Terry bought 5 pizzas. AFter his siters had eaten some, there were 3 and 3/4 pizzas left. He ate 7/8 fewer pizza than his siters. How many pizzas were eaten in all?

Winnie prepare 9 litres of syrup. She poured them equally into 4 similar containers and gave one container of syrup to her neighbour. How many litres of syrup did her neugh bour receive

solve fraction mode

Let's break down each problem.

### Problem 1: Terry's Pizzas

- Terry bought 5 pizzas.
- After his sisters ate some, there were \(3 \frac{3}{4}\) pizzas left.
- Terry ate \( \frac{7}{8} \) fewer pizzas than his sisters.

Let’s start by calculating how many pizzas were eaten by Terry and his sisters together.

#### Step 1: Find out how many pizzas were eaten by Terry and his sisters.
The number of pizzas eaten is the total amount Terry bought minus the amount left:

\[
\text{Pizzas eaten} = 5 - 3 \frac{3}{4} = 5 - \frac{15}{4} = \frac{20}{4} - \frac{15}{4} = \frac{5}{4} \text{ pizzas}
\]

So, Terry and his sisters together ate \( \frac{5}{4} \) pizzas.

#### Step 2: Determine how many pizzas Terry's sisters ate.
Let’s call the amount Terry ate \( T \) and the amount his sisters ate \( S \).

From the problem, we know:
- \( S + T = \frac{5}{4} \) pizzas were eaten in total.
- Terry ate \( \frac{7}{8} \) fewer pizzas than his sisters, so \( T = S - \frac{7}{8} \).

Now we can substitute \( T \) in the total equation:
\[
S + (S - \frac{7}{8}) = \frac{5}{4}
\]
\[
2S - \frac{7}{8} = \frac{5}{4}
\]

#### Step 3: Solve for \( S \) (how much the sisters ate).
First, let’s add \( \frac{7}{8} \) to both sides to isolate \( 2S \):
\[
2S = \frac{5}{4} + \frac{7}{8}
\]

We need a common denominator to add these fractions. The least common denominator of 4 and 8 is 8, so:

\[
\frac{5}{4} = \frac{10}{8}
\]

Now we can add:
\[
2S = \frac{10}{8} + \frac{7}{8} = \frac{17}{8}
\]

Now, divide by 2:
\[
S = \frac{17}{8} \div 2 = \frac{17}{16}
\]

#### Step 4: Find \( T \) (how much Terry ate).
Now that we know the sisters ate \( \frac{17}{16} \) pizzas, we can find how much Terry ate:
\[
T = S - \frac{7}{8} = \frac{17}{16} - \frac{7}{8}
\]

Again, we need a common denominator. Converting \( \frac{7}{8} \) to have a denominator of 16:
\[
\frac{7}{8} = \frac{14}{16}
\]

Now subtract:
\[
T = \frac{17}{16} - \frac{14}{16} = \frac{3}{16}
\]

#### Final Answer for Problem 1:
- Terry ate \( \frac{3}{16} \) pizzas.
- His sisters ate \( \frac{17}{16} \) pizzas.
- Together, they ate \( \frac{5}{4} \) pizzas, or 1 and \( \frac{1}{4} \) pizzas.

### Problem 2: Winnie’s Syrup

- Winnie prepared 9 liters of syrup.
- She poured it equally into 4 containers.
- She gave one container of syrup to her neighbor.

#### Step 1: Determine how much syrup each container holds.
Since the syrup is equally distributed among 4 containers, each container holds:

\[
\text{Syrup per container} = \frac{9}{4} = 2 \frac{1}{4} \text{ liters}
\]

#### Final Answer for Problem 2:
Winnie’s neighbor received \( 2 \frac{1}{4} \) liters of syrup, or \( 2.25 \) liters.

---

Would you like further details on any of these steps or have any questions?

### 5 Related Questions:
1. What if Terry had eaten the same amount as his sisters? How much pizza would they have eaten together?
2. If Terry’s sisters had left only 1 pizza, how much more would they have eaten compared to Terry?
3. How many more pizzas would Terry need to buy if they wanted to have at least 6 pizzas left?
4. If Winnie poured the syrup into 6 containers, how much syrup would each container hold?
5. How much syrup would Winnie’s neighbor have received if she gave them two containers?

### Tip:
When dealing with mixed numbers and fractions, always convert them to improper fractions to simplify the calculations.

Terry bought 5 pizzas. After his sisters had eaten some, there were 3 and 3/4 pizzas left. He ate 7/8 fewer pizzas than his sisters. How many pizzas were eaten in all? Winnie prepared 9 litres of syrup. She poured them equally into 4 similar containers and gave one container of syrup to her neighbour. How many litres of syrup did her neighbour receive?

Solve fraction problems involving pizzas and syrup distribution. Learn how Terry and his sisters divided pizzas using fractions, and how Winnie distributed 9 litres of syrup into containers. Suitable for Grades 5-7, this problem covers key fraction concepts, mixed numbers, and simple division.

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