Question

1. circle all of the following that are between 10 and 40.

3² □
4² □
5² □
6² □
7² □

1. what is the value of the underlined digit in the number 328.06?

○ a. \\(\frac{6}{10}\\)
○ b. \\(\frac{6}{100}\\)
○ c. \\(\frac{6}{1000}\\)
○ d. \\(\frac{6}{10000}\\)

1. \\(\

$$\begin{bmatrix}\\frac{1}{2}\\\\ \\frac{2}{3}\\\\ \\frac{3}{4}\\end{bmatrix}$$

= \frac{□}{□}\\)

1. circle the fractions that reduce to \\(\frac{1}{4}\\):

\\(\frac{2}{8}\\) □
\\(\frac{4}{12}\\) □
\\(\frac{3}{12}\\) □
\\(\frac{12}{38}\\) □

1. in about how many seconds could a 9 - year - old boy run 100 meters?

○ a. 5 sec.
○ b. 10 sec.
○ c. 20 sec.

Explanation:

Problem 1:

Step1: Calculate each square

Calculate \(3^2 = 9\), \(4^2 = 16\), \(5^2 = 25\), \(6^2 = 36\), \(7^2 = 49\).

Step2: Identify values between 10 and 40

Check which of these results are between 10 and 40. \(16\) (from \(4^2\)), \(25\) (from \(5^2\)), \(36\) (from \(6^2\)) are between 10 and 40. \(9\) (from \(3^2\)) is less than 10, \(49\) (from \(7^2\)) is greater than 40.

Step1: Identify the place value of the underlined digit

In the number \(328.\underline{0}6\), the underlined digit \(0\) is in the tenths place? Wait, no, wait. Wait, the number is \(328.06\), the underlined digit is \(0\) which is in the tenths place? Wait, no, the options are fractions. Wait, the place value of the digit: the digit \(0\) is in the tenths place? Wait, no, \(328.06\) has digits: 3 (hundreds), 2 (tens), 8 (ones), 0 (tenths), 6 (hundredths). So the value of the underlined digit (0 in tenths place) is \(0\times\frac{1}{10}=0\)? Wait, no, maybe I misread. Wait, the options are \(\frac{6}{10}\), \(\frac{6}{100}\), \(\frac{6}{1000}\), \(\frac{6}{10000}\). Wait, maybe the underlined digit is 6? Wait, the number is \(328.\underline{0}6\)? Wait, maybe a typo, maybe the underlined digit is 6? Wait, no, the original problem says "the underlined digit in the number 328.06". Wait, if the underlined digit is 0, its value is \(0\times\frac{1}{10} = 0\), but the options are about 6. Wait, maybe the underlined digit is 6? Then 6 is in the hundredths place, so its value is \(\frac{6}{100}\). So the correct option is b.

Step1: Observe the pattern in the fractions

The first fraction is \(\frac{1}{2}\), second \(\frac{2}{3}\), third \(\frac{3}{4}\). Wait, no, the way it's written: \(

$$\begin{bmatrix}\frac{1}{2}\\\frac{2}{3}\\\frac{3}{4}\end{bmatrix}$$

\)? Wait, maybe it's a sequence of fractions where numerator and denominator increase by 1. Wait, the question is to fill the square? Wait, maybe it's a pattern where each fraction is \(\frac{n}{n + 1}\) for \(n = 1,2,3\). Wait, but the problem is to find what the matrix equals? Wait, maybe it's a typo, but if we consider the pattern, the next fraction? Wait, no, maybe the problem is to simplify or find a pattern. Wait, maybe the answer is \(\frac{3}{4}\) or something, but the way it's written is a bit unclear. Wait, maybe it's a sequence of fractions: \(\frac{1}{2}\), \(\frac{2}{3}\), \(\frac{3}{4}\), so the next one would be \(\frac{4}{5}\), but the problem is to fill the square. Wait, maybe the question is to find the sum or something, but the image shows a matrix of fractions \(

$$\begin{bmatrix}\frac{1}{2}\\\frac{2}{3}\\\frac{3}{4}\end{bmatrix}$$

\) and an equal sign with a fraction \(\frac{\square}{\square}\). Maybe it's a mistake, but if we consider the pattern, maybe the sum? But that's not clear. Alternatively, maybe it's a typo and the problem is different. Wait, maybe the intended problem is to find the pattern, but given the options (the square), maybe the answer is \(\frac{3}{4}\) or another fraction. Wait, maybe I misinterpret. Alternatively, maybe the problem is to find the value of the matrix, but it's a column matrix of fractions. Maybe the answer is \(\frac{3}{4}\) (the last fraction), but I'm not sure. Wait, maybe the problem is to find the common difference or something, but the fractions are \(\frac{1}{2}\), \(\frac{2}{3}\), \(\frac{3}{4}\), which have differences in numerator and denominator of 1. So the next fraction would be \(\frac{4}{5}\), but the square is for a single fraction. Maybe the problem is to find the sum: \(\frac{1}{2}+\frac{2}{3}+\frac{3}{4}=\frac{6 + 8 + 9}{12}=\frac{23}{12}\), but that's not a simple fraction. Alternatively, maybe the problem is to find the product: \(\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}=\frac{1}{4}\). So the square would be \(\frac{1}{4}\)? Wait, let's check: \(\frac{1}{2}\times\frac{2}{3}=\frac{1}{3}\), then \(\frac{1}{3}\times\frac{3}{4}=\frac{1}{4}\). So the product is \(\frac{1}{4}\). So the fraction is \(\frac{1}{4}\).

Answer:

Circle \(4^2\), \(5^2\), \(6^2\)

Problem 2: