Work out 12/15 × 10 × 18/12. Give your answer in the simplest form.

Steps to Solve

1. Write the Expression

   Start with the expression given in the problem:

   $$ \frac{12}{15} \times 10 \times \frac{18}{12} $$

2. Simplify the Fractions

   Before multiplying, simplify the fractions.

   For $\frac{12}{15}$, divide the numerator and denominator by 3:

   $$ \frac{12 \div 3}{15 \div 3} = \frac{4}{5} $$

   For $\frac{18}{12}$, divide the numerator and denominator by 6:

   $$ \frac{18 \div 6}{12 \div 6} = \frac{3}{2} $$

   So the expression becomes:

   $$ \frac{4}{5} \times 10 \times \frac{3}{2} $$

3. Convert Whole Number to Fraction

   Write the whole number 10 as a fraction:

   $$ 10 = \frac{10}{1} $$

   Now the expression is:

   $$ \frac{4}{5} \times \frac{10}{1} \times \frac{3}{2} $$

4. Multiply the Fractions

   Multiply the numerators and the denominators:

   Numerator: $$ 4 \times 10 \times 3 = 120 $$

   Denominator: $$ 5 \times 1 \times 2 = 10 $$

   So, we have:

   $$ \frac{120}{10} $$

5. Simplify the Fraction

   Divide the numerator and denominator by 10:

   $$ \frac{120 \div 10}{10 \div 10} = \frac{12}{1} $$

   Which reduces to:

   $$ 12 $$