Question

1 the expression \\(-490 \div (-7)\\) is equal to:
a 483
b 70
c -70
d -497

2 the figure 2613.23 rounded to 3 significant figures is:
a 2610
b 2600
c 2613.230
d 26

3 which of the following is not written correct to 2 significant figures?
a 41
b 0.0049
c 1.7
d 0.06

4 which of the following is not a simplified ratio?
a 2:3
b 13:2
c 7:2
d 16:48

5 the ratio of \\(a : b\\) is \\(3 : 4\\), the ratio of \\(b : c\\) is \\(7 : 5\\).
which of the following is the correct ratio of \\(a\\) to \\(c\\)?
a 3:5
b 4:12
c 20:21
d 21:20

6 a truck carries apples, bananas and coconuts. the ratio of fruits are \\(2 : 3 : 5\\) respectively.
if there are 24 bananas, what is the total amount of fruit?
a 16
b 40
c 56
d 80

Explanation:

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<reasoning>

Question 1: Divide the integers

\[
-490 \div (-7) = 70
\]

Question 2: Round to 3 significant figures

\[
2613.23 \approx 2610
\]

Question 3: Identify incorrect significant figures

\[

$$\begin{aligned} &\text{A: } 41 \text{ (2 sig figs)} \\ &\text{B: } 0.0049 \text{ (2 sig figs)} \\ &\text{C: } 1.7 \text{ (2 sig figs)} \\ &\text{D: } 0.06 \text{ (1 sig fig)} \end{aligned}$$

\]

Question 4: Identify unsimplified ratio

\[
16:48 = 1:3
\]

Question 5: Find the ratio of A to C

\[

$$\begin{aligned} &A:B = 3:4 = 21:28 \\ &B:C = 7:5 = 28:20 \\ &A:C = 21:20 \end{aligned}$$

\]

Question 6: Calculate total amount of fruit

\[

$$\begin{aligned} &\text{Bananas} = 3x = 24 \implies x = 8 \\ &\text{Total} = (2 + 3 + 5)x = 10 \times 8 = 80 \end{aligned}$$

\]
</reasoning>

<answer>

Question 1

<mcq-option>A 483</mcq-option>
<mcq-correct>(B) 70</mcq-correct>
<mcq-option>C -70</mcq-option>
<mcq-option>D -497</mcq-option>

Question 2

<mcq-correct>(A) 2610</mcq-correct>
<mcq-option>B 2600</mcq-option>
<mcq-option>C 2613.230</mcq-option>
<mcq-option>D 26</mcq-option>

Question 3

<mcq-option>A 41</mcq-option>
<mcq-option>B 0.0049</mcq-option>
<mcq-option>C 1.7</mcq-option>
<mcq-correct>D 0.06</mcq-correct>

Question 4

<mcq-option>A 2:3</mcq-option>
<mcq-option>B 13:2</mcq-option>
<mcq-option>C 7:2</mcq-option>
<mcq-correct>D 16:48</mcq-correct>

Question 5

<mcq-option>A 3:5</mcq-option>
<mcq-option>B 4:12</mcq-option>
<mcq-option>C 20:21</mcq-option>
<mcq-correct>D 21:20</mcq-correct>

Question 6

<mcq-option>A 16</mcq-option>
<mcq-option>B 40</mcq-option>
<mcq-option>C 56</mcq-option>
<mcq-correct>D 80</mcq-correct>
</answer>

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]
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</post_analysis>

Answer:

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"quick"
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"concepts_used": [],
"new_concepts": [
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"Three-part Ratios"
],
"current_concepts": [
"Integer Division",
"Significant Figures",
"Ratio Simplification",
"Three-part Ratios"
]
}
</pre_analysis>

<reasoning>

Question 1: Divide the integers

\[
-490 \div (-7) = 70
\]

Question 2: Round to 3 significant figures

\[
2613.23 \approx 2610
\]

Question 3: Identify incorrect significant figures

\[

$$\begin{aligned} &\text{A: } 41 \text{ (2 sig figs)} \\ &\text{B: } 0.0049 \text{ (2 sig figs)} \\ &\text{C: } 1.7 \text{ (2 sig figs)} \\ &\text{D: } 0.06 \text{ (1 sig fig)} \end{aligned}$$

\]

Question 4: Identify unsimplified ratio

\[
16:48 = 1:3
\]

Question 5: Find the ratio of A to C

\[

$$\begin{aligned} &A:B = 3:4 = 21:28 \\ &B:C = 7:5 = 28:20 \\ &A:C = 21:20 \end{aligned}$$

\]

Question 6: Calculate total amount of fruit

\[

$$\begin{aligned} &\text{Bananas} = 3x = 24 \implies x = 8 \\ &\text{Total} = (2 + 3 + 5)x = 10 \times 8 = 80 \end{aligned}$$

\]
</reasoning>

<answer>

Question 1

<mcq-option>A 483</mcq-option>
<mcq-correct>(B) 70</mcq-correct>
<mcq-option>C -70</mcq-option>
<mcq-option>D -497</mcq-option>

Question 2

<mcq-correct>(A) 2610</mcq-correct>
<mcq-option>B 2600</mcq-option>
<mcq-option>C 2613.230</mcq-option>
<mcq-option>D 26</mcq-option>

Question 3

<mcq-option>A 41</mcq-option>
<mcq-option>B 0.0049</mcq-option>
<mcq-option>C 1.7</mcq-option>
<mcq-correct>D 0.06</mcq-correct>

Question 4

<mcq-option>A 2:3</mcq-option>
<mcq-option>B 13:2</mcq-option>
<mcq-option>C 7:2</mcq-option>
<mcq-correct>D 16:48</mcq-correct>

Question 5

<mcq-option>A 3:5</mcq-option>
<mcq-option>B 4:12</mcq-option>
<mcq-option>C 20:21</mcq-option>
<mcq-correct>D 21:20</mcq-correct>

Question 6

<mcq-option>A 16</mcq-option>
<mcq-option>B 40</mcq-option>
<mcq-option>C 56</mcq-option>
<mcq-correct>D 80</mcq-correct>
</answer>

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