1. **Problem 15:** A student reads $\frac{3}{8}$ of a book on Monday and $\frac{1}{4}$ on Tuesday. We need to find the fraction of the book that remains unread.
2. The total fraction read is the sum of the fractions read on Monday and Tuesday:
$$\frac{3}{8} + \frac{1}{4}$$
3. Convert $\frac{1}{4}$ to eighths to add easily:
$$\frac{1}{4} = \frac{2}{8}$$
4. Add the fractions:
$$\frac{3}{8} + \frac{2}{8} = \frac{5}{8}$$
5. The fraction unread is the whole book minus the fraction read:
$$1 - \frac{5}{8}$$
6. Convert 1 to eighths:
$$\frac{8}{8} - \frac{5}{8}$$
7. Subtract:
$$\frac{8}{8} - \frac{5}{8} = \frac{3}{8}$$
8. **Answer for Question 15:** The fraction of the book unread is $\frac{3}{8}$.
---
9. **Problem 16:** A bottle contains $\frac{2}{3}$ litre of juice shared equally among 4 children. Find how much juice each child receives.
10. Use the formula for equal sharing:
$$\text{Amount per child} = \frac{\text{Total juice}}{\text{Number of children}}$$
11. Substitute values:
$$\frac{2}{3} \div 4$$
12. Division by 4 is multiplication by its reciprocal:
$$\frac{2}{3} \times \frac{1}{4}$$
13. Multiply numerators and denominators:
$$\frac{2 \times 1}{3 \times 4} = \frac{2}{12}$$
14. Simplify the fraction by dividing numerator and denominator by 2:
$$\frac{\cancel{2}}{\cancel{12}} = \frac{1}{6}$$
15. **Answer for Question 16:** Each child receives $\frac{1}{6}$ litre of juice.
Fraction Operations 8E8189
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.