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Answer :
We start by breaking the problem into its three parts:
1. Convert 68% to a Fraction
A percentage is simply a number out of 100. So, we can write
[tex]$$
68\% = \frac{68}{100}.
$$[/tex]
Next, we simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4:
[tex]$$
\frac{68}{100} = \frac{68 \div 4}{100 \div 4} = \frac{17}{25}.
$$[/tex]
Thus, the fraction in simplest form is
[tex]$$
\frac{17}{25}.
$$[/tex]
2. What Pattern Comes Next?
The pattern question does not have enough details provided to determine what the next element should be. Without additional information or context, we cannot define a clear pattern.
3. Find the Missing Number in [tex]\(\frac{4}{\ldots} = \frac{12}{21}\)[/tex]
Let the missing number be [tex]\( x \)[/tex]. The proportion is given by
[tex]$$
\frac{4}{x} = \frac{12}{21}.
$$[/tex]
To solve for [tex]\( x \)[/tex], cross multiply:
[tex]$$
4 \times 21 = 12 \times x.
$$[/tex]
Calculating the left-hand side:
[tex]$$
4 \times 21 = 84,
$$[/tex]
so the equation becomes
[tex]$$
84 = 12x.
$$[/tex]
Dividing both sides by 12 gives:
[tex]$$
x = \frac{84}{12} = 7.
$$[/tex]
Thus, the missing number is
[tex]$$
7.
$$[/tex]
---
Summary of Answers:
1. The fraction equivalent of 68% is [tex]\( \frac{17}{25} \)[/tex].
2. The pattern question is ambiguous due to missing details.
3. The missing number in the proportion is [tex]\( 7 \)[/tex].
1. Convert 68% to a Fraction
A percentage is simply a number out of 100. So, we can write
[tex]$$
68\% = \frac{68}{100}.
$$[/tex]
Next, we simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 4:
[tex]$$
\frac{68}{100} = \frac{68 \div 4}{100 \div 4} = \frac{17}{25}.
$$[/tex]
Thus, the fraction in simplest form is
[tex]$$
\frac{17}{25}.
$$[/tex]
2. What Pattern Comes Next?
The pattern question does not have enough details provided to determine what the next element should be. Without additional information or context, we cannot define a clear pattern.
3. Find the Missing Number in [tex]\(\frac{4}{\ldots} = \frac{12}{21}\)[/tex]
Let the missing number be [tex]\( x \)[/tex]. The proportion is given by
[tex]$$
\frac{4}{x} = \frac{12}{21}.
$$[/tex]
To solve for [tex]\( x \)[/tex], cross multiply:
[tex]$$
4 \times 21 = 12 \times x.
$$[/tex]
Calculating the left-hand side:
[tex]$$
4 \times 21 = 84,
$$[/tex]
so the equation becomes
[tex]$$
84 = 12x.
$$[/tex]
Dividing both sides by 12 gives:
[tex]$$
x = \frac{84}{12} = 7.
$$[/tex]
Thus, the missing number is
[tex]$$
7.
$$[/tex]
---
Summary of Answers:
1. The fraction equivalent of 68% is [tex]\( \frac{17}{25} \)[/tex].
2. The pattern question is ambiguous due to missing details.
3. The missing number in the proportion is [tex]\( 7 \)[/tex].
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