Sure! Let's solve the given problem step-by-step.
1. Fraction Operation (Addition):
[tex]\[
\frac{1}{2} + \frac{3}{4}
\][/tex]
To add these fractions, we need a common denominator. The common denominator of 2 and 4 is 4.
[tex]\[
\frac{1}{2} = \frac{2}{4}
\][/tex]
Now we can add:
[tex]\[
\frac{2}{4} + \frac{3}{4} = \frac{5}{4} = 1.25
\][/tex]
So, the result of [tex]\(\frac{1}{2} + \frac{3}{4}\)[/tex] is [tex]\(1.25\)[/tex].
2. Arithmetic Sequence (First Sequence):
We have a sequence starting with 4 and increasing by 2 each step:
[tex]\[
4, 6, 8, 10
\][/tex]
3. Arithmetic Sequence (Second Sequence):
We have a sequence starting with 8 and increasing by 4 each step:
[tex]\[
8, 12, 16, 20
\][/tex]
4. Fraction Operation (Division):
[tex]\[
\frac{1}{2} \div \frac{2}{4}
\][/tex]
Division of fractions is equivalent to multiplying by the reciprocal. The reciprocal of [tex]\(\frac{2}{4}\)[/tex] which simplifies to [tex]\(\frac{1}{2}\)[/tex] is [tex]\(\frac{4}{2}\)[/tex] or 2.
[tex]\[
\frac{1}{2} \div \frac{2}{4} = \frac{1}{2} \times 2 = 1.0
\][/tex]
5. Fraction Operation (Multiplication):
[tex]\[
\frac{3}{4} \times \frac{1}{2}
\][/tex]
To multiply fractions, multiply the numerators and the denominators:
[tex]\[
\frac{3 \times 1}{4 \times 2} = \frac{3}{8} = 0.375
\][/tex]
Summary of results:
1. [tex]\(\frac{1}{2} + \frac{3}{4} = 1.25\)[/tex]
2. Sequence: [tex]\(4, 6, 8, 10\)[/tex]
3. Sequence: [tex]\(8, 12, 16, 20\)[/tex]
4. [tex]\(\frac{1}{2} \div \frac{2}{4} = 1.0\)[/tex]
5. [tex]\(\frac{3}{4} \times \frac{1}{2} = 0.375\)[/tex]
Therefore, the detailed solutions to the given mathematical operations are as follows:
[tex]\[
(1.25, [4, 6, 8, 10], [8, 12, 16, 20], 1.0, 0.375)
\][/tex]
