Certainly! Let's solve the problem step-by-step:
We are given:
- The product of two fractions is [tex]\(59 \frac{1}{2}\)[/tex].
- One of the fractions is [tex]\(8 \frac{3}{9}\)[/tex].
We need to find the other fraction.
### Step 1: Convert the mixed numbers to improper fractions or decimals
#### 1.1 Convert [tex]\(59 \frac{1}{2}\)[/tex]
1. Convert the fraction part to a decimal.
[tex]\( \frac{1}{2} = 0.5 \)[/tex]
2. Add this decimal to the whole number.
[tex]\( 59 + 0.5 = 59.5 \)[/tex]
So, [tex]\(59 \frac{1}{2} = 59.5\)[/tex].
#### 1.2 Convert [tex]\(8 \frac{3}{9}\)[/tex]
1. Convert the fraction part to a decimal.
To convert [tex]\(\frac{3}{9}\)[/tex] to a decimal:
[tex]\( \frac{3}{9} = \frac{1}{3} \approx 0.3333... \)[/tex]
2. Add this decimal to the whole number.
[tex]\( 8 + 0.3333... = 8.3333... \)[/tex]
So, [tex]\(8 \frac{3}{9} \approx 8.333... \)[/tex].
### Step 2: Set up the equation to find the other fraction
Let the other fraction be [tex]\(x\)[/tex].
We are given that the product of the two fractions is [tex]\(59.5\)[/tex]. Therefore,
[tex]\[ 59.5 = x \times 8.3333... \][/tex]
### Step 3: Solve for [tex]\(x\)[/tex]
To isolate [tex]\(x\)[/tex], divide both sides of the equation by [tex]\(8.3333...\)[/tex]:
[tex]\[ x = \frac{59.5}{8.3333...} \][/tex]
Using the given accurate result for the calculation:
[tex]\[ x \approx 7.14 \][/tex]
Therefore, the other fraction is approximately [tex]\(7.14\)[/tex].
In conclusion:
- The product of the given fractions is [tex]\(59.5\)[/tex].
- One of the fractions is approximately [tex]\(8.3333...\)[/tex].
- The other fraction is approximately [tex]\(7.14\)[/tex].
