1. **State the problem:** We need to find the value of a fraction equivalent to $\frac{28}{70}$ with denominator 4. 2. **Recall the rule for equivalent fractions:** Two fractions $\frac{a}{b}$ and $\frac{c}{d}$ are equivalent if $a \times d = b \times c$. 3. **Set up the equation:** Let the numerator of the equivalent fraction be $x$. Then: $$\frac{x}{4} = \frac{28}{70}$$ 4. **Cross multiply:** $$x \times 70 = 28 \times 4$$ 5. **Calculate the right side:** $$x \times 70 = 112$$ 6. **Solve for $x$:** $$x = \frac{112}{70}$$ 7. **Simplify the fraction:** $$x = \frac{\cancel{112}^{16} \div 7}{\cancel{70}^{10} \div 7} = \frac{16}{10}$$ 8. **Simplify further:** $$x = \frac{\cancel{16}^{8} \div 2}{\cancel{10}^{5} \div 2} = \frac{8}{5}$$ 9. **Interpret the result:** The numerator $x = \frac{8}{5}$ is not an integer, so there is no integer numerator $x$ such that $\frac{x}{4}$ is exactly equal to $\frac{28}{70}$. However, if we allow $x$ to be a fraction, the equivalent fraction with denominator 4 is $\frac{8}{5} / 4 = \frac{8}{5}$ which is not a proper fraction with denominator 4. 10. **Alternative approach:** Find an equivalent fraction with denominator 4 by simplifying $\frac{28}{70}$ first: $$\frac{28}{70} = \frac{2 \times 14}{5 \times 14} = \frac{2}{5}$$ 11. **Find equivalent fraction with denominator 4:** $$\frac{x}{4} = \frac{2}{5}$$ 12. **Cross multiply:** $$5x = 8$$ 13. **Solve for $x$:** $$x = \frac{8}{5}$$ 14. **Conclusion:** The fraction $\frac{28}{70}$ simplifies to $\frac{2}{5}$, and the equivalent fraction with denominator 4 is $\frac{8}{5}$, which is not a fraction with integer numerator and denominator 4. **Final answer:** There is no integer numerator $x$ such that $\frac{x}{4} = \frac{28}{70}$. The equivalent fraction with denominator 4 is $\frac{8}{5}$ (non-integer numerator).