Math Problem Statement

only 1.23

Solution

Let's solve the exercises in "OPPGAVE 1.23" one by one.

a) 2(38+14)2 \cdot \left( \frac{3}{8} + \frac{1}{4} \right)

  1. Find a common denominator for 38\frac{3}{8} and 14\frac{1}{4}: 14=28\frac{1}{4} = \frac{2}{8} So, 38+28=58\frac{3}{8} + \frac{2}{8} = \frac{5}{8}
  2. Multiply by 2: 258=108=542 \cdot \frac{5}{8} = \frac{10}{8} = \frac{5}{4}

b) (5629)35\left( \frac{5}{6} - \frac{2}{9} \right) \cdot \frac{3}{5}

  1. Find a common denominator for 56\frac{5}{6} and 29\frac{2}{9}: 56=1518and29=418\frac{5}{6} = \frac{15}{18} \quad \text{and} \quad \frac{2}{9} = \frac{4}{18} So, 1518418=1118\frac{15}{18} - \frac{4}{18} = \frac{11}{18}
  2. Multiply by 35\frac{3}{5}: 111835=3390=1130\frac{11}{18} \cdot \frac{3}{5} = \frac{33}{90} = \frac{11}{30}

c) (536+112):29\left( \frac{5}{36} + \frac{1}{12} \right) : \frac{2}{9}

  1. Find a common denominator for 536\frac{5}{36} and 112\frac{1}{12}: 112=336\frac{1}{12} = \frac{3}{36} So, 536+336=836=29\frac{5}{36} + \frac{3}{36} = \frac{8}{36} = \frac{2}{9}
  2. Division by 29\frac{2}{9} is equivalent to multiplying by the reciprocal: 29÷29=2992=1\frac{2}{9} \div \frac{2}{9} = \frac{2}{9} \cdot \frac{9}{2} = 1

d) (7669)(15+14)\left( \frac{7}{6} - \frac{6}{9} \right) \left( \frac{1}{5} + \frac{1}{4} \right)

  1. Find a common denominator for 76\frac{7}{6} and 69\frac{6}{9}: 76=2118and69=1218\frac{7}{6} = \frac{21}{18} \quad \text{and} \quad \frac{6}{9} = \frac{12}{18} So, 21181218=918=12\frac{21}{18} - \frac{12}{18} = \frac{9}{18} = \frac{1}{2}
  2. Find a common denominator for 15\frac{1}{5} and 14\frac{1}{4}: 15=420and14=520\frac{1}{5} = \frac{4}{20} \quad \text{and} \quad \frac{1}{4} = \frac{5}{20} So, 420+520=920\frac{4}{20} + \frac{5}{20} = \frac{9}{20}
  3. Multiply the two results: 12920=940\frac{1}{2} \cdot \frac{9}{20} = \frac{9}{40}

Would you like further details on any of these solutions or have any other questions?

Here are 5 questions you might want to ask:

  1. Can you explain how to find a common denominator in more detail?
  2. What is the process for multiplying fractions?
  3. How do you simplify fractions?
  4. What are the steps for adding and subtracting fractions?
  5. Can you show how to solve another example problem with fractions?

Tip: When working with fractions, always find a common denominator for addition and subtraction and remember to multiply by the reciprocal for division.

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Math Problem Analysis

Mathematical Concepts

Fractions
Operations with fractions
Common denominators
Multiplication of fractions
Division of fractions

Formulas

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Theorems

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Suitable Grade Level

Grades 5-8