To multiply the whole number [tex]\( 6 \)[/tex] by the fraction [tex]\( \frac{1}{3} \)[/tex], we can follow these steps:
1. Multiply the whole number by the numerator of the fraction:
- The whole number is [tex]\( 6 \)[/tex].
- The numerator of the fraction is [tex]\( 1 \)[/tex].
- Multiply these together: [tex]\( 6 \times 1 = 6 \)[/tex].
2. Keep the denominator of the fraction the same:
- The denominator of the fraction is [tex]\( 3 \)[/tex].
- So the product of the whole number and the fraction will have a denominator of [tex]\( 3 \)[/tex].
3. Form the new fraction:
- We now have the fraction [tex]\( \frac{6}{3} \)[/tex].
4. Simplify the fraction:
- Divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of [tex]\( 6 \)[/tex] and [tex]\( 3 \)[/tex] is [tex]\( 3 \)[/tex].
- Divide the numerator [tex]\( 6 \)[/tex] by [tex]\( 3 \)[/tex]: [tex]\( 6 \div 3 = 2 \)[/tex].
- Divide the denominator [tex]\( 3 \)[/tex] by [tex]\( 3 \)[/tex]: [tex]\( 3 \div 3 = 1 \)[/tex].
- Thus, the fraction simplifies to [tex]\( \frac{2}{1} \)[/tex], which is simply [tex]\( 2 \)[/tex].
Therefore, [tex]\( 6 \cdot \frac{1}{3} = 2 \)[/tex].
