Question

a) $8\frac{3}{20} = 8\frac{15}{100} = 8.15$ (with multiplication by 5 arrows)
b) $3\frac{6}{25} = \underline{\quad\quad} = \underline{\quad\quad}$
c) $24\frac{1}{500} = \underline{\quad\quad} = \underline{\quad\quad}$
d) $\underline{\quad\quad} = \underline{\quad\quad} = 9.45$
e) $\underline{\quad\quad} = \underline{\quad\quad} = 25.012$
f) $\underline{\quad\quad} = \underline{\quad\quad} = 7.64$

Explanation:

Step1: Convert fraction to hundredths

For $3\frac{6}{25}$: multiply numerator/denominator by 4.
$\frac{6\times4}{25\times4}=\frac{24}{100}$

Step2: Rewrite as decimal

Combine whole number and decimal.
$3 + \frac{24}{100}=3.24$

Step3: Convert fraction to thousandths

For $24\frac{1}{500}$: multiply numerator/denominator by 2.
$\frac{1\times2}{500\times2}=\frac{2}{1000}$

Step4: Rewrite as decimal

Combine whole number and decimal.
$24 + \frac{2}{1000}=24.002$

Step5: Convert decimal to fraction

For $9.45$: split whole and decimal parts.
$9 + \frac{45}{100}$

Step6: Simplify the fraction

Reduce $\frac{45}{100}$ by GCD 5.
$\frac{45\div5}{100\div5}=\frac{9}{20}$, so $9\frac{9}{20}$

Step7: Convert decimal to fraction

For $25.012$: split whole and decimal parts.
$25 + \frac{12}{1000}$

Step8: Simplify the fraction

Reduce $\frac{12}{1000}$ by GCD 4.
$\frac{12\div4}{1000\div4}=\frac{3}{250}$, so $25\frac{3}{250}$

Step9: Convert decimal to fraction

For $7.64$: split whole and decimal parts.
$7 + \frac{64}{100}$

Step10: Simplify the fraction

Reduce $\frac{64}{100}$ by GCD 4.
$\frac{64\div4}{100\div4}=\frac{16}{25}$, so $7\frac{16}{25}$

Answer:

b) $3\frac{24}{100}$, $3.24$
c) $24\frac{2}{1000}$, $24.002$
d) $9\frac{45}{100}$, $9\frac{9}{20}$
e) $25\frac{12}{1000}$, $25\frac{3}{250}$
f) $7\frac{64}{100}$, $7\frac{16}{25}$