Sure, let's break down the solution step-by-step:
12. Arrange in ascending order:
We need to compare the following numbers:
- [tex]\(\frac{31}{40}\)[/tex]
- 76%
- 0.7
- Convert each number to a decimal form for comparison:
- [tex]\(\frac{31}{40} = 0.775\)[/tex]
- 76% = [tex]\(0.76\)[/tex]
- 0.7 (already in decimal form)
Now, arrange these numbers in ascending order:
[tex]$
0.7, 0.76, 0.775
$[/tex]
1.3 Write 400 m out of 5 km as a percentage:
- Convert both measurements to the same unit.
5 km = 5000 m
- Find the fraction:
[tex]$
\frac{400 \text{ m}}{5000 \text{ m}}
$[/tex]
- Convert this fraction to a percentage:
[tex]$
\left( \frac{400}{5000} \right) \times 100 = 8.0\%
$[/tex]
1.4 Keenan got [tex]\(\frac{13}{25}\)[/tex] for his Mathematics test.
1.4.1 Write down two equivalent fractions for this mark:
We can find equivalent fractions by multiplying the numerator and the denominator by the same number.
- Multiply by 2:
[tex]$
\frac{13}{25} \times \frac{2}{2} = \frac{26}{50}
$[/tex]
- Multiply by 4:
[tex]$
\frac{13}{25} \times \frac{4}{4} = \frac{52}{100}
$[/tex]
So, the two equivalent fractions are:
[tex]$
\frac{26}{50} \text{ and } \frac{52}{100}
$[/tex]
1.4.2 Write this fraction as a decimal fraction:
- Divide the numerator by the denominator:
[tex]$
\frac{13}{25} = 0.52
$[/tex]
1.4.3 If the pass percentage for a Mathematics class test is 40%, did Keenan pass this test and what was his percentage?
- Convert [tex]\(\frac{13}{25}\)[/tex] to a percentage:
[tex]$
0.52 \times 100 = 52\%
$[/tex]
- Compare his percentage to the pass mark:
[tex]$
52\% > 40\%
$[/tex]
Thus, Keenan did pass the test with a percentage of:
[tex]$
52\%
$[/tex]
