Certainly! Let's break down the division of the mixed numbers [tex]\(5 \frac{1}{2} \div 3 \frac{1}{3}\)[/tex] step by step.
### Step 1: Convert the mixed numbers to improper fractions.
#### For [tex]\(5 \frac{1}{2}\)[/tex]:
1. Multiply the whole number part (5) by the denominator of the fractional part (2):
[tex]\[ 5 \times 2 = 10 \][/tex]
2. Add the numerator of the fractional part (1) to this product:
[tex]\[ 10 + 1 = 11 \][/tex]
3. The improper fraction is:
[tex]\[ \frac{11}{2} \][/tex]
#### For [tex]\(3 \frac{1}{3}\)[/tex]:
1. Multiply the whole number part (3) by the denominator of the fractional part (3):
[tex]\[ 3 \times 3 = 9 \][/tex]
2. Add the numerator of the fractional part (1) to this product:
[tex]\[ 9 + 1 = 10 \][/tex]
3. The improper fraction is:
[tex]\[ \frac{10}{3} \][/tex]
### Step 2: Perform the division of the improper fractions by multiplying by the reciprocal.
Division of fractions is equivalent to multiplying by the reciprocal of the divisor:
[tex]\[ \frac{11}{2} \div \frac{10}{3} = \frac{11}{2} \times \frac{3}{10} \][/tex]
### Step 3: Multiply the fractions.
Multiply the numerators together and the denominators together:
[tex]\[ \frac{11 \times 3}{2 \times 10} = \frac{33}{20} \][/tex]
### Step 4: Simplify the result (if needed).
In this case, [tex]\(\frac{33}{20}\)[/tex] is already in its simplest form, but it can also be expressed as a decimal.
### Step 5: Convert to a decimal (if desired).
Divide the numerator by the denominator:
[tex]\[ \frac{33}{20} = 1.65 \][/tex]
### Step 6: Result interpretation.
So, the result of the division [tex]\(5 \frac{1}{2} \div 3 \frac{1}{3}\)[/tex] is:
[tex]\[ 1.65 \][/tex]
Hence, [tex]\(5 \frac{1}{2} \div 3 \frac{1}{3} = 1.65 \)[/tex]. This result tells us that [tex]\(5 \frac{1}{2}\)[/tex] is 1.65 times [tex]\(3 \frac{1}{3}\)[/tex]. Additionally, the improper fractions corresponding to the mixed numbers are [tex]\(5.5\)[/tex] and [tex]\(3.3333333333333335\)[/tex].
