Question: (3) -1 2/3 + 1/15 = -1 10/15 + 1/15
(4) -1 2/3 - 1/15 = -1 10/15 - 1/15
(5) - 2/3 + 2 1/15 =
(6) 2/3 - 2 1/15 =User:
1. **Problem:** Simplify and verify the equality for (3) $-1 \frac{2}{3} + \frac{1}{15} = -1 \frac{10}{15} + \frac{1}{15}$.
2. Convert mixed numbers to improper fractions:
$$-1 \frac{2}{3} = -\left(1 + \frac{2}{3}\right) = -\frac{5}{3}$$
$$-1 \frac{10}{15} = -\left(1 + \frac{10}{15}\right) = -\frac{25}{15}$$
3. Express all fractions with a common denominator 15:
$$-\frac{5}{3} = -\frac{5 \times 5}{3 \times 5} = -\frac{25}{15}$$
4. Substitute back:
$$-\frac{25}{15} + \frac{1}{15} = -\frac{25}{15} + \frac{1}{15}$$
5. Add the fractions:
$$-\frac{25}{15} + \frac{1}{15} = -\frac{24}{15}$$
6. Simplify the fraction by dividing numerator and denominator by 3:
$$-\frac{\cancel{24}}{\cancel{15}} = -\frac{8}{5}$$
7. Similarly, the right side:
$$-\frac{25}{15} + \frac{1}{15} = -\frac{24}{15} = -\frac{8}{5}$$
8. Both sides equal $-\frac{8}{5}$, so the equality holds.
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1. **Problem:** Simplify and verify the equality for (4) $-1 \frac{2}{3} - \frac{1}{15} = -1 \frac{10}{15} - \frac{1}{15}$.
2. Using previous conversions:
$$-1 \frac{2}{3} = -\frac{25}{15}$$
3. Substitute:
$$-\frac{25}{15} - \frac{1}{15} = -\frac{25}{15} - \frac{1}{15}$$
4. Add the fractions:
$$-\frac{25}{15} - \frac{1}{15} = -\frac{26}{15}$$
5. Right side:
$$-1 \frac{10}{15} - \frac{1}{15} = -\frac{25}{15} - \frac{1}{15} = -\frac{26}{15}$$
6. Both sides equal $-\frac{26}{15}$, so the equality holds.
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1. **Problem:** Simplify (5) $- \frac{2}{3} + 2 \frac{1}{15}$.
2. Convert mixed number to improper fraction:
$$2 \frac{1}{15} = \frac{31}{15}$$
3. Express $-\frac{2}{3}$ with denominator 15:
$$-\frac{2}{3} = -\frac{10}{15}$$
4. Add:
$$-\frac{10}{15} + \frac{31}{15} = \frac{21}{15}$$
5. Simplify by dividing numerator and denominator by 3:
$$\frac{\cancel{21}}{\cancel{15}} = \frac{7}{5}$$
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1. **Problem:** Simplify (6) $\frac{2}{3} - 2 \frac{1}{15}$.
2. Convert mixed number:
$$2 \frac{1}{15} = \frac{31}{15}$$
3. Express $\frac{2}{3}$ with denominator 15:
$$\frac{2}{3} = \frac{10}{15}$$
4. Subtract:
$$\frac{10}{15} - \frac{31}{15} = -\frac{21}{15}$$
5. Simplify:
$$-\frac{\cancel{21}}{\cancel{15}} = -\frac{7}{5}$$