1. **State the problem:** Multiply the mixed fraction $1 \frac{3}{4}$ by 40. 2. **Convert the mixed fraction to an improper fraction:** $$1 \frac{3}{4} = \frac{4 \times 1 + 3}{4} = \frac{7}{4}$$ 3. **Set up the multiplication:** $$\frac{7}{4} \times 40$$ 4. **Rewrite 40 as a fraction:** $$\frac{7}{4} \times \frac{40}{1}$$ 5. **Multiply the numerators and denominators:** $$\frac{7 \times 40}{4 \times 1} = \frac{280}{4}$$ 6. **Simplify the fraction by dividing numerator and denominator by 4:** $$\frac{\cancel{280}^{70}}{\cancel{4}^{1}} = 70$$ 7. **Final answer:** $$70$$ So, $1 \frac{3}{4} \times 40 = 70$.