Sure, let's break down the problem step-by-step and identify any mistakes.
### Step 1: Expressing the Percentage as a Fraction
To convert [tex]\( 45\% \)[/tex] to a fraction, we understand that [tex]\( 45\% \)[/tex] means 45 out of 100. Therefore:
[tex]\[ 45\% = \frac{45}{100} \][/tex]
### Step 2: Reducing the Fraction
Next, we reduce the fraction to its simplest form. To do this, we find the greatest common divisor (GCD) of the numerator (45) and the denominator (100).
The GCD of 45 and 100 is 5. Now we reduce the fraction:
[tex]\[ \frac{45 \div 5}{100 \div 5} = \frac{9}{20} \][/tex]
Hence, the reduced fraction of [tex]\( 45\% \)[/tex] is:
[tex]\[ \frac{9}{20} \][/tex]
### Step 3: Converting the Percentage to a Decimal
To convert [tex]\( 45\% \)[/tex] to a decimal, we divide 45 by 100:
[tex]\[ \frac{45}{100} = 0.45 \][/tex]
### Jenny's Mistake
Jenny's work was:
[tex]\[ 45\% = \frac{45}{100} = \frac{9}{20} = 4.5 \][/tex]
The mistake Jenny made is in the decimal conversion step. She incorrectly converted [tex]\( \frac{45}{100} \)[/tex] to 4.5 instead of the correct value, which is 0.45.
### Final Summary
- The equivalent fraction of [tex]\( 45\% \)[/tex] is [tex]\( \frac{45}{100} \)[/tex].
- The reduced fraction is [tex]\( \frac{9}{20} \)[/tex].
- The correct decimal equivalent is 0.45.
Jenny’s error was in converting [tex]\( \frac{45}{100} \)[/tex] to 4.5 instead of 0.45.
