Work out $4 \div \frac{20}{3}$. Give your answer in its simplest form.
Answer (2)
To divide by a fraction, multiply by its reciprocal: 4 ÷ 3 20 = 4 × 20 3 .
Multiply the numbers: 4 × 20 3 = 20 12 .
Simplify the fraction by dividing by the greatest common divisor (GCD): 20 12 = 20 ÷ 4 12 ÷ 4 = 5 3 .
The answer in its simplest form is 5 3 .
Explanation
Understanding the Problem We need to divide the number 4 by the fraction 3 20 . The answer should be given in its simplest form.
Dividing by a Fraction To divide by a fraction, we multiply by its reciprocal. So, 4 ÷ 3 20 = 4 × 20 3 .
Multiplying the Numbers Multiply the numbers: 4 × 20 3 = 20 4 × 3 = 20 12 .
Simplifying the Fraction Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 12 and 20 is 4. Divide both the numerator and the denominator by 4: 20 ÷ 4 12 ÷ 4 = 5 3 .
Final Answer The simplified fraction is 5 3 .
Examples
Understanding fractions and division is crucial in everyday situations, such as splitting a pizza or sharing ingredients while cooking. For instance, if you have 4 cups of flour and a recipe requires you to use 3 20 cups per batch of cookies, calculating 4 ÷ 3 20 helps you determine how many batches you can make. This problem demonstrates a practical application of fraction division, ensuring you can accurately adjust recipes or divide resources.
To divide 4 by the fraction 3 20 , we first multiply 4 by the reciprocal of the fraction, giving us 4 × 20 3 = 20 12 . After simplifying, we find the answer is 5 3 .
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