5Th Grade Math Quiz - Free Printable

Let's solve the problems step by step as presented in the image.

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

- Expression: The product of 6 and 9 is \(6 \times 9\). Eight less than this product is \(6 \times 9 - 8\).
- Solution:
\[
6 \times 9 = 54
\]
\[
54 - 8 = 46
\]
Answer: \(46\)

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Problem 2: Model and solve \(0.3 \times 0.5\).

- Model: Use a grid to represent \(0.3 \times 0.5\). A 10x10 grid represents 1 whole, so:
- Shade 3 rows (representing 0.3) and 5 columns (representing 0.5).
- The overlapping area represents the product.
- There are 15 small squares shaded out of 100, which is \(0.15\).
- Solution:
\[
0.3 \times 0.5 = 0.15
\]
Answer: \(0.15\)

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Problem 3: Solve using area models.

#### Part (a): \(\frac{1}{4} + \frac{1}{2}\)
- Area Model: Divide a square into 4 equal parts. Shade 1 part for \(\frac{1}{4}\) and 2 parts for \(\frac{1}{2}\). Together, they shade 3 parts out of 4.
- Solution:
\[
\frac{1}{4} + \frac{1}{2} = \frac{1}{4} + \frac{2}{4} = \frac{3}{4}
\]
Answer: \(\frac{3}{4}\)

#### Part (b): \(\frac{1}{4} \times \frac{1}{2}\)
- Area Model: Divide a square into 4 equal parts and shade 1 part for \(\frac{1}{4}\). Then divide each of those 4 parts into 2 equal parts, shading half of the shaded \(\frac{1}{4}\). This results in 1 part out of 8.
- Solution:
\[
\frac{1}{4} \times \frac{1}{2} = \frac{1}{8}
\]
Answer: \(\frac{1}{8}\)

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Problem 4: What is the value of the underlined digits?

#### Part (a): \(32.580\) (underline on 5)
- The digit 5 is in the tenths place, so its value is \(5 \times 0.1 = 0.5\).
Answer: \(0.5\)

#### Part (b): \(1.687\) (underline on 8)
- The digit 8 is in the hundredths place, so its value is \(8 \times 0.01 = 0.08\).
Answer: \(0.08\)

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Problem 5: Word Form and Expanded Form of 3,659

#### Word Form:
- Three thousand, six hundred fifty-nine.
Answer: Three thousand, six hundred fifty-nine

#### Expanded Form:
- Break down the number into its place values:
\[
3,659 = 3,000 + 600 + 50 + 9
\]
Answer: \(3,000 + 600 + 50 + 9\)

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Problem 6: Ordered pairs for points A, B, C, D

- Point A: Located at (3, 7).
- Point B: Located at (8, 6).
- Point C: Located at (6, 2).
- Point D: Located at (9, 3).
Answers:
- A: (3, 7)
- B: (8, 6)
- C: (6, 2)
- D: (9, 3)

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Problem 7: Compare \(0.16\) and \(0.7\)

- Compare the numbers:
\[
0.16 < 0.7
\]
Answer: \(<\)

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Problem 8: Model and solve \(3 \times \frac{1}{2}\)

- Model: Divide a whole into 2 equal parts and take 3 of those halves. This results in \(1 \frac{1}{2}\) or \(1.5\).
- Solution:
\[
3 \times \frac{1}{2} = \frac{3}{2} = 1.5
\]
Answer: \(1.5\)

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Problem 9: Model and solve \(0.36 - 0.19\)

- Model: Subtract the decimals directly.
- Solution:
\[
0.36 - 0.19 = 0.17
\]
Answer: \(0.17\)

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Problem 10: Model and solve \(\frac{1}{4} \times \frac{1}{2}\)

- Model: As explained in Problem 3(b), the result is \(\frac{1}{8}\).
- Solution:
\[
\frac{1}{4} \times \frac{1}{2} = \frac{1}{8}
\]
Answer: \(\frac{1}{8}\)

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Final Answer:

\[
\boxed{46, 0.15, \frac{3}{4}, \frac{1}{8}, 0.5, 0.08, \text{Three thousand, six hundred fifty-nine}, 3,000 + 600 + 50 + 9, (3, 7), (8, 6), (6, 2), (9, 3), <, 1.5, 0.17, \frac{1}{8}}
\]