$$ \begin{array}{lll}\frac{1}{2}-\frac{5}{6} & ext { 22. } & \frac{1}{2} imes \frac{5}{6} \ 2 \frac{1}{4} imes 1 \frac{3}{5} & ext { 26. } & 1 \frac{1}{15}+2 \frac{1}{2}\end{array} $$

Question

$$ \begin{array}{lll}\frac{1}{2}-\frac{5}{6} & 	ext { 22. } & \frac{1}{2} 	imes \frac{5}{6} \ 2 \frac{1}{4} 	imes 1 \frac{3}{5} & 	ext { 26. } & 1 \frac{1}{15}+2 \frac{1}{2}\end{array} $$

UpStudy AI · Accepted Answer

Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1}{2}\times \frac{5}{6}$$
- step1: Multiply the fractions:
  $$\frac{5}{2\times 6}$$
- step2: Multiply:
  $$\frac{5}{12}$$
Calculate or simplify the expression $$ \frac{1}{2}-\frac{5}{6} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1}{2}-\frac{5}{6}$$
- step1: Reduce fractions to a common denominator:
  $$\frac{3}{2\times 3}-\frac{5}{6}$$
- step2: Multiply the numbers:
  $$\frac{3}{6}-\frac{5}{6}$$
- step3: Transform the expression:
  $$\frac{3-5}{6}$$
- step4: Subtract the numbers:
  $$\frac{-2}{6}$$
- step5: Reduce the fraction:
  $$\frac{-1}{3}$$
- step6: Rewrite the fraction:
  $$-\frac{1}{3}$$
Calculate or simplify the expression $$ 2+\frac{1}{4} \times 1+\frac{3}{5} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$2+\frac{1}{4}\times 1+\frac{3}{5}$$
- step1: Multiply:
  $$2+\frac{1}{4}+\frac{3}{5}$$
- step2: Reduce fractions to a common denominator:
  $$\frac{2\times 4\times 5}{4\times 5}+\frac{5}{4\times 5}+\frac{3\times 4}{5\times 4}$$
- step3: Multiply the numbers:
  $$\frac{2\times 4\times 5}{20}+\frac{5}{4\times 5}+\frac{3\times 4}{5\times 4}$$
- step4: Multiply the numbers:
  $$\frac{2\times 4\times 5}{20}+\frac{5}{20}+\frac{3\times 4}{5\times 4}$$
- step5: Multiply the numbers:
  $$\frac{2\times 4\times 5}{20}+\frac{5}{20}+\frac{3\times 4}{20}$$
- step6: Transform the expression:
  $$\frac{2\times 4\times 5+5+3\times 4}{20}$$
- step7: Multiply the terms:
  $$\frac{40+5+3\times 4}{20}$$
- step8: Multiply the numbers:
  $$\frac{40+5+12}{20}$$
- step9: Add the numbers:
  $$\frac{57}{20}$$
Calculate or simplify the expression $$ 1+\frac{1}{15}+2+\frac{1}{2} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$1+\frac{1}{15}+2+\frac{1}{2}$$
- step1: Add the numbers:
  $$3+\frac{1}{15}+\frac{1}{2}$$
- step2: Reduce fractions to a common denominator:
  $$\frac{3\times 15\times 2}{15\times 2}+\frac{2}{15\times 2}+\frac{15}{2\times 15}$$
- step3: Multiply the numbers:
  $$\frac{3\times 15\times 2}{30}+\frac{2}{15\times 2}+\frac{15}{2\times 15}$$
- step4: Multiply the numbers:
  $$\frac{3\times 15\times 2}{30}+\frac{2}{30}+\frac{15}{2\times 15}$$
- step5: Multiply the numbers:
  $$\frac{3\times 15\times 2}{30}+\frac{2}{30}+\frac{15}{30}$$
- step6: Transform the expression:
  $$\frac{3\times 15\times 2+2+15}{30}$$
- step7: Multiply the terms:
  $$\frac{90+2+15}{30}$$
- step8: Add the numbers:
  $$\frac{107}{30}$$
Let's solve each of the expressions step by step.

1. **Expression:** $$ \frac{1}{2} - \frac{5}{6} $$

To subtract these fractions, we need a common denominator. The least common multiple of 2 and 6 is 6.

$$
   \frac{1}{2} = \frac{3}{6}
   $$

Now we can perform the subtraction:

$$
   \frac{3}{6} - \frac{5}{6} = \frac{3 - 5}{6} = -\frac{2}{6} = -\frac{1}{3}
   $$

**Result:** $$ -\frac{1}{3} $$

2. **Expression:** $$ 2 \frac{1}{4} \times 1 \frac{3}{5} $$

First, convert the mixed numbers to improper fractions:

$$
   2 \frac{1}{4} = \frac{9}{4}, \quad 1 \frac{3}{5} = \frac{8}{5}
   $$

Now multiply the fractions:

$$
   \frac{9}{4} \times \frac{8}{5} = \frac{9 \times 8}{4 \times 5} = \frac{72}{20}
   $$

Simplifying $$ \frac{72}{20} $$:

$$
   \frac{72 \div 4}{20 \div 4} = \frac{18}{5} = 3 \frac{3}{5}
   $$

**Result:** $$ 3 \frac{3}{5} $$

3. **Expression:** $$ 1 \frac{1}{15} + 2 \frac{1}{2} $$

Convert the mixed numbers to improper fractions:

$$
   1 \frac{1}{15} = \frac{16}{15}, \quad 2 \frac{1}{2} = \frac{5}{2}
   $$

To add these fractions, we need a common denominator. The least common multiple of 15 and 2 is 30.

Convert both fractions:

$$
   \frac{16}{15} = \frac{32}{30}, \quad \frac{5}{2} = \frac{75}{30}
   $$

Now add them:

$$
   \frac{32}{30} + \frac{75}{30} = \frac{32 + 75}{30} = \frac{107}{30}
   $$

Converting back to a mixed number:

$$
   107 \div 30 = 3 \quad \text{(remainder 17)}
   $$

So, $$ \frac{107}{30} = 3 \frac{17}{30} $$.

**Result:** $$ 3 \frac{17}{30} $$

4. **Expression:** $$ \frac{1}{2} \times \frac{5}{6} $$

Multiply the fractions:

$$
   \frac{1}{2} \times \frac{5}{6} = \frac{1 \times 5}{2 \times 6} = \frac{5}{12}
   $$

**Result:** $$ \frac{5}{12} $$

### Summary of Results:
- $$ \frac{1}{2} - \frac{5}{6} = -\frac{1}{3} $$
- $$ 2 \frac{1}{4} \times 1 \frac{3}{5} = 3 \frac{3}{5} $$
- $$ 1 \frac{1}{15} + 2 \frac{1}{2} = 3 \frac{17}{30} $$
- $$ \frac{1}{2} \times \frac{5}{6} = \frac{5}{12} $$
- $$ \frac{1}{2} - \frac{5}{6} = -\frac{1}{3} $$ - $$ 2 \frac{1}{4} \times 1 \frac{3}{5} = 3 \frac{3}{5} $$ - $$ 1 \frac{1}{15} + 2 \frac{1}{2} = 3 \frac{17}{30} $$ - $$ \frac{1}{2} \times \frac{5}{6} = \frac{5}{12} $$

Upstudy AI Solution

Answer

Solution

Summary of Results:

The Deep Dive

Related Questions

Latest Arithmetic Questions