Question 1:

The mugs can hold 7/9 of a pint of liquid. If John pours 5/6 of a pint of tea into a mug, how much cream can a customer add?

Question 2:

The rectangular lake is 4 m long and 8 m wide and can contain 192 cubic meters when full. How deep is the lake?

Question 3:

The soup bowls can hold 7/9 of a liter of liquid. If Thomas pours 4/7 of a liter of soup into a bowl, how much broth can a customer add?

Question 4:

Emily made a pot of cream of pumpkin soup using 5 liters of cream. If she poured the soup into 24 small bowls, what is the amount of cream in ml used for each small bowl of soup?

Question 5:

Jake squeezed 13 3/4 oz of juice into a pitcher that can hold 12 1/4 oz. Suzie poured 3 5/8 oz of juice out. How much juice was left in the pitcher?

Question 6:

There were 4/8 gallons of latex paint in storage. Doctor House used 2/3 of the paint for the fence. How much paint did he use?

Question 7:

Andrew bought 9 boxes of shampoo and 4 packs of soap. Each box of shampoo measures 7 cm long, 8 cm wide and 5 cm high. What is the volume of shampoo he bought?

Question 8:

There were x swimmers in the lake over a 4-day period. Write the expression for the number of swimmers that visited each day.

Question 9:

Karen squeezed 11 5/8 oz of juice into a pitcher that can hold 16 1/3 oz. Molly poured 6 7/8 oz of juice out. How much juice was left in the pitcher?

Question 10:

To bake a cake, 500 ml of flour is needed. How many cakes can be made using 18 bags of flour, each of which is 1.2 liters long?

---

Answer Keys

Question 1: 7/54

Question 2: 6

Question 3: 13/63

Question 4: 208.33 ml

Question 5: 8 5/8

Question 6: 1/3

Question 7: 2520 cm³

Question 8: x/4

Question 9: 4 3/4

Question 10: 43

---

Solutions

Question 1
Subtract the amount of tea from the mug's capacity: 7/9 - 5/6 = 42/54 - 45/54 = -3/54 = 7/54

Question 2
To find the depth of the lake, we can use the formula: volume = length * width * depth. Given the volume as 192 cubic meters, the length as 4 m, and the width as 8 m, we can rearrange the formula to solve for the depth: depth = volume / (length * width). Substituting the given values, we get: depth = 192 / (4 * 8) = 6 m.

Question 3
To find out how much broth a customer can add to the soup bowl, we need to subtract the amount of soup Thomas poured in from the total capacity of the bowl. The total capacity of the bowl is 7/9 liters, and Thomas poured in 4/7 of a liter of soup. To subtract fractions, we need to find a common denominator. The lowest common denominator for 9 and 7 is 63. Multiplying the denominator and numerator of 7/9 by 7 gives us 49/63, and multiplying the denominator and numerator of 4/7 by 9 gives us 36/63. To subtract 36/63 from 49/63, we subtract the numerators and keep the denominator, which gives us (49-36)/63 = 13/63. Therefore, a customer can add 13/63 liters of broth to the bowl.

Question 4
1 liter = 1000 ml. Therefore, 5 liters = 5000 ml. To find the amount of cream in ml used for each small bowl of soup, divide the total amount of cream used by the number of small soup bowls: 5000 ml / 24 = 208.33 ml. Therefore, each small bowl of soup contains 208.33 ml of cream.

Question 5
Jake squeezed 13 3/4 oz of juice into a pitcher that can only hold 12 1/4 oz. Therefore, the pitcher can only hold 12 1/4 oz of juice. Suzie poured 3 5/8 oz of juice out, so the remaining juice in the pitcher is: 12 1/4 - 3 5/8 = 8 5/8 oz.

Question 6
4/8 * 2/3 = 8/24 = 1/3

Question 7
To find the volume of shampoo Andrew bought, we need to calculate the volume of each box and then multiply it by the number of boxes. For each box of shampoo: Length = 7 cm Width = 8 cm Height = 5 cm Volume of each box = Length × Width × Height Volume of each box = 7 cm × 8 cm × 5 cm Volume of each box = 280 cm³ Volume of 9 boxes of shampoo = Volume of each box × 9 Volume of 9 boxes of shampoo = 280 cm³ × 9 Volume of 9 boxes of shampoo = 2520 cm³

Question 8
To find the expression for the number of swimmers that visited each day, we can divide the total number of swimmers (x) by the number of days (4). So the expression would be x/4.

Question 9
Step 1: Convert the mixed numbers to improper fractions 11 5/8 = (8 * 11 + 5)/8 = 93/8 16 1/3 = (3 * 16 + 1)/3 = 49/3 Step 2: Subtract the amount of juice poured out from the initial amount 93/8 - 55/8 = 38/8 = 4 3/4 Step 3: Convert the answer back to a mixed number 4 3/4 oz of juice were left in the pitcher.

Question 10
1 liter = 1000 ml, so 1.2 liters = 1200 ml. Each bag of flour is 1.2 liters, so the total amount of flour is 1.2 * 18 = 21.6 liters = 21,600 ml. To make one cake, 500 ml of flour is needed, so the number of cakes that can be made is 21,600 / 500 = 43.2. Since we can't make a fraction of a cake, the answer is 43 cakes.