Area Fraction Fraction Of B
1. Stating the problem for question 22:
Express the area of the living room (26 m²) as a fraction of the area of the kitchen (16.4 m²) and simplify.
2. Write the fraction:
$$\frac{26}{16.4}$$
3. Convert 16.4 to a fraction for easier simplification:
$$16.4 = \frac{164}{10}$$
So the fraction becomes:
$$\frac{26}{\frac{164}{10}} = 26 \times \frac{10}{164} = \frac{260}{164}$$
4. Simplify the fraction by dividing numerator and denominator by their greatest common divisor (GCD). GCD of 260 and 164 is 4.
$$\frac{260 \div 4}{164 \div 4} = \frac{65}{41}$$
5. Final answer for question 22:
$$\frac{65}{41}$$
---
6. Stating the problem for question 23:
Find C as a fraction of B given:
$$B = \frac{7}{4} A$$
$$C = A + 150\% \text{ of } A = A + 1.5 A = 2.5 A$$
7. Express C in terms of B:
Substitute $A$ from $B = \frac{7}{4} A$:
$$A = \frac{4}{7} B$$
8. Calculate C:
$$C = 2.5 A = 2.5 \times \frac{4}{7} B = \frac{10}{4} \times \frac{4}{7} B = \frac{10}{7} B$$
9. Final answer for question 23:
$$C = \frac{10}{7} B$$