3/4 of a number is 60. Which of the following is the number?                       60×3/5.           60÷5/3.              3/5÷60.             60×5/3

We are given that 3/4 of a number is 60. Let's first solve for the number.

Let the unknown number be \( x \). The equation can be set up as:

\[
\frac{3}{4} \times x = 60
\]

To solve for \( x \), multiply both sides of the equation by the reciprocal of \( \frac{3}{4} \), which is \( \frac{4}{3} \):

\[
x = 60 \times \frac{4}{3}
\]

Now, calculate:

\[
x = \frac{60 \times 4}{3} = \frac{240}{3} = 80
\]

Thus, the number is 80.

Now, we will check which of the options gives the number 80:

1. \( 60 \times \frac{3}{5} = \frac{60 \times 3}{5} = \frac{180}{5} = 36 \) (not 80)
2. \( 60 \div \frac{5}{3} = 60 \times \frac{3}{5} = 36 \) (not 80)
3. \( \frac{3}{5} \div 60 = \frac{3}{5} \times \frac{1}{60} = \frac{3}{300} = 0.01 \) (not 80)
4. \( 60 \times \frac{5}{3} = \frac{60 \times 5}{3} = \frac{300}{3} = 100 \) (not 80)

None of the options directly match 80.

Would you like details on solving this or have any further questions?

### Related questions:
1. What is the reciprocal of a fraction, and how is it used in equations?
2. How can we simplify fractions in division problems?
3. What are the steps to solve for an unknown in fractional equations?
4. How do we multiply fractions with whole numbers?
5. How do we handle mixed operations involving fractions and whole numbers?

**Tip:** Always remember to apply the reciprocal when solving for a variable multiplied by a fraction!

3/4 of a number is 60. Which of the following is the number? 60×3/5, 60÷5/3, 3/5÷60, 60×5/3

Discover how to solve the equation 3/4 of a number is 60 with a step-by-step algebraic solution. This problem involves understanding the reciprocal of a fraction and applying basic fraction multiplication. Suitable for students in Grades 6-8.

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