\(\frac { 1} { 2} \) divided by \(\frac { 3} { 4} \) in simplest form.

1. Set up the division: 

\[\frac { 1} { 2} \div \frac { 3} { 4} \] 
2. Multiply by the reciprocal: 

\[\frac { 1} { 2} \times \frac { 4} { 3} \] 
3. Multiply the numerators and denominators: 

\[\frac { 1 \times 4} { 2 \times 3} = \frac { 4} { 6} \] 
4. Simplify the fraction: 

\[\frac { 4} { 6} = \frac { 2} { 3} \]

Supplemental Knowledge:

Dividing fractions involves multiplying by the reciprocal of the divisor. Here’s a step-by-step guide to dividing fractions:

1. Identify the Fractions:
The dividend is \(1/2\). 
The divisor is \(3/4\).

2. Find the Reciprocal of the Divisor:
The reciprocal of \(3/4\) is \(4/3\).

3. Multiply the Dividend by the Reciprocal of the Divisor:
\(\frac { 1} { 2} \times \frac { 4} { 3} \)

4. Multiply the Numerators and Denominators:
Numerator: \(1 \times 4 = 4\) 
Denominator: \(2 \times 3 = 6\)

5. Simplify the Fraction if Possible:
The fraction obtained is \(4/6\). 
Simplify by dividing both numerator and denominator by their greatest common divisor, which is 2: 
\[\frac { 4 ÷ 2} { 6 ÷ 2}  = \frac { 2} { 3} \]

Everyday Examples:

Imagine you're cooking and need to adjust a recipe. Knowing how to divide fractions can be invaluable when trying to determine how much of an ingredient you actually require; say for instance a half-cup recipe calls for three quarters instead, knowing fractions is invaluable in helping determine how much is actually necessary for its completion.

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