Alright! Let's solve each part of the question step by step:
### 1. [tex]\( 2 \times \frac{1}{2} \)[/tex]
To find the product of [tex]\( 2 \)[/tex] and [tex]\( \frac{1}{2} \)[/tex]:
[tex]\[ 2 \times \frac{1}{2} = 1.0 \][/tex]
### 2. [tex]\( 2 \frac{1}{4} \times 3 \frac{1}{3} \)[/tex]
First, convert the mixed numbers to improper fractions:
[tex]\[ 2 \frac{1}{4} = 2 + \frac{1}{4} = 2.25 \][/tex]
[tex]\[ 3 \frac{1}{3} = 3 + \frac{1}{3} = 3.333 \][/tex]
Next, multiply these two quantities:
[tex]\[ 2.25 \times 3.333 = 7.5 \][/tex]
Then, multiply [tex]\(\frac{1}{8}\)[/tex] by [tex]\(\frac{1}{4}\)[/tex]:
[tex]\[ \frac{1}{8} \times \frac{1}{4} = 0.03125 \][/tex]
### 3. [tex]\( 3 - (3 \frac{1}{2} \times 3 \frac{2}{5}) \)[/tex]
First, convert the mixed numbers to improper fractions:
[tex]\[ 3 \frac{1}{2} = 3 + \frac{1}{2} = 3.5 \][/tex]
[tex]\[ 3 \frac{2}{5} = 3 + \frac{2}{5} = 3.4 \][/tex]
Next, multiply these quantities:
[tex]\[ 3.5 \times 3.4 = 11.9 \][/tex]
Finally, subtract this product from 3:
[tex]\[ 3 - 11.9 = -8.9 \][/tex]
### 4. [tex]\( 4 \frac{3}{5} + 5 \frac{3}{4} \)[/tex]
First, convert the mixed numbers to improper fractions:
[tex]\[ 4 \frac{3}{5} = 4 + \frac{3}{5} = 4.6 \][/tex]
[tex]\[ 5 \frac{3}{4} = 5 + \frac{3}{4} = 5.75 \][/tex]
Next, add these two quantities:
[tex]\[ 4.6 + 5.75 = 10.35 \][/tex]
### 5. [tex]\( \frac{1}{2} \times 3 \frac{4}{1} \)[/tex]
First, convert the mixed number to improper fractions:
[tex]\[ 3 \frac{4}{1} = 3 + 4 = 7 \][/tex]
Next, multiply [tex]\( \frac{1}{2} \)[/tex] by 7:
[tex]\[ \frac{1}{2} \times 7 = 3.5 \][/tex]
In conclusion, the final answers for the given questions are:
1. [tex]\( 2 \times \frac{1}{2} = 1.0 \)[/tex]
2. [tex]\( 2 \frac{1}{4} \times 3 \frac{1}{3} = 7.5 \)[/tex]
3. [tex]\( \frac{1}{8} \times \frac{1}{4} = 0.03125 \)[/tex]
4. [tex]\( 3 - (3 \frac{1}{2} \times 3 \frac{2}{5}) = -8.9 \)[/tex]
5. [tex]\( 4 \frac{3}{5} + 5 \frac{3}{4} = 10.35 \)[/tex]
6. [tex]\( \frac{1}{2} \times 3 \frac{4}{1} = 3.5 \)[/tex]
