Complete the fraction to solve 5 x 2/6
The Correct Answer and Explanation is :
To solve (5 \times \frac{2}{6}):
- Multiply the whole number by the fraction:
[
5 \times \frac{2}{6} = \frac{5 \times 2}{6} = \frac{10}{6}
] - Simplify the fraction:
The fraction (\frac{10}{6}) can be simplified by dividing both the numerator (10) and the denominator (6) by their greatest common divisor (GCD), which is 2.
[
\frac{10 \div 2}{6 \div 2} = \frac{5}{3}
]
So, (5 \times \frac{2}{6} = \frac{5}{3}), or approximately 1.67 in decimal form.
Explanation:
When multiplying a whole number by a fraction, you can treat the whole number as a fraction by giving it a denominator of 1. For example, (5) can be rewritten as (\frac{5}{1}). Therefore, multiplying 5 by (\frac{2}{6}) becomes:
[
\frac{5}{1} \times \frac{2}{6} = \frac{5 \times 2}{1 \times 6} = \frac{10}{6}
]
At this point, the fraction (\frac{10}{6}) is an improper fraction (where the numerator is larger than the denominator). You simplify it by finding the greatest common divisor (GCD) of 10 and 6. The GCD is 2, so you divide both the numerator and the denominator by 2 to simplify the fraction:
[
\frac{10 \div 2}{6 \div 2} = \frac{5}{3}
]
If you want to convert the improper fraction (\frac{5}{3}) into a mixed number, you would divide 5 by 3:
[
5 \div 3 = 1 \text{ remainder } 2
]
So, (\frac{5}{3}) is equivalent to (1 \frac{2}{3}).
Alternatively, in decimal form, (\frac{5}{3} \approx 1.67). Thus, (5 \times \frac{2}{6}) equals (\frac{5}{3}), a simplified improper fraction, or approximately 1.67.