Multiply or divide as indicated. Write answers in lowest terms as needed. $two fifths divided by 30$

Verified step by step guidance

Identify the problem as a division of fractions: $ \frac{2}{5} \div 30 $. Remember that dividing by a whole number is the same as dividing by a fraction with denominator 1, so rewrite 30 as $ \frac{30}{1} $.

Rewrite the division of fractions as multiplication by the reciprocal: $ \frac{2}{5} \div \frac{30}{1} = \frac{2}{5} \times \frac{1}{30} $.

Multiply the numerators together and the denominators together: $ \frac{2 \times 1}{5 \times 30} = \frac{2}{150} $.

Simplify the fraction $ \frac{2}{150} $ by finding the greatest common divisor (GCD) of 2 and 150, then divide both numerator and denominator by the GCD.

Write the simplified fraction as the final answer in lowest terms.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Division of Fractions

Dividing fractions involves multiplying the first fraction by the reciprocal of the second. For example, dividing by 30 is the same as multiplying by 1/30. This method simplifies complex fraction division problems.

Simplifying Fractions

After performing operations, fractions should be simplified to their lowest terms by dividing numerator and denominator by their greatest common divisor (GCD). This makes the answer clearer and easier to interpret.

Multiplication of Fractions

Multiplying fractions requires multiplying the numerators together and the denominators together. This operation is straightforward and essential when converting division problems into multiplication by reciprocals.

Recommended video:

Guided course

05:45

Radical Expressions with Fractions

Related Practice

Textbook Question

Find each product. (4x²-5y)(4x²+5y)

Textbook Question

Determine whether each statement is true or false. {2, 5, 8, 9} = {2, 5, 9, 8}

Textbook Question

Find each root. ∜(5 + 2m)⁴

Textbook Question