Decimals and Fractions Mixed (A) - Free Printable

Let's solve each expression step by step, following the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right). We'll work with decimals and fractions carefully.

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1. $ 3.9 \times 0.5 + 4\frac{5}{6} \div 3\frac{3}{7} $

#### Step 1: Convert mixed numbers to improper fractions
- $ 4\frac{5}{6} = \frac{29}{6} $
- $ 3\frac{3}{7} = \frac{24}{7} $

#### Step 2: Perform multiplication and division
- $ 3.9 \times 0.5 = 1.95 $
- $ \frac{29}{6} \div \frac{24}{7} = \frac{29}{6} \times \frac{7}{24} = \frac{203}{144} \approx 1.4097 $

#### Step 3: Add
- $ 1.95 + \frac{203}{144} $
- Convert 1.95 to fraction: $ 1.95 = \frac{195}{100} = \frac{39}{20} $
- Find common denominator: LCM of 20 and 144 is 720
- $ \frac{39}{20} = \frac{39 \times 36}{720} = \frac{1404}{720} $
- $ \frac{203}{144} = \frac{203 \times 5}{720} = \frac{1015}{720} $
- Add: $ \frac{1404 + 1015}{720} = \frac{2419}{720} \approx 3.36 $

✔ Answer: $ \boxed{\frac{2419}{720}} $ or approximately $ \boxed{3.36} $

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2. $ \left( \frac{5}{3} \times 4\frac{5}{6} \right) \div 1.75 + \frac{5}{3} $

#### Step 1: Convert mixed number
- $ 4\frac{5}{6} = \frac{29}{6} $

#### Step 2: Multiply inside parentheses
- $ \frac{5}{3} \times \frac{29}{6} = \frac{145}{18} $

#### Step 3: Divide by 1.75
- $ 1.75 = \frac{7}{4} $
- $ \frac{145}{18} \div \frac{7}{4} = \frac{145}{18} \times \frac{4}{7} = \frac{580}{126} = \frac{290}{63} $

#### Step 4: Add $ \frac{5}{3} $
- $ \frac{290}{63} + \frac{5}{3} = \frac{290}{63} + \frac{105}{63} = \frac{395}{63} \approx 6.27 $

✔ Answer: $ \boxed{\frac{395}{63}} $ or approximately $ \boxed{6.27} $

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3. $ \left(9 + \frac{1}{6}\right) \div \left(1.7 + 2\frac{3}{4}\right) $

#### Step 1: Simplify both sides
- Left: $ 9 + \frac{1}{6} = \frac{54}{6} + \frac{1}{6} = \frac{55}{6} $
- Right: $ 1.7 = \frac{17}{10} $, $ 2\frac{3}{4} = \frac{11}{4} $
- $ \frac{17}{10} + \frac{11}{4} = \frac{34}{20} + \frac{55}{20} = \frac{89}{20} $

#### Step 2: Divide
- $ \frac{55}{6} \div \frac{89}{20} = \frac{55}{6} \times \frac{20}{89} = \frac{1100}{534} = \frac{550}{267} \approx 2.06 $

✔ Answer: $ \boxed{\frac{550}{267}} $ or approximately $ \boxed{2.06} $

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4. $ 2 \times \left(3\frac{6}{7} - 2.3\right) \div 5\frac{2}{9} $

#### Step 1: Convert mixed numbers
- $ 3\frac{6}{7} = \frac{27}{7} $
- $ 5\frac{2}{9} = \frac{47}{9} $

#### Step 2: Convert 2.3 to fraction: $ 2.3 = \frac{23}{10} $

#### Step 3: Subtract inside parentheses
- $ \frac{27}{7} - \frac{23}{10} = \frac{270}{70} - \frac{161}{70} = \frac{109}{70} $

#### Step 4: Multiply by 2
- $ 2 \times \frac{109}{70} = \frac{218}{70} = \frac{109}{35} $

#### Step 5: Divide by $ \frac{47}{9} $
- $ \frac{109}{35} \div \frac{47}{9} = \frac{109}{35} \times \frac{9}{47} = \frac{981}{1645} \approx 0.596 $

✔ Answer: $ \boxed{\frac{981}{1645}} $ or approximately $ \boxed{0.596} $

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5. $ 5.2 + 2.1 \div \left(4.5 - 4\frac{1}{7}\right) $

#### Step 1: Convert $ 4\frac{1}{7} = \frac{29}{7} \approx 4.1429 $

#### Step 2: Subtract
- $ 4.5 - 4.1429 = 0.3571 $, or exactly:
- $ 4.5 = \frac{9}{2} = \frac{63}{14} $, $ \frac{29}{7} = \frac{58}{14} $
- $ \frac{63}{14} - \frac{58}{14} = \frac{5}{14} $

#### Step 3: Divide $ 2.1 \div \frac{5}{14} $
- $ 2.1 = \frac{21}{10} $
- $ \frac{21}{10} \div \frac{5}{14} = \frac{21}{10} \times \frac{14}{5} = \frac{294}{50} = \frac{147}{25} = 5.88 $

