Answer :
To determine how many cookies the baker can make with the available cookie dough, we need to follow these steps:
1. Understand the Given Values:
- The baker has [tex]\(4 \frac{3}{4}\)[/tex] pounds of cookie dough.
- Each cookie requires [tex]\(\frac{1}{16}\)[/tex] pound of dough.
2. Convert the Mixed Number to an Improper Fraction:
- Convert [tex]\(4 \frac{3}{4}\)[/tex] into an improper fraction.
- First, multiply the whole number 4 by the denominator 4, which gives 16.
- Add the numerator 3 to get [tex]\(16 + 3 = 19\)[/tex].
- So, [tex]\(4 \frac{3}{4}\)[/tex] is equivalent to [tex]\(\frac{19}{4}\)[/tex] pounds of dough.
3. Divide to Find the Number of Cookies:
- We divide the total amount of dough by the amount needed for each cookie.
- This means dividing [tex]\(\frac{19}{4}\)[/tex] by [tex]\(\frac{1}{16}\)[/tex].
- Dividing by a fraction is the same as multiplying by its reciprocal, so:
[tex]\[
\frac{19}{4} \div \frac{1}{16} = \frac{19}{4} \times \frac{16}{1}
\][/tex]
- Multiply the numerators: [tex]\(19 \times 16 = 304\)[/tex].
- Multiply the denominators: [tex]\(4 \times 1 = 4\)[/tex].
- So, we have [tex]\(\frac{304}{4}\)[/tex], which simplifies when we divide 304 by 4.
4. Simplify the Result:
- Divide 304 by 4 to get 76.
Therefore, the baker can make 76 cookies with the dough available.
1. Understand the Given Values:
- The baker has [tex]\(4 \frac{3}{4}\)[/tex] pounds of cookie dough.
- Each cookie requires [tex]\(\frac{1}{16}\)[/tex] pound of dough.
2. Convert the Mixed Number to an Improper Fraction:
- Convert [tex]\(4 \frac{3}{4}\)[/tex] into an improper fraction.
- First, multiply the whole number 4 by the denominator 4, which gives 16.
- Add the numerator 3 to get [tex]\(16 + 3 = 19\)[/tex].
- So, [tex]\(4 \frac{3}{4}\)[/tex] is equivalent to [tex]\(\frac{19}{4}\)[/tex] pounds of dough.
3. Divide to Find the Number of Cookies:
- We divide the total amount of dough by the amount needed for each cookie.
- This means dividing [tex]\(\frac{19}{4}\)[/tex] by [tex]\(\frac{1}{16}\)[/tex].
- Dividing by a fraction is the same as multiplying by its reciprocal, so:
[tex]\[
\frac{19}{4} \div \frac{1}{16} = \frac{19}{4} \times \frac{16}{1}
\][/tex]
- Multiply the numerators: [tex]\(19 \times 16 = 304\)[/tex].
- Multiply the denominators: [tex]\(4 \times 1 = 4\)[/tex].
- So, we have [tex]\(\frac{304}{4}\)[/tex], which simplifies when we divide 304 by 4.
4. Simplify the Result:
- Divide 304 by 4 to get 76.
Therefore, the baker can make 76 cookies with the dough available.
