Problem 3:
Patricia has \(1 \frac{5}{7}\) cookies in her jar right now. The day before, she knew she had \(3 \frac{4}{7}\) cookies in her jar. How many cookies were eaten?
#### Step-by-Step Solution:
1.
Convert mixed numbers to improper fractions:
- \(1 \frac{5}{7} = \frac{7 \times 1 + 5}{7} = \frac{12}{7}\)
- \(3 \frac{4}{7} = \frac{7 \times 3 + 4}{7} = \frac{25}{7}\)
2.
Determine the number of cookies eaten:
- The number of cookies eaten is the difference between the number of cookies Patricia had the day before and the number she has now.
- This can be calculated as:
\[
\text{Cookies eaten} = \text{Cookies yesterday} - \text{Cookies today}
\]
- Substituting the values:
\[
\text{Cookies eaten} = \frac{25}{7} - \frac{12}{7}
\]
3.
Subtract the fractions:
- Since the denominators are the same, subtract the numerators directly:
\[
\frac{25}{7} - \frac{12}{7} = \frac{25 - 12}{7} = \frac{13}{7}
\]
4.
Convert the improper fraction back to a mixed number (if necessary):
- \(\frac{13}{7} = 1 \frac{6}{7}\)
#### Final Answer for Problem 3:
\[
\boxed{1 \frac{6}{7}}
\]
---
Problem 4:
Timothy is only allowed \(\frac{7}{2}\) hours to play video games per day. He already played video games for \(\frac{4}{2}\) hours today. How many hours can Timothy still play video games today?
#### Step-by-Step Solution:
1.
Simplify the fractions if possible:
- \(\frac{7}{2}\) is already in simplest form.
- \(\frac{4}{2} = 2\) (since \(4 \div 2 = 2\)).
2.
Determine the remaining hours Timothy can play:
- The remaining hours are the difference between the total allowed hours and the hours he has already played.
- This can be calculated as:
\[
\text{Remaining hours} = \text{Total allowed hours} - \text{Hours already played}
\]
- Substituting the values:
\[
\text{Remaining hours} = \frac{7}{2} - 2
\]
3.
Convert the whole number to a fraction with the same denominator:
- \(2\) can be written as \(\frac{4}{2}\) (since \(2 = \frac{2 \times 2}{2}\)).
4.
Subtract the fractions:
- Now, subtract \(\frac{4}{2}\) from \(\frac{7}{2}\):
\[
\frac{7}{2} - \frac{4}{2} = \frac{7 - 4}{2} = \frac{3}{2}
\]
5.
Convert the improper fraction back to a mixed number (if necessary):
- \(\frac{3}{2} = 1 \frac{1}{2}\)
#### Final Answer for Problem 4:
\[
\boxed{1 \frac{1}{2}}
\]
---
Summary of Answers:
1.
Problem 3: \(\boxed{1 \frac{6}{7}}\)
2.
Problem 4: \(\boxed{1 \frac{1}{2}}\)
Parent Tip: Review the logic above to help your child master the concept of common core fractions grade 4 worksheet.
