To solve for [tex]\( h \)[/tex] in the equation
[tex]\[
h \div \frac{2}{3} = \frac{9}{10}
\][/tex]
follow these steps:
1. Understand the Equation: The given equation is [tex]\( h \)[/tex] divided by [tex]\( \frac{2}{3} \)[/tex] equals [tex]\( \frac{9}{10} \)[/tex]. In other words:
[tex]\[
\frac{h}{\frac{2}{3}} = \frac{9}{10}
\][/tex]
2. Isolate [tex]\( h \)[/tex]: To isolate [tex]\( h \)[/tex], we need to get rid of the division by [tex]\( \frac{2}{3} \)[/tex]. To do this, we multiply both sides of the equation by [tex]\( \frac{2}{3} \)[/tex]:
[tex]\[
h = \left(\frac{9}{10}\right) \times \frac{2}{3}
\][/tex]
3. Perform the Multiplication: Next, we'll multiply the fractions [tex]\( \frac{9}{10} \)[/tex] and [tex]\( \frac{2}{3} \)[/tex]:
[tex]\[
h = \frac{9 \times 2}{10 \times 3} = \frac{18}{30}
\][/tex]
4. Simplify the Fraction: Simplify [tex]\( \frac{18}{30} \)[/tex] by finding the greatest common divisor (GCD) of 18 and 30, which is 6, and divide the numerator and the denominator by 6:
[tex]\[
h = \frac{18 \div 6}{30 \div 6} = \frac{3}{5}
\][/tex]
5. Convert to Decimal: Finally, express [tex]\( \frac{3}{5} \)[/tex] as a decimal. Since 3 divided by 5 is 0.6:
[tex]\[
h = 0.6
\][/tex]
Hence, the value of [tex]\( h \)[/tex] is [tex]\( 0.6 \)[/tex].
