To solve the equation [tex]\( d \div \frac{3}{2} = 1 \frac{1}{7} \)[/tex] for [tex]\( d \)[/tex], follow these steps:
1. Understand the equation: We have the equation [tex]\( d \div \frac{3}{2} = 1 \frac{1}{7} \)[/tex].
2. Convert the mixed number to an improper fraction: The mixed number [tex]\( 1 \frac{1}{7} \)[/tex] can be converted to an improper fraction.
[tex]\[
1 \frac{1}{7} = 1 + \frac{1}{7} = \frac{7}{7} + \frac{1}{7} = \frac{8}{7}
\][/tex]
3. Rewrite the equation using the improper fraction: Now, substitute [tex]\( 1 \frac{1}{7} \)[/tex] with [tex]\( \frac{8}{7} \)[/tex] in the equation.
[tex]\[
d \div \frac{3}{2} = \frac{8}{7}
\][/tex]
4. Divide by a fraction: Dividing by [tex]\( \frac{3}{2} \)[/tex] is the same as multiplying by its reciprocal [tex]\( \frac{2}{3} \)[/tex].
[tex]\[
d \times \frac{2}{3} = \frac{8}{7}
\][/tex]
5. Multiply both sides by [tex]\( \frac{3}{2} \)[/tex] to isolate [tex]\( d \)[/tex]:
[tex]\[
d = \frac{8}{7} \times \frac{3}{2}
\][/tex]
6. Perform the multiplication of fractions: Multiply the numerators together and the denominators together.
[tex]\[
d = \frac{8 \times 3}{7 \times 2} = \frac{24}{14} = \frac{12}{7}
\][/tex]
7. Convert the improper fraction to decimal form: [tex]\( \frac{12}{7} \)[/tex] as a decimal is approximately:
[tex]\[
d \approx 1.7142857142857142
\][/tex]
Thus, the value of [tex]\( d \)[/tex] is approximately [tex]\( 1.7142857142857142 \)[/tex].
