Answer :
The required number is 147 divided by the mixed number 15 3/4.
We perform the division of 147 by 15 3/4:
= 147 / ( 15/3/4)
= 147 / (63/4)
= 147 *4 / 63
= 9.333333333333333333.
We obtain a decimal value of 9.333333333333333333... The ellipsis (...) indicates that the digit 3 repeats infinitely. To represent this repeating pattern in a more concise manner, we can use a horizontal bar over digit 3 to indicate that it repeats indefinitely.
So, the statement 147 ÷ 15 3/4 = 9.333 signifies that the decimal part of the quotient consists of the digit 3 repeating infinitely. This notation helps us represent the exact value of the decimal without having to write an infinite number of threes.
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147 divided by 15 3/4 is [tex]\( 9 \frac{1}{3} \)[/tex].
To calculate,
1. Convert 15 3/4 to an improper fraction:
[tex]\[ 15 \frac{3}{4} = 15 \times 4 + 3 = 60 + 3 = 63/4 \][/tex]
2. Now, divide 147 by the improper fraction 63/4: [tex]\[ \frac{147}{\frac{63}{4}} \][/tex]
3. To divide by a fraction, we multiply by its reciprocal:[tex]\[ \frac{147}{\frac{63}{4}} = 147 \times \frac{4}{63} \][/tex]
4. Simplify the multiplication: [tex]\[ 147 \times \frac{4}{63} = \frac{147 \times 4}{63} \][/tex]
5. Divide both the numerator and the denominator by their greatest common divisor (GCD) to simplify the fraction. The GCD of 147 and 63 is 21:
[tex]\[ \frac{147 \times 4}{63} = \frac{147 \div 21 \times 4}{63 \div 21} \][/tex]
[tex]\[ \frac{7 \times 4}{3} \][/tex]
6. Now multiply the numerators and the denominators: [tex]\[ \frac{7 \times 4}{3} = \frac{28}{3} \][/tex]
7. Convert the improper fraction back to a mixed number if needed:
[tex]\[ \frac{28}{3} = 9 \frac{1}{3} \][/tex]
So, 147 divided by 15 3/4 is [tex]\( 9 \frac{1}{3} \)[/tex].
