (d): [tex]\( 9 + (5 + 10) = \_ + (9 + 5) \)[/tex]
1. Start by simplifying both sides of the equation:
- Left side: [tex]\( 9 + (5 + 10) \)[/tex]
- First, calculate the parentheses [tex]\( 5 + 10 \)[/tex]:
[tex]\[ 5 + 10 = 15 \][/tex]
- Then add [tex]\( 9 \)[/tex] to the result:
[tex]\[ 9 + 15 = 24 \][/tex]
- Right side: [tex]\( \_ + (9 + 5) \)[/tex]
- First, calculate the parentheses [tex]\( 9 + 5 \)[/tex]:
[tex]\[ 9 + 5 = 14 \][/tex]
2. To balance the equation, the right side should also equal 24:
[tex]\[ \_ + 14 = 24 \][/tex]
3. Solve for the missing number:
[tex]\[ \_ = 24 - 14 \][/tex]
[tex]\[ \_ = 10 \][/tex]
So, the missing number is 10.
### Summary
- (a) The missing number is [tex]\( 5 \)[/tex].
- (c) The missing number is [tex]\( 4 \)[/tex].
- (d) The missing number is [tex]\( 10 \)[/tex].
