Let's solve each problem step-by-step:
### Problem 1:
Rochelle prepares sauce for her roasted fish to be used in their family reunion. She has [tex]\( \frac{3}{4} \)[/tex] cup of calamansi juice, and [tex]\( \frac{3}{4} \)[/tex] cup of soy sauce. How many cups of mixture does she have?
1. Add the amounts of calamansi juice and soy sauce.
[tex]\[
\frac{3}{4} + \frac{3}{4} = \frac{6}{4} = \frac{3}{2}
\][/tex]
So, Rochelle has 1.5 cups of mixture.
### Problem 2:
Mark takes [tex]\( 3 \frac{2}{3} \)[/tex] hours in cutting a pole and [tex]\( 5 \frac{1}{3} \)[/tex] hours in making a frame. How long does Mark work?
1. Convert mixed numbers to improper fractions:
[tex]\[
3 \frac{2}{3} = 3 + \frac{2}{3} = \frac{9}{3} + \frac{2}{3} = \frac{11}{3}
\][/tex]
[tex]\[
5 \frac{1}{3} = 5 + \frac{1}{3} = \frac{15}{3} + \frac{1}{3} = \frac{16}{3}
\][/tex]
2. Add the improper fractions:
[tex]\[
\frac{11}{3} + \frac{16}{3} = \frac{27}{3} = 9
\][/tex]
So, Mark works 9 hours in total.
### Problem 3:
Carol bought [tex]\( \frac{2}{3} \)[/tex] kg of pork and [tex]\( \frac{1}{4} \)[/tex] kg of chicken. How many kilograms of meat did she buy?
1. Add the amounts of pork and chicken.
[tex]\[
\frac{2}{3} + \frac{1}{4}
\][/tex]
2. Find the common denominator (12):
[tex]\[
\frac{2}{3} = \frac{8}{12}, \quad \frac{1}{4} = \frac{3}{12}
\][/tex]
3. Add the fractions:
[tex]\[
\frac{8}{12} + \frac{3}{12} = \frac{11}{12}
\][/tex]
So, Carol bought [tex]\( \frac{11}{12} \)[/tex] kg or approximately 0.9167 kg of meat.
### Problem 4:
In Music class, the pupils spend [tex]\( \frac{1}{2} \)[/tex] hour in singing and [tex]\( \frac{1}{3} \)[/tex] hour in vocalizing. How many hours did they spend in all?
1. Add the amounts of time spent singing and vocalizing.
[tex]\[
\frac{1}{2} + \frac{1}{3}
\][/tex]
2. Find the common denominator (6):
[tex]\[
\frac{1}{2} = \frac{3}{6}, \quad \frac{1}{3} = \frac{2}{6}
\][/tex]
3. Add the fractions:
[tex]\[
\frac{3}{6} + \frac{2}{6} = \frac{5}{6}
\][/tex]
So, the pupils spent [tex]\( \frac{5}{6} \)[/tex] of an hour, or approximately 0.8333 hours.
### Problem 5:
Alyana has a visitor. She served her with pineapple juice. She mixed [tex]\( \frac{1}{3} \)[/tex] glass of sweetened pineapple juice and [tex]\( \frac{3}{4} \)[/tex] glass of water. How much is the mixture?
1. Add the amounts of pineapple juice and water.
[tex]\[
\frac{1}{3} + \frac{3}{4}
\][/tex]
2. Find the common denominator (12):
[tex]\[
\frac{1}{3} = \frac{4}{12}, \quad \frac{3}{4} = \frac{9}{12}
\][/tex]
3. Add the fractions:
[tex]\[
\frac{4}{12} + \frac{9}{12} = \frac{13}{12} = 1 \frac{1}{12}
\][/tex]
So, Alyana's mixture is [tex]\( \frac{13}{12} \)[/tex] glasses or approximately 1.0833 glasses.
In summary:
1. Rochelle's mixture: 1.5 cups
2. Mark's working time: 9 hours
3. Carol's meat: 0.9167 kg
4. Pupils' music class time: 0.8333 hours
5. Alyana's juice mixture: 1.0833 glasses
