Multiply 9(5/6)
The question is asking for the product of the number 9 and the mixed fraction 5/6. To compute this, one would typically convert the mixed fraction into an improper fraction and then multiply it by the whole number.
$9 \left(\right. \frac{5}{6} \left.\right)$
Answer
Solution:
Step 1: Simplify by eliminating common factors.
Step 1.1: Extract the factor of 3 from 9.
$3 \times 3 \frac{5}{6}$
Step 1.2: Extract the factor of 3 from 6.
$3 \times 3 \frac{5}{3 \times 2}$
Step 1.3: Remove the common factor of 3.
$ \cancel{3} \times 3 \frac{5}{\cancel{3} \times 2}$
Step 1.4: Present the simplified expression.
$3 \times \frac{5}{2}$
Step 2: Merge the integer 3 with the fraction $\frac{5}{2}$.
$\frac{3 \times 5}{2}$
Step 3: Perform the multiplication of 3 and 5.
$\frac{15}{2}$
Step 4: Express the result in various formats.
- Exact Form: $\frac{15}{2}$
- Decimal Form: $7.5$
- Mixed Number Form: $7 \frac{1}{2}$
Knowledge Notes:
The problem involves multiplying an integer by a fraction. The process can be streamlined by simplifying the expression before carrying out the multiplication. This is achieved through the following knowledge points:
Factorization: Breaking down numbers into their constituent factors can reveal common factors that can be cancelled out to simplify the expression.
Cancellation: When a factor appears in both the numerator and denominator, it can be cancelled out. This is based on the property that any number divided by itself equals one.
Multiplication of Fractions: To multiply a whole number by a fraction, you can treat the whole number as a fraction with a denominator of 1 and then multiply across the numerators and denominators.
Simplification: After cancelling common factors, the expression becomes simpler and easier to work with.
Conversion to Mixed Number: A fraction where the numerator is greater than the denominator can be converted to a mixed number, which is a combination of a whole number and a proper fraction.
Decimal Representation: Fractions can also be expressed as decimals by performing the division indicated by the fraction (dividing the numerator by the denominator).
By applying these concepts, the multiplication of 9 by $\frac{5}{6}$ is simplified to multiplying 3 by $\frac{5}{2}$, and the result is presented in various forms for clarity and convenience.
