Grade 4 Maths Year-end Exam: Paper 1 - Free Printable

Let's solve each question step by step:

---

Question 1.1: The product of 278 and 34 is:

We need to calculate \( 278 \times 34 \).

#### Step-by-Step Calculation:
1. Break down the multiplication:
\[
278 \times 34 = 278 \times (30 + 4) = (278 \times 30) + (278 \times 4)
\]

2. Calculate \( 278 \times 30 \):
\[
278 \times 30 = 278 \times 3 \times 10 = 834 \times 10 = 8340
\]

3. Calculate \( 278 \times 4 \):
\[
278 \times 4 = 1112
\]

4. Add the results:
\[
8340 + 1112 = 9452
\]

#### Final Answer:
\[
\boxed{B}
\]

---

Question 1.2: A number multiplied by one and divided by one will have the same value as:

When a number is multiplied by 1, it remains unchanged. Similarly, when a number is divided by 1, it also remains unchanged.

#### Explanation:
- Multiplying any number \( x \) by 1: \( x \times 1 = x \)
- Dividing any number \( x \) by 1: \( x \div 1 = x \)

Thus, the result is the number itself.

#### Final Answer:
\[
\boxed{D}
\]

---

Question 1.3: Seventy-eight sweets are divided equally between 9 children. How many sweets are left over?

We need to divide 78 by 9 and find the remainder.

#### Step-by-Step Calculation:
1. Perform the division:
\[
78 \div 9 = 8 \text{ remainder } 6
\]
- \( 9 \times 8 = 72 \)
- \( 78 - 72 = 6 \)

#### Final Answer:
\[
\boxed{B}
\]

---

Question 1.4: What is the place value of the underlined digit in the number 7,000?

The number given is 7,000, and the underlined digit is 7.

#### Explanation:
- In the number 7,000, the digit 7 is in the thousands place.

#### Final Answer:
\[
\boxed{B}
\]

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Question 1.5: What is the answer if 78 Hundreds are added to 24 Tens?

We need to convert the hundreds and tens into their numerical values and then add them.

#### Step-by-Step Calculation:
1. Convert 78 Hundreds:
\[
78 \text{ Hundreds} = 78 \times 100 = 7800
\]

2. Convert 24 Tens:
\[
24 \text{ Tens} = 24 \times 10 = 240
\]

3. Add the two values:
\[
7800 + 240 = 8040
\]

#### Final Answer:
\[
\boxed{D}
\]

---

Question 1.6: Circle the fraction where the shaded part represents three quarters.

We need to identify which option shows a fraction that represents \( \frac{3}{4} \).

#### Analysis of Each Option:
- Option A: The grid has 3 out of 6 squares shaded. This represents \( \frac{3}{6} = \frac{1}{2} \).
- Option B: The grid has 3 out of 4 rectangles shaded. This represents \( \frac{3}{4} \).
- Option C: The grid has 6 out of 9 squares shaded. This represents \( \frac{6}{9} = \frac{2}{3} \).
- Option D: The grid has 2 out of 4 rectangles shaded. This represents \( \frac{2}{4} = \frac{1}{2} \).

#### Correct Option:
Option B represents \( \frac{3}{4} \).

#### Final Answer:
\[
\boxed{B}
\]

---

Question 1.7: What number is represented by the following equation:

\[
(8 \times 1000) + (7 \times 1000) + (3 \times 100) = ?
\]

#### Step-by-Step Calculation:
1. Calculate each term:
- \( 8 \times 1000 = 8000 \)
- \( 7 \times 1000 = 7000 \)
- \( 3 \times 100 = 300 \)

2. Add the results:
\[
8000 + 7000 + 300 = 15300
\]

#### Final Answer:
\[
\boxed{C}
\]

---

Question 1.8: Which fraction is bigger than \( \frac{1}{3} \)?

We need to compare each fraction with \( \frac{1}{3} \).

#### Analysis of Each Option:
- Option A: \( \frac{1}{4} \)
- \( \frac{1}{4} < \frac{1}{3} \) because 4 is larger than 3.
- Option B: \( \frac{1}{2} \)
- \( \frac{1}{2} > \frac{1}{3} \) because 2 is smaller than 3.
- Option C: \( \frac{2}{10} \)
- Simplify \( \frac{2}{10} = \frac{1}{5} \).
- \( \frac{1}{5} < \frac{1}{3} \) because 5 is larger than 3.
- Option D: \( \frac{1}{6} \)
- \( \frac{1}{6} < \frac{1}{3} \) because 6 is larger than 3.

#### Correct Option:
Option B (\( \frac{1}{2} \)) is greater than \( \frac{1}{3} \).

#### Final Answer:
\[
\boxed{B}
\]

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Final Answers:

1.1: \(\boxed{B}\)
1.2: \(\boxed{D}\)
1.3: \(\boxed{B}\)
1.4: \(\boxed{B}\)
1.5: \(\boxed{D}\)
1.6: \(\boxed{B}\)
1.7: \(\boxed{C}\)
1.8: \(\boxed{B}\)