QuestionMultiply and simplify: .
Studdy Solution
STEP 1
Assumptions1. We are multiplying two mixed numbers. . The result should be reduced to its lowest terms if possible.
STEP 2
First, we need to convert each mixed number to an improper fraction. An improper fraction is a fraction where the numerator (top number) is greater than or equal to the denominator (bottom number).
For the first mixed number, the conversion formula is
STEP 3
Now, plug in the values for the whole number, numerator, and denominator from the first mixed number into the conversion formula.
STEP 4
Calculate the improper fraction for the first mixed number.
So, the improper fraction for the first mixed number is .
STEP 5
Repeat the same process for the second mixed number.
STEP 6
Calculate the improper fraction for the second mixed number.
So, the improper fraction for the second mixed number is .
STEP 7
Now that we have both mixed numbers converted to improper fractions, we can multiply them together. The formula for multiplying fractions is
STEP 8
Plug in the values for a, b, c, and d from the two improper fractions.
STEP 9
Calculate the multiplication of the numerators and the denominators.
STEP 10
Now, reduce the fraction to its lowest terms by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of286 and24 is2.
STEP 11
Calculate the reduced fraction.
So, the result of the multiplication of the two mixed numbers is , which is an improper fraction.
STEP 12
To express the result as a mixed number, we divide the numerator by the denominator.
So, the result of the multiplication of the two mixed numbers, reduced to its lowest terms, is .
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