Question

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Explanation:

Identify place value of digit 4

The number is \(23419\).
The digit \(4\) is in the hundreds place.
Its value is \(4 \times 100 = 400\).

Determine tally marks for 7

A group of five tally marks is represented by four vertical lines crossed by a diagonal line.
The number \(7\) is represented by one group of five and two individual vertical lines.
This matches option (d).

Convert fraction to decimal

The fraction is \(\frac{7}{8}\).
Dividing \(7\) by \(8\) gives \(0.875\).
This matches option (d).

Convert Roman numeral to Hindu-Arabic

The Roman numeral is MMCDXLVII.

• \(\text{MM} = 2000\)
• \(\text{CD} = 400\)
• \(\text{XL} = 40\)
• \(\text{VII} = 7\)

Summing these gives \(2000 + 400 + 40 + 7 = 2447\).
This matches option (a).

Correct Roman numeral error

Gabe wrote IX (which is 9) instead of IV (which is 4).
To correct IX to IV, he needs to change the X to V.
This matches option (a).

Convert decimal to fraction

The decimal is \(0.45\).
As a fraction, this is \(\frac{45}{100}\).
Simplifying by dividing numerator and denominator by 5 gives \(\frac{9}{20}\).
This matches option (b).

Calculate number of boys in school

Total students is \(900\).
The fraction of boys is \(\frac{3}{5}\).
Number of boys is \(\frac{3}{5} \times 900 = 3 \times 180 = 540\).
This matches option (c).

Evaluate fraction expression

The expression is \((\frac{1}{2})^2 \times \frac{2}{3}\).

• \((\frac{1}{2})^2 = \frac{1}{4}\)
• \(\frac{1}{4} \times \frac{2}{3} = \frac{2}{12} = \frac{1}{6}\)

This matches option (b).

Add mixed numbers

The expression is \(2\frac{1}{3} + 2\frac{1}{2}\).
Convert to improper fractions:

• \(2\frac{1}{3} = \frac{7}{3}\)
• \(2\frac{1}{2} = \frac{5}{2}\)

Find a common denominator (6):

• \(\frac{7}{3} = \frac{14}{6}\)
• \(\frac{5}{2} = \frac{15}{6}\)

Add the fractions:

• \(\frac{14}{6} + \frac{15}{6} = \frac{29}{6} = 4\frac{5}{6}\)

This matches option (c).

Identify equivalent set

The set is \(\{a, b, c, d\}\), which has a cardinality of 4.
An equivalent set must have the same number of elements (cardinality of 4).

• Option (a) \(\{4\}\) has 1 element.
• Option (b) \(\{a, b, c\}\) has 3 elements.
• Option (c) \(\{p, q, r, s\}\) has 4 elements.
• Option (d) \(\{1, 2, 3, 4, 5\}\) has 5 elements.

Thus, \(\{p, q, r, s\}\) is equivalent.
This matches option (c).

Identify infinite set

An infinite set has an unlimited number of elements.

• Option (a) \(\{\text{factors of } 20\}\) is finite.
• Option (b) \(\{\text{multiples of } 3\}\) is infinite because multiples go on forever.
• Option (c) \(\{\text{odd numbers between } 10 \text{ and } 20\}\) is finite.
• Option (d) \(\{\text{prime numbers less than } 10\}\) is finite.

Thus, the set of multiples of 3 is infinite.
This matches option (b).

Answer:

Question 1

• (a) 4
• (b) 40
• (c) 400 (Correct answer)
• (d) 1000

Question 2

• (a) 5 + 2 vertical lines
• (b) 4 vertical lines + 3 vertical lines
• (c) 6 vertical lines + 1 vertical line
• (d) 5 vertical lines crossed + 2 vertical lines (Correct answer)

Question 3

• (a) 0.125
• (b) 0.7
• (c) 0.78
• (d) 0.875 (Correct answer)

Question 4

• (a) 2447 (Correct answer)
• (b) 2457
• (c) 2547
• (d) 2477

Question 5

• (a) change the X to V (Correct answer)
• (b) change the I to X
• (c) change the X to I
• (d) change the I to V

Question 6

• (a) \(\frac{4}{5}\)
• (b) \(\frac{9}{20}\) (Correct answer)
• (c) \(\frac{9}{2}\)
• (d) \(\frac{45}{10}\)

Question 7

• (a) 180
• (b) 300
• (c) 540 (Correct answer)
• (d) 720

Question 8

• (a) \(\frac{2}{3}\)
• (b) \(\frac{1}{6}\) (Correct answer)
• (c) \(\frac{1}{12}\)
• (d) \(\frac{1}{18}\)

Question 9

• (a) \(4\frac{2}{5}\)
• (b) \(4\frac{1}{3}\)
• (c) \(4\frac{5}{6}\) (Correct answer)
• (d) \(4\frac{5}{12}\)

Question 10

• (a) \(\{4\}\)
• (b) \(\{a, b, c\}\)
• (c) \(\{p, q, r, s\}\) (Correct answer)
• (d) \(\{1, 2, 3, 4, 5\}\)

Question 11

• (a) \(\{\text{factors of } 20\}\)
• (b) \(\{\text{multiples of } 3\}\) (Correct answer)
• (c) \(\{\text{odd numbers between } 10 \text{ and } 20\}\)
• (d) \(\{\text{prime numbers less than } 10\}\)