5Th Grade Math Quiz - Free Printable

Let's go through each problem on the 5-A-Day Math Assessment: Week 1 worksheet step by step and solve them with explanations.

---

1. Write and solve an expression for the following situation: "8 less than the product of 6 and 9"

- Step 1: Find the product of 6 and 9
$ 6 \times 9 = 54 $

- Step 2: Subtract 8 from that product
$ 54 - 8 = 46 $

✔ Answer: $ (6 \times 9) - 8 = 46 $

---

2. Model and solve the problem:

$$
0.3 \times 0.5
$$

- Modeling using a grid (hundredths grid):
- A 10x10 grid represents 1 whole.
- Shade 3 columns (0.3) and 5 rows (0.5).
- The overlapping area is $ 3 \times 5 = 15 $ squares.
- So, $ 0.3 \times 0.5 = 0.15 $

✔ Answer: $ 0.15 $

---

3. Solve using area models:

#### a) $ \frac{1}{4} = $ ?

- Draw a rectangle divided into 4 equal parts.
- Shade 1 part → This represents $ \frac{1}{4} $
- As a decimal: $ \frac{1}{4} = 0.25 $

✔ Answer: $ \frac{1}{4} = 0.25 $

#### b) $ \frac{1}{2} = $ ?

- Divide a rectangle into 2 equal parts.
- Shade 1 part → $ \frac{1}{2} $
- As a decimal: $ \frac{1}{2} = 0.5 $

✔ Answer: $ \frac{1}{2} = 0.5 $

---

4. What is the value of the underlined digits?

#### a) $ 32,\underline{5}80 $

- The underlined digit is 5, in the hundreds place.
- So, its value is $ 5 \times 100 = 500 $

✔ Answer: 500

#### b) $ 1.\underline{6}87 $

- The underlined digit is 6, in the tenths place.
- So, its value is $ 6 \times 0.1 = 0.6 $

✔ Answer: 0.6

---

5. Word Form and Expanded Form for 3,659

#### Word Form:
- Three thousand six hundred fifty-nine

✔ Answer: Three thousand six hundred fifty-nine

#### Expanded Form:
- Break down by place values:
$$
3,000 + 600 + 50 + 9
$$

✔ Answer: $ 3,000 + 600 + 50 + 9 $

---

6. Long Division: $ 3 \div 41.58 $

Wait — this seems like a typo. It says:

```
3 ) 41.58
```

But it’s written as $ 3 \div 41.58 $? That would be small.

Actually, it looks like it's meant to be $ 41.58 \div 3 $ — dividing 41.58 by 3.

Let’s do that:

$$
\begin{array}{r|l}
3 & 41.58 \\
\hline
& 13.86 \\
\end{array}
$$

- $ 3 \times 13 = 39 $, subtract: $ 41 - 39 = 2 $
- Bring down 5 → 25 → $ 3 \times 8 = 24 $, remainder 1
- Bring down 8 → 18 → $ 3 \times 6 = 18 $
- So, $ 41.58 \div 3 = 13.86 $

✔ Answer: $ 13.86 $

---

7. Write the ordered pair for each point

From the coordinate grid:

- A: At (5, 8)
- B: At (9, 6)
- C: At (3, 3)
- D: At (8, 1)

✔ Answers:
- A: (5, 8)
- B: (9, 6)
- C: (3, 3)
- D: (8, 1)

---

8. Compare: $ 0.16 \quad \boxed{\phantom{<}} \quad 0.7 $

- Compare decimals:
- $ 0.16 $ vs $ 0.70 $
- Since $ 16 < 70 $, then $ 0.16 < 0.7 $

✔ Answer: $ 0.16 < 0.7 $

---

9. Model and solve the problem: $ 0.1 \div 0.4 $

Wait — this is unusual. Usually we divide larger numbers by smaller ones.

But let’s interpret: $ 0.1 \div 0.4 $

We can rewrite as:
$$
\frac{0.1}{0.4} = \frac{1}{4} = 0.25
$$

But modeling this using a grid?

Alternatively, perhaps it's a typo and meant to be $ 0.4 \div 0.1 $? But let's follow what's written.

But looking at the grid: it's a 10x10 grid.

To model $ 0.1 \div 0.4 $, think of how many times 0.4 fits into 0.1 → it doesn't even fit once.

So $ 0.1 \div 0.4 = 0.25 $

✔ Answer: $ 0.25 $

But if the problem is actually $ 0.4 \div 0.1 $, that would be 4. But based on the notation: $ 0.1 \div 0.4 $, answer is 0.25

Let’s double-check:
$ 0.4 \times 0.25 = 0.1 $ → Yes.

✔ Answer: $ 0.25 $

---

10. $ 0.36 - 0.19 $

- Align decimals:
```
0.36
- 0.19
------
0.17
```

✔ Answer: $ 0.17 $

---

11. Model and solve: $ 3 \times \frac{1}{2} $

- Use circles or a model:
- Draw 3 circles.
- Each circle is split in half.
- Shade one half of each → total shaded = $ 3 \times \frac{1}{2} = \frac{3}{2} = 1\frac{1}{2} $

✔ Answer: $ 1\frac{1}{2} $ or $ \frac{3}{2} $

---

12. Model and solve: $ \frac{1}{4} \times \frac{1}{2} $

- Use a rectangle model:
- Divide a rectangle into 4 equal parts vertically (for $ \frac{1}{4} $)
- Divide it into 2 equal parts horizontally (for $ \frac{1}{2} $)
- The overlapping area is $ \frac{1}{8} $

So:
$$
\frac{1}{4} \times \frac{1}{2} = \frac{1}{8}
$$

✔ Answer: $ \frac{1}{8} $

---

## ✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | $ (6 \times 9) - 8 = 46 $ |
| 2 | $ 0.3 \times 0.5 = 0.15 $ |
| 3a | $ \frac{1}{4} = 0.25 $ |
| 3b | $ \frac{1}{2} = 0.5 $ |
| 4a | 500 |
| 4b | 0.6 |
| 5 | Word: Three thousand six hundred fifty-nine; Expanded: $ 3,000 + 600 + 50 + 9 $ |
| 6 | $ 41.58 \div 3 = 13.86 $ |
| 7 | A: (5,8), B: (9,6), C: (3,3), D: (8,1) |
| 8 | $ 0.16 < 0.7 $ |
| 9 | $ 0.1 \div 0.4 = 0.25 $ |
| 10 | $ 0.36 - 0.19 = 0.17 $ |
| 11 | $ 3 \times \frac{1}{2} = 1\frac{1}{2} $ |
| 12 | $ \frac{1}{4} \times \frac{1}{2} = \frac{1}{8} $ |

Let me know if you'd like visual models drawn out!