Sure, let's solve this problem step-by-step:
1. Identify the amounts of sugar used:
- Ron used [tex]\(1 \frac{3}{4}\)[/tex] cups of sugar for the cake.
- He used [tex]\(\frac{3}{4}\)[/tex] cup of sugar for the icing.
2. Convert the mixed fraction to an improper fraction:
- [tex]\(1 \frac{3}{4}\)[/tex] can be converted to an improper fraction:
[tex]\[
1 \frac{3}{4} = 1 + \frac{3}{4} = \frac{4}{4} + \frac{3}{4} = \frac{7}{4}
\][/tex]
3. Simplify and combine the fractions:
- To find the total amount of sugar used, add the fraction for the cake and the fraction for the icing:
[tex]\[
\frac{7}{4} + \frac{3}{4}
\][/tex]
4. Add the fractions:
- Since the denominators are the same, you can add the numerators directly:
[tex]\[
\frac{7}{4} + \frac{3}{4} = \frac{7+3}{4} = \frac{10}{4}
\][/tex]
5. Simplify the fraction (if possible):
- [tex]\(\frac{10}{4}\)[/tex] can be simplified by dividing both the numerator and the denominator by 2, the greatest common divisor:
[tex]\[
\frac{10}{4} = \frac{10 \div 2}{4 \div 2} = \frac{5}{2} = 2 \frac{1}{2}
\][/tex]
6. Convert the improper fraction or mixed number to a decimal:
- [tex]\(\frac{7}{4}\)[/tex] is equivalent to 1.75 when expressed as a decimal.
- [tex]\(\frac{3}{4}\)[/tex] is already a decimal equivalent to 0.75.
- When we sum these values:
[tex]\[
1.75 + 0.75 = 2.50
\][/tex]
In conclusion, Ron used 2.5 cups of sugar in total.