#### Step 4: Add $ 5.2 + 5.88 = 11.08 $

✔ Answer: $ \boxed{11.08} $

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6. $ \left(0.75 \times 1\frac{4}{9}\right) \div \left(4\frac{1}{6} + 1.75\right) $

#### Step 1: Convert all values
- $ 0.75 = \frac{3}{4} $
- $ 1\frac{4}{9} = \frac{13}{9} $
- $ 4\frac{1}{6} = \frac{25}{6} $
- $ 1.75 = \frac{7}{4} $

#### Step 2: Multiply in numerator
- $ \frac{3}{4} \times \frac{13}{9} = \frac{39}{36} = \frac{13}{12} $

#### Step 3: Add in denominator
- $ \frac{25}{6} + \frac{7}{4} = \frac{50}{12} + \frac{21}{12} = \frac{71}{12} $

#### Step 4: Divide
- $ \frac{13}{12} \div \frac{71}{12} = \frac{13}{12} \times \frac{12}{71} = \frac{13}{71} \approx 0.1831 $

✔ Answer: $ \boxed{\frac{13}{71}} $ or approximately $ \boxed{0.183} $

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7. $ \left(\frac{3}{2}\right)^2 - 1 + 6 $

#### Step 1: Square
- $ \left(\frac{3}{2}\right)^2 = \frac{9}{4} $

#### Step 2: Subtract 1
- $ \frac{9}{4} - 1 = \frac{5}{4} $

#### Step 3: Add 6
- $ \frac{5}{4} + 6 = \frac{5}{4} + \frac{24}{4} = \frac{29}{4} = 7.25 $

✔ Answer: $ \boxed{\frac{29}{4}} $ or $ \boxed{7.25} $

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8. $ 0.8 \div \left(1.5 + \frac{2}{3}\right)^2 $

#### Step 1: Convert decimals to fractions
- $ 0.8 = \frac{4}{5} $
- $ 1.5 = \frac{3}{2} $

#### Step 2: Add inside parentheses
- $ \frac{3}{2} + \frac{2}{3} = \frac{9}{6} + \frac{4}{6} = \frac{13}{6} $

#### Step 3: Square it
- $ \left(\frac{13}{6}\right)^2 = \frac{169}{36} $

#### Step 4: Divide
- $ \frac{4}{5} \div \frac{169}{36} = \frac{4}{5} \times \frac{36}{169} = \frac{144}{845} \approx 0.1703 $

✔ Answer: $ \boxed{\frac{144}{845}} $ or approximately $ \boxed{0.170} $

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9. $ \frac{2}{9} \left(10\frac{1}{6} - 3\frac{3}{7} - 1\right) $

#### Step 1: Convert mixed numbers
- $ 10\frac{1}{6} = \frac{61}{6} $
- $ 3\frac{3}{7} = \frac{24}{7} $

#### Step 2: Subtract
- $ \frac{61}{6} - \frac{24}{7} - 1 $
- First: $ \frac{61}{6} - \frac{24}{7} = \frac{427}{42} - \frac{144}{42} = \frac{283}{42} $
- Then: $ \frac{283}{42} - 1 = \frac{283}{42} - \frac{42}{42} = \frac{241}{42} $

#### Step 3: Multiply by $ \frac{2}{9} $
- $ \frac{2}{9} \times \frac{241}{42} = \frac{482}{378} = \frac{241}{189} \approx 1.275 $

✔ Answer: $ \boxed{\frac{241}{189}} $ or approximately $ \boxed{1.275} $

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10. $ \left(7 \times \frac{10}{7}\right) \div 1.2 + 1\frac{3}{4} $

#### Step 1: Multiply
- $ 7 \times \frac{10}{7} = 10 $

#### Step 2: Divide by 1.2
- $ 10 \div 1.2 = \frac{10}{1.2} = \frac{100}{12} = \frac{25}{3} \approx 8.333 $

#### Step 3: Add $ 1\frac{3}{4} = \frac{7}{4} $
- $ \frac{25}{3} + \frac{7}{4} = \frac{100}{12} + \frac{21}{12} = \frac{121}{12} \approx 10.083 $

✔ Answer: $ \boxed{\frac{121}{12}} $ or approximately $ \boxed{10.08} $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ \frac{2419}{720} \approx 3.36 $ |
| 2 | $ \frac{395}{63} \approx 6.27 $ |
| 3 | $ \frac{550}{267} \approx 2.06 $ |
| 4 | $ \frac{981}{1645} \approx 0.596 $ |
| 5 | $ 11.08 $ |
| 6 | $ \frac{13}{71} \approx 0.183 $ |
| 7 | $ \frac{29}{4} = 7.25 $ |
| 8 | $ \frac{144}{845} \approx 0.170 $ |
| 9 | $ \frac{241}{189} \approx 1.275 $ |
| 10 | $ \frac{121}{12} \approx 10.08 $ |

Let me know if you'd like these simplified further or converted to mixed numbers!