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Answer :
To simplify the rational expression [tex]\(1 \frac{32}{40}\)[/tex], follow these steps:
1. Understand the Expression: The expression [tex]\(1 \frac{32}{40}\)[/tex] is a mixed number. It consists of a whole number part (1) and a fractional part ([tex]\(\frac{32}{40}\)[/tex]).
2. Simplify the Fraction: Let's simplify the fractional part, [tex]\(\frac{32}{40}\)[/tex].
- First, find the greatest common divisor (GCD) of the numerator (32) and the denominator (40). The GCD of 32 and 40 is 8.
- Divide both the numerator and the denominator by their GCD to simplify the fraction:
[tex]\[
\frac{32 \div 8}{40 \div 8} = \frac{4}{5}
\][/tex]
- So, [tex]\(\frac{32}{40}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex].
3. Combine with the Whole Number: Now that we have simplified the fraction to [tex]\(\frac{4}{5}\)[/tex], combine it with the whole number 1:
[tex]\[
1 + \frac{4}{5}
\][/tex]
To express this as a decimal, you can convert [tex]\(\frac{4}{5}\)[/tex] to a decimal, which is 0.8.
4. Final Answer: Adding the whole number 1 and 0.8 gives 1.8.
Therefore, the simplified form of [tex]\(1 \frac{32}{40}\)[/tex] is 1.8.
1. Understand the Expression: The expression [tex]\(1 \frac{32}{40}\)[/tex] is a mixed number. It consists of a whole number part (1) and a fractional part ([tex]\(\frac{32}{40}\)[/tex]).
2. Simplify the Fraction: Let's simplify the fractional part, [tex]\(\frac{32}{40}\)[/tex].
- First, find the greatest common divisor (GCD) of the numerator (32) and the denominator (40). The GCD of 32 and 40 is 8.
- Divide both the numerator and the denominator by their GCD to simplify the fraction:
[tex]\[
\frac{32 \div 8}{40 \div 8} = \frac{4}{5}
\][/tex]
- So, [tex]\(\frac{32}{40}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex].
3. Combine with the Whole Number: Now that we have simplified the fraction to [tex]\(\frac{4}{5}\)[/tex], combine it with the whole number 1:
[tex]\[
1 + \frac{4}{5}
\][/tex]
To express this as a decimal, you can convert [tex]\(\frac{4}{5}\)[/tex] to a decimal, which is 0.8.
4. Final Answer: Adding the whole number 1 and 0.8 gives 1.8.
Therefore, the simplified form of [tex]\(1 \frac{32}{40}\)[/tex] is 1.8.
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