Sure, let's solve the expression [tex]\( 4 \times \frac{5}{6} \)[/tex] step-by-step.
1. Identify the Components:
- Numerator of the fraction: [tex]\( 5 \)[/tex]
- Denominator of the fraction: [tex]\( 6 \)[/tex]
- Integer to be multiplied: [tex]\( 4 \)[/tex]
2. Convert the Integer to a Fraction:
- [tex]\( 4 \)[/tex] can be written as [tex]\( \frac{4}{1} \)[/tex] to match the form of the fraction we are multiplying.
3. Perform the Multiplication:
- To multiply fractions, we multiply the numerators together and the denominators together.
[tex]\[
\frac{4}{1} \times \frac{5}{6} = \frac{4 \times 5}{1 \times 6} = \frac{20}{6}
\][/tex]
4. Simplify the Fraction:
- The fraction [tex]\( \frac{20}{6} \)[/tex] can be simplified. Both the numerator and the denominator can be divided by their greatest common divisor, which is [tex]\( 2 \)[/tex]:
[tex]\[
\frac{20 \div 2}{6 \div 2} = \frac{10}{3}
\][/tex]
5. Convert to Decimal (if needed):
- The fraction [tex]\( \frac{10}{3} \)[/tex] can be converted to a decimal. Dividing [tex]\( 10 \)[/tex] by [tex]\( 3 \)[/tex]:
[tex]\[
\frac{10}{3} \approx 3.3333333333333335
\][/tex]
The result of multiplying [tex]\( 4 \)[/tex] by [tex]\( \frac{5}{6} \)[/tex] is approximately [tex]\( 3.3333333333333335 \)[/tex].
