1. The problem is to solve the equation $30 - 7 \frac{1}{4} = 21 \frac{2}{3}$ and verify if it is true. 2. First, convert the mixed numbers to improper fractions for easier calculation. - $7 \frac{1}{4} = \frac{7 \times 4 + 1}{4} = \frac{29}{4}$ - $21 \frac{2}{3} = \frac{21 \times 3 + 2}{3} = \frac{65}{3}$ 3. Rewrite the equation with improper fractions: $$30 - \frac{29}{4} = \frac{65}{3}$$ 4. Convert 30 to a fraction with denominator 1: $$\frac{30}{1} - \frac{29}{4} = \frac{65}{3}$$ 5. Find a common denominator to subtract the fractions on the left side. The least common denominator (LCD) of 1 and 4 is 4. $$\frac{30 \times 4}{1 \times 4} - \frac{29}{4} = \frac{65}{3}$$ $$\frac{120}{4} - \frac{29}{4} = \frac{65}{3}$$ 6. Subtract the fractions on the left: $$\frac{120 - 29}{4} = \frac{91}{4}$$ 7. Now the equation is: $$\frac{91}{4} = \frac{65}{3}$$ 8. To check if these fractions are equal, cross-multiply: $$91 \times 3 = 65 \times 4$$ $$273 = 260$$ 9. Since $273 \neq 260$, the equation is false. Final answer: The equation $30 - 7 \frac{1}{4} = 21 \frac{2}{3}$ is not true.