Question

monday
sarah has ¼ of a pizza and her mother has ⅓ of a pizza. how much pizza do they have altogether?
a recipe calls for 2 ¼ cups of flour. if you want to make the recipe 4 times, how many cups of flour will you need?
maria’s family orders 3 large pizzas. her family eats 1 4/6 pizzas and saves the rest for tomorrow. how much pizza did they save?
a carpenter has 8 feet of wood. he needs to cut it into pieces that are each ¼ feet long. how many pieces can he make?
emma walks 6.39 miles on monday and 3.85 miles on tuesday. how many miles did she walk in total?
tuesday
a carpenter needs 3 ⅔ feet of wood for one shelf and 6 ¼ feet of wood for another. how much wood does the carpenter need in total?
john has ½ of a chocolate bar. he gives his sister ⅓ of what he has. what fraction of the whole chocolate bar did his sister receive?
tom has 7 ⅔ gallons of paint. he uses 4 7/10 of what he has. how many gallons of paint does he have left?
the school garden has 17 square meters of space. if each vegetable plot needs ½ square meters, what is the maximum amount of plots that can be made?
a water tank contains 15.8 gallons. if you use 3.25 gallons each day, how many gallons will be left after 2 days?

Explanation:

Monday Problems

Problem 1: Add pizza fractions

Step1: Find common denominator (20)
$\frac{3}{4} + \frac{1}{5} = \frac{15}{20} + \frac{4}{20}$
Step2: Sum the numerators
$\frac{15+4}{20} = \frac{19}{20}$

Problem 2: Multiply flour amount by 4

Step1: Convert mixed number to fraction
$2\frac{1}{4} = \frac{9}{4}$
Step2: Multiply by recipe batches
$\frac{9}{4} \times 4 = 9$

Problem 3: Subtract eaten pizza from total

Step1: Simplify eaten pizza fraction
$1\frac{4}{6} = 1\frac{2}{3} = \frac{5}{3}$
Step2: Convert total pizza to thirds
$3 = \frac{9}{3}$
Step3: Subtract eaten from total
$\frac{9}{3} - \frac{5}{3} = \frac{4}{3} = 1\frac{1}{3}$

Problem 4: Divide wood length by piece size

Step1: Rewrite division as multiplication
$8 \div \frac{1}{4} = 8 \times 4$
Step2: Calculate the product
$8 \times 4 = 32$

Problem 5: Add total miles walked

Step1: Sum the two distances
$6.39 + 3.85 = 10.24$

Tuesday Problems

Problem 1: Add wood lengths

Step1: Add whole numbers and fractions
$3\frac{1}{4} + 6\frac{1}{2} = (3+6) + (\frac{1}{4} + \frac{2}{4})$
Step2: Calculate total
$9 + \frac{3}{4} = 9\frac{3}{4}$

Problem 2: Multiply chocolate fractions

Step1: Find fraction sister receives
$\frac{1}{2} \times \frac{1}{3} = \frac{1 \times 1}{2 \times 3}$
Step2: Simplify the product
$\frac{1}{6}$

Problem 3: Calculate remaining paint

Step1: Find used paint fraction
$1 - \frac{7}{10} = \frac{3}{10}$
Step2: Convert mixed number to fraction
$7\frac{1}{5} = \frac{36}{5}$
Step3: Multiply by remaining fraction
$\frac{36}{5} \times \frac{3}{10} = \frac{108}{50} = 2\frac{8}{50} = 2\frac{4}{25}$

Problem 4: Divide garden space by plot size

Step1: Rewrite division as multiplication
$17 \div \frac{1}{2} = 17 \times 2$
Step2: Calculate the product
$17 \times 2 = 34$

Problem 5: Calculate remaining water

Step1: Find total water used
$3.25 \times 2 = 6.5$
Step2: Subtract used from total
$15.8 - 6.5 = 9.3$

Answer:

Monday Answers:

1. $\frac{19}{20}$
2. 9 cups
3. $1\frac{1}{3}$ pizzas
4. 32 pieces
5. 10.24 miles

Tuesday Answers:

1. $9\frac{3}{4}$ feet
2. $\frac{1}{6}$
3. $2\frac{4}{25}$ gallons
4. 34 plots
5. 9.3 gallons