Math Problem Statement

Work out 4 ÷ (20/3). Give your answer as a fraction in its simplest form.

Solution

To solve 4÷2034 \div \frac{20}{3} and give the answer as a fraction in its simplest form, let's go through the steps:

  1. Rewrite the division as multiplication: Dividing by a fraction is the same as multiplying by its reciprocal. 4÷203=4×3204 \div \frac{20}{3} = 4 \times \frac{3}{20}

  2. Convert 4 to a fraction: We can write 44 as 41\frac{4}{1} to make multiplication easier. 41×320\frac{4}{1} \times \frac{3}{20}

  3. Multiply the fractions: Multiply the numerators and denominators. 4×31×20=1220\frac{4 \times 3}{1 \times 20} = \frac{12}{20}

  4. Simplify the fraction: Divide both the numerator and the denominator by their greatest common divisor, which is 4. 12÷420÷4=35\frac{12 \div 4}{20 \div 4} = \frac{3}{5}

Therefore, the answer is: 35\frac{3}{5}

Would you like more details on any step or have any questions?


Here are five related questions you might find helpful:

  1. How do you convert a whole number to a fraction?
  2. What is the rule for dividing by a fraction?
  3. How do you find the reciprocal of a fraction?
  4. How do you simplify fractions to their lowest terms?
  5. What is the importance of the greatest common divisor in fraction simplification?

Tip: When dividing by a fraction, always remember to multiply by its reciprocal for a quicker and easier calculation.

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Math Problem Analysis

Mathematical Concepts

Division of Fractions
Fraction Simplification

Formulas

a ÷ (b/c) = a × (c/b)
Simplify fractions by dividing the numerator and denominator by their GCD

Theorems

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Suitable Grade Level

Grade 6-8