Write 2.35 as an improper fraction in lowest terms.
The Correct Answer and Explanation is:
Correct Answer:
2.35 as an improper fraction in lowest terms is 4720\boxed{\frac{47}{20}}
Explanation):
To convert a decimal like 2.35 into an improper fraction, we follow a step-by-step process. Here’s how:
Step 1: Separate the whole number and decimal part
2.35 consists of:
- Whole number: 2
- Decimal part: 0.35
Step 2: Convert the decimal part (0.35) to a fraction
The decimal 0.35 means 35 hundredths, or: 0.35=351000.35 = \frac{35}{100}
Now, reduce this fraction to its lowest terms.
The greatest common divisor (GCD) of 35 and 100 is 5.
So divide both numerator and denominator by 5: 35÷5100÷5=720\frac{35 \div 5}{100 \div 5} = \frac{7}{20}
Step 3: Combine with the whole number
We now combine the whole number 2 and the fraction 720\frac{7}{20}.
To do that, we convert the whole number to a fraction with the same denominator: 2=40202 = \frac{40}{20}
Add: 4020+720=4720\frac{40}{20} + \frac{7}{20} = \frac{47}{20}
Final Answer:
2.35=47202.35 = \frac{47}{20}
This is already in its lowest terms, since 47 is a prime number and shares no common factor with 20.
Why This Matters:
Converting decimals to improper fractions is useful in algebra, measurements, and technical calculations. Improper fractions are especially useful when performing arithmetic operations, because fractions keep the relationship between numerator and denominator exact, unlike rounded decimals.
This process reinforces:
- Decimal place value understanding
- Fraction reduction
- Adding mixed numbers
Being able to fluently convert between forms helps build strong foundational math skills.
