Find the following product and write it in lowest terms 15 5 28 15 5 28 (Type a whole number or a fraction:)
The Correct Answer and Explanation is:
The product of the two fractions 45×1528\frac{4}{5} \times \frac{15}{28} simplifies to:
4×155×28=60140\frac{4 \times 15}{5 \times 28} = \frac{60}{140}
Next, reduce the fraction by dividing both numerator and denominator by their greatest common divisor. The greatest common divisor of 60 and 140 is 20:
60÷20140÷20=37\frac{60 \div 20}{140 \div 20} = \frac{3}{7}
Final Answer: 37\frac{3}{7}
Explanation
To multiply two fractions and write the result in lowest terms, begin by multiplying the numerators together and then the denominators. In this case, the numerators are 4 and 15. Multiply them to get:
4×15=604 \times 15 = 60
Now move on to the denominators. The denominators are 5 and 28. Multiply these:
5×28=1405 \times 28 = 140
The product of the fractions is therefore 60140\frac{60}{140}. However, this is not the final answer, since it is not in its simplest form. The goal is to express the result in lowest terms. That means we must simplify the fraction by dividing both the top and bottom by their greatest common divisor, or GCD.
To find the GCD, list out the factors. Factors of 60 include 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. Factors of 140 include 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, and 140. The largest common factor is 20. Divide both numerator and denominator by 20:
60÷20=3and140÷20=760 \div 20 = 3 \quad \text{and} \quad 140 \div 20 = 7
This gives us the simplified fraction 37\frac{3}{7}. Since 3 and 7 have no common factors other than 1, this is the lowest possible form. Thus, multiplying 45\frac{4}{5} and 1528\frac{15}{28} gives a final answer of 37\frac{3}{7}.
