Subjects algebra

Rational Addition 13E102

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1. **State the problem:** We need to evaluate the expression where the first two rational numbers are added instead of multiplied. Suppose the original expression was $\frac{a}{b} \times \frac{c}{d} \times \frac{e}{f}$, now it becomes $\frac{a}{b} + \frac{c}{d} \times \frac{e}{f}$. 2. **Recall the order of operations:** Multiplication is performed before addition unless parentheses indicate otherwise. 3. **Write the expression:** $$\frac{a}{b} + \frac{c}{d} \times \frac{e}{f}$$ 4. **Calculate the multiplication first:** $$\frac{c}{d} \times \frac{e}{f} = \frac{c \times e}{d \times f}$$ 5. **Rewrite the expression:** $$\frac{a}{b} + \frac{c e}{d f}$$ 6. **Find a common denominator:** The common denominator is $b d f$. 7. **Rewrite each fraction with the common denominator:** $$\frac{a}{b} = \frac{a d f}{b d f}$$ $$\frac{c e}{d f} = \frac{c e b}{b d f}$$ 8. **Add the numerators:** $$\frac{a d f + c e b}{b d f}$$ 9. **Simplify if possible.** **Final answer:** $$\frac{a d f + c e b}{b d f}$$ This is the sum of the first rational number and the product of the second and third rational numbers. Note: Since the user did not provide specific numbers, the answer is given in terms of variables $a,b,c,d,e,f$ representing the numerators and denominators of the three rational numbers.