Write equivalent fractions for 2/3 and 3/5 using 15 as the common denominator.
The correct answer and explanation is:
To write equivalent fractions for 23\frac{2}{3} and 35\frac{3}{5} using 15 as the common denominator, follow these steps:
Step 1: Find the equivalent fraction for 23\frac{2}{3}.
The denominator of 23\frac{2}{3} is 3, and we want to convert this fraction to have 15 as the denominator. To do that, multiply both the numerator and denominator of 23\frac{2}{3} by 5, because 3×5=153 \times 5 = 15. 23×55=2×53×5=1015\frac{2}{3} \times \frac{5}{5} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}
So, 23\frac{2}{3} is equivalent to 1015\frac{10}{15}.
Step 2: Find the equivalent fraction for 35\frac{3}{5}.
Next, for 35\frac{3}{5}, the denominator is 5, and we want it to be 15. To do this, multiply both the numerator and denominator of 35\frac{3}{5} by 3, because 5×3=155 \times 3 = 15. 35×33=3×35×3=915\frac{3}{5} \times \frac{3}{3} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}
So, 35\frac{3}{5} is equivalent to 915\frac{9}{15}.
Final Answer:
- 23=1015\frac{2}{3} = \frac{10}{15}
- 35=915\frac{3}{5} = \frac{9}{15}
Explanation:
In both cases, the process involved finding the appropriate factor to multiply both the numerator and the denominator of each fraction so that the denominator would become 15. This is a standard approach to creating equivalent fractions. By multiplying the numerators and denominators by the same number, the value of the fraction doesn’t change, but it now has the desired common denominator. This technique is useful in operations involving fractions, such as addition or subtraction, where a common denominator is needed.