To determine how much flour goes into each cake, let's follow these steps:
1. Identify the total amount of flour: Baker John has [tex]\(\frac{2}{3}\)[/tex] pound of flour available.
2. Identify the number of cakes: John needs to divide the flour between 2 cakes.
3. Calculate the amount of flour per cake:
- We divide the total flour by the number of cakes.
- The amount of flour per cake is [tex]\(\frac{2}{3} \div 2\)[/tex].
4. Simplify the division:
- Recall that dividing by a number is equivalent to multiplying by its reciprocal. The reciprocal of 2 is [tex]\(\frac{1}{2}\)[/tex].
- Therefore, [tex]\(\frac{2}{3} \div 2\)[/tex] can be rewritten as [tex]\(\frac{2}{3} \times \frac{1}{2}\)[/tex].
5. Multiply the fractions:
- Multiply the numerators: [tex]\(2 \times 1 = 2\)[/tex].
- Multiply the denominators: [tex]\(3 \times 2 = 6\)[/tex].
- This results in the fraction [tex]\(\frac{2}{6}\)[/tex].
6. Simplify the fraction:
- [tex]\(\frac{2}{6}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
- [tex]\(\frac{2 \div 2}{6 \div 2} = \frac{1}{3}\)[/tex].
Therefore, each cake will receive [tex]\(\frac{1}{3}\)[/tex] pound of flour. To further confirm, the result is approximately [tex]\(0.333\)[/tex] when converted to a decimal.
So, each cake gets [tex]\(0.333\)[/tex] pounds of flour.
