Let's tackle each part of this question step-by-step:
### (i) How many parts do you shade in one sheet of paper?
To find out how many parts you shade in one sheet of paper:
- First, note that each sheet is divided into 2 equal parts.
- You shade 3 parts, but since one sheet only has 2 parts, you have effectively shaded 3/2 parts of one sheet.
Thus, you shade 1.5 parts in one sheet of paper.
### (ii) How many parts do you shade in another sheet of paper?
The division of parts in the second sheet of paper is identical to the first sheet:
- Since you again need to shade 3 parts and each sheet is divided into 2 parts, you shade 3/2 parts of the second sheet.
Thus, you also shade 1.5 parts in the other sheet of paper.
### (iii) What fraction of the two sheets of paper do you shade?
Next, let's find the fraction of the two sheets of paper that you shade:
- You have shaded a total of 3 parts in each sheet, making it 3 + 3 = 6 parts in total.
- Each sheet consists of 2 parts, so for two sheets, the total number of integral parts is 2 sheets x 2 parts/sheet = 4 parts.
Thus, the total fraction shaded is:
[tex]\[
\frac{6}{4} = 1.5
\][/tex]
You shade [tex]\( \frac{6}{4} \)[/tex] or 1.5 of the two sheets of paper.
### (iv) Is the fraction proper or improper? Give reason.
To determine whether the fraction is proper or improper:
- A proper fraction has a numerator smaller than the denominator.
- Here, the numerator (6) is larger than the denominator (4).
Therefore, the fraction [tex]\( \frac{6}{4} \)[/tex] is an improper fraction because the numerator is greater than the denominator.
The fraction is improper because 6 is greater than 4.
### (v) Convert this fraction into a mixed number.
To convert the improper fraction [tex]\( \frac{6}{4} \)[/tex] into a mixed number:
- Divide the numerator by the denominator:
[tex]\[
6 \div 4 = 1 \text{ (whole number part)}
\][/tex]
- Find the remainder:
[tex]\[
6 \mod 4 = 2 \text{ (remainder)}
\][/tex]
- The mixed number will combine the whole number part with the fractional part:
[tex]\[
1 \frac{2}{4}
\][/tex]
- The fractional part can be simplified:
[tex]\[
\frac{2}{4} = \frac{1}{2}
\][/tex]
Thus, the mixed number is:
[tex]\[
1 \frac{1}{2}
\][/tex]
The improper fraction [tex]\( \frac{6}{4} \)[/tex] converts to the mixed number [tex]\( 1 \frac{1}{2} \)[/tex].
