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Answer :
Sure! Let's work through the problem step-by-step to solve it.
We need to calculate [tex]\( \frac{4}{5} \times 1 \frac{1}{6} \)[/tex].
1. Convert the Mixed Number to an Improper Fraction:
A mixed number like [tex]\( 1 \frac{1}{6} \)[/tex] is made up of a whole number part and a fraction part. To convert it to an improper fraction, follow these steps:
- Multiply the whole number (1) by the denominator of the fraction (6): [tex]\( 1 \times 6 = 6 \)[/tex].
- Add the numerator of the fraction (1) to this result: [tex]\( 6 + 1 = 7 \)[/tex].
- Place this result over the original denominator to get: [tex]\( \frac{7}{6} \)[/tex].
2. Multiply the Fractions:
Now, we multiply the two fractions:
[tex]\[
\frac{4}{5} \times \frac{7}{6} = \frac{4 \times 7}{5 \times 6} = \frac{28}{30}
\][/tex]
3. Simplify the Fraction:
Simplify [tex]\( \frac{28}{30} \)[/tex] by finding the greatest common divisor (GCD) of 28 and 30, which is 2:
- Divide both numerator and denominator by 2:
[tex]\[
\frac{28 \div 2}{30 \div 2} = \frac{14}{15}
\][/tex]
Therefore, the result of [tex]\( \frac{4}{5} \times 1 \frac{1}{6} \)[/tex] is [tex]\( \frac{14}{15} \)[/tex]. This fraction is approximately equal to 0.93333 when converted to decimal form.
This decimal value closely matches one of the given choices, confirming the calculation is correct.
We need to calculate [tex]\( \frac{4}{5} \times 1 \frac{1}{6} \)[/tex].
1. Convert the Mixed Number to an Improper Fraction:
A mixed number like [tex]\( 1 \frac{1}{6} \)[/tex] is made up of a whole number part and a fraction part. To convert it to an improper fraction, follow these steps:
- Multiply the whole number (1) by the denominator of the fraction (6): [tex]\( 1 \times 6 = 6 \)[/tex].
- Add the numerator of the fraction (1) to this result: [tex]\( 6 + 1 = 7 \)[/tex].
- Place this result over the original denominator to get: [tex]\( \frac{7}{6} \)[/tex].
2. Multiply the Fractions:
Now, we multiply the two fractions:
[tex]\[
\frac{4}{5} \times \frac{7}{6} = \frac{4 \times 7}{5 \times 6} = \frac{28}{30}
\][/tex]
3. Simplify the Fraction:
Simplify [tex]\( \frac{28}{30} \)[/tex] by finding the greatest common divisor (GCD) of 28 and 30, which is 2:
- Divide both numerator and denominator by 2:
[tex]\[
\frac{28 \div 2}{30 \div 2} = \frac{14}{15}
\][/tex]
Therefore, the result of [tex]\( \frac{4}{5} \times 1 \frac{1}{6} \)[/tex] is [tex]\( \frac{14}{15} \)[/tex]. This fraction is approximately equal to 0.93333 when converted to decimal form.
This decimal value closely matches one of the given choices, confirming the calculation is correct.
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