4) $$ \frac{2}{10}-2 \frac{3}{10}= $$ 6) $$ 7 \frac{1}{3}-4 \frac{2}{3}= $$

Question

UpStudy AI · Accepted Answer

Calculate the value by following steps:
- step0: Calculate:
  $$\frac{2}{10}-2\frac{3}{10}$$
- step1: Reduce the fraction:
  $$\frac{1}{5}-2\frac{3}{10}$$
- step2: Convert the expressions:
  $$\frac{1}{5}-\frac{23}{10}$$
- step3: Reduce fractions to a common denominator:
  $$\frac{2}{5\times 2}-\frac{23}{10}$$
- step4: Multiply the numbers:
  $$\frac{2}{10}-\frac{23}{10}$$
- step5: Transform the expression:
  $$\frac{2-23}{10}$$
- step6: Subtract the numbers:
  $$\frac{-21}{10}$$
- step7: Rewrite the fraction:
  $$-\frac{21}{10}$$
Calculate or simplify the expression $$ 7 \frac{1}{3}-4 \frac{2}{3} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$7\frac{1}{3}-4\frac{2}{3}$$
- step1: Convert the expressions:
  $$\frac{22}{3}-\frac{14}{3}$$
- step2: Transform the expression:
  $$\frac{22-14}{3}$$
- step3: Subtract the numbers:
  $$\frac{8}{3}$$
Let's solve the two problems step by step.

### Problem 4: $$ \frac{2}{10} - 2 \frac{3}{10} $$

1. **Convert Mixed Number to Improper Fraction**:
   - The mixed number $$ 2 \frac{3}{10} $$ can be converted to an improper fraction:
     $$
     2 \frac{3}{10} = \frac{2 \times 10 + 3}{10} = \frac{20 + 3}{10} = \frac{23}{10}
     $$

2. **Perform the Subtraction**:
   - Now we can rewrite the expression:
     $$
     \frac{2}{10} - \frac{23}{10}
     $$
   - Since the denominators are the same, we can subtract the numerators:
     $$
     \frac{2 - 23}{10} = \frac{-21}{10}
     $$

3. **Final Result**:
   - The result can also be expressed as a mixed number:
     $$
     -\frac{21}{10} = -2 \frac{1}{10}
     $$

### Problem 6: $$ 7 \frac{1}{3} - 4 \frac{2}{3} $$

1. **Convert Mixed Numbers to Improper Fractions**:
   - For $$ 7 \frac{1}{3} $$:
     $$
     7 \frac{1}{3} = \frac{7 \times 3 + 1}{3} = \frac{21 + 1}{3} = \frac{22}{3}
     $$
   - For $$ 4 \frac{2}{3} $$:
     $$
     4 \frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3}
     $$

2. **Perform the Subtraction**:
   - Now we can rewrite the expression:
     $$
     \frac{22}{3} - \frac{14}{3}
     $$
   - Since the denominators are the same, we can subtract the numerators:
     $$
     \frac{22 - 14}{3} = \frac{8}{3}
     $$

3. **Final Result**:
   - The result can also be expressed as a mixed number:
     $$
     \frac{8}{3} = 2 \frac{2}{3}
     $$

### Summary of Results:
- For Problem 4: $$ \frac{2}{10} - 2 \frac{3}{10} = -\frac{21}{10} $$ or $$ -2 \frac{1}{10} $$
- For Problem 6: $$ 7 \frac{1}{3} - 4 \frac{2}{3} = \frac{8}{3} $$ or $$ 2 \frac{2}{3} $$
Problem 4: $$ \frac{2}{10} - 2 \frac{3}{10} = -\frac{21}{10} $$ or $$ -2 \frac{1}{10} $$ Problem 6: $$ 7 \frac{1}{3} - 4 \frac{2}{3} = \frac{8}{3} $$ or $$ 2 \frac{2}{3} $$

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Problem 4:

Problem 6:

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