Answer :
Sure, let's solve each problem step-by-step using mental math techniques.
### Problem 1: [tex]\( 8.6 + 23.4 + 1.4 \)[/tex]
First, we add [tex]\( 8.6 \)[/tex] and [tex]\( 1.4 \)[/tex]:
[tex]\[ 8.6 + 1.4 = 10 \][/tex]
Then, we add the result to [tex]\( 23.4 \)[/tex]:
[tex]\[ 10 + 23.4 = 33.4 \][/tex]
So, the sum is:
[tex]\[ 8.6 + 23.4 + 1.4 = 33.4 \][/tex]
### Problem 2: [tex]\( 27 - 9.9 \)[/tex]
For this, we can think of subtracting [tex]\( 10 \)[/tex] and then adding back [tex]\( 0.1 \)[/tex]:
[tex]\[ 27 - 10 = 17 \][/tex]
[tex]\[ 17 + 0.1 = 17.1 \][/tex]
So, the difference is:
[tex]\[ 27 - 9.9 = 17.1 \][/tex]
### Problem 3: [tex]\( 13.5 + 5.7 + 36.5 \)[/tex]
First, add [tex]\( 13.5 \)[/tex] and [tex]\( 36.5 \)[/tex]:
[tex]\[ 13.5 + 36.5 = 50 \][/tex]
Next, add [tex]\( 5.7 \)[/tex] to [tex]\( 50 \)[/tex]:
[tex]\[ 50 + 5.7 = 55.7 \][/tex]
So, the sum is:
[tex]\[ 13.5 + 5.7 + 36.5 = 55.7 \][/tex]
### Problem 4: [tex]\( 205.4 - 99.7 \)[/tex]
One way to do this is by adjusting [tex]\( 99.7 \)[/tex] to [tex]\( 100 \)[/tex] and then compensating:
Subtract [tex]\( 100 \)[/tex] from [tex]\( 205.4 \)[/tex]:
[tex]\[ 205.4 - 100 = 105.4 \][/tex]
Then, add back the [tex]\( 0.3 \)[/tex] difference:
[tex]\[ 105.4 + 0.3 = 105.7 \][/tex]
So, the difference is:
[tex]\[ 205.4 - 99.7 = 105.7 \][/tex]
### Summary of Solutions:
1. [tex]\( 8.6 + 23.4 + 1.4 = 33.4 \)[/tex]
2. [tex]\( 27 - 9.9 = 17.1 \)[/tex]
3. [tex]\( 13.5 + 5.7 + 36.5 = 55.7 \)[/tex]
4. [tex]\( 205.4 - 99.7 = 105.7 \)[/tex]
These are the calculated answers for each of the problems.
### Problem 1: [tex]\( 8.6 + 23.4 + 1.4 \)[/tex]
First, we add [tex]\( 8.6 \)[/tex] and [tex]\( 1.4 \)[/tex]:
[tex]\[ 8.6 + 1.4 = 10 \][/tex]
Then, we add the result to [tex]\( 23.4 \)[/tex]:
[tex]\[ 10 + 23.4 = 33.4 \][/tex]
So, the sum is:
[tex]\[ 8.6 + 23.4 + 1.4 = 33.4 \][/tex]
### Problem 2: [tex]\( 27 - 9.9 \)[/tex]
For this, we can think of subtracting [tex]\( 10 \)[/tex] and then adding back [tex]\( 0.1 \)[/tex]:
[tex]\[ 27 - 10 = 17 \][/tex]
[tex]\[ 17 + 0.1 = 17.1 \][/tex]
So, the difference is:
[tex]\[ 27 - 9.9 = 17.1 \][/tex]
### Problem 3: [tex]\( 13.5 + 5.7 + 36.5 \)[/tex]
First, add [tex]\( 13.5 \)[/tex] and [tex]\( 36.5 \)[/tex]:
[tex]\[ 13.5 + 36.5 = 50 \][/tex]
Next, add [tex]\( 5.7 \)[/tex] to [tex]\( 50 \)[/tex]:
[tex]\[ 50 + 5.7 = 55.7 \][/tex]
So, the sum is:
[tex]\[ 13.5 + 5.7 + 36.5 = 55.7 \][/tex]
### Problem 4: [tex]\( 205.4 - 99.7 \)[/tex]
One way to do this is by adjusting [tex]\( 99.7 \)[/tex] to [tex]\( 100 \)[/tex] and then compensating:
Subtract [tex]\( 100 \)[/tex] from [tex]\( 205.4 \)[/tex]:
[tex]\[ 205.4 - 100 = 105.4 \][/tex]
Then, add back the [tex]\( 0.3 \)[/tex] difference:
[tex]\[ 105.4 + 0.3 = 105.7 \][/tex]
So, the difference is:
[tex]\[ 205.4 - 99.7 = 105.7 \][/tex]
### Summary of Solutions:
1. [tex]\( 8.6 + 23.4 + 1.4 = 33.4 \)[/tex]
2. [tex]\( 27 - 9.9 = 17.1 \)[/tex]
3. [tex]\( 13.5 + 5.7 + 36.5 = 55.7 \)[/tex]
4. [tex]\( 205.4 - 99.7 = 105.7 \)[/tex]
These are the calculated answers for each of the problems.
