Subjects algebra

Area Fraction Fraction Of B

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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: $$C = \frac{10}{7} B$$