Solved on Feb 13, 2024

What fraction of students in a class of 258 passed a term test if 16 students failed? Express the answer in lowest terms.
$\frac{242}{258}$

STEP 1

Assumptions
1. The total number of students in the class is 258.
2. The number of students who failed the term test is 16.
3. We want to find the fraction of students who passed the test.
4. The fraction should be expressed in its lowest terms.

STEP 2

First, we need to calculate the number of students who passed the test. We can do this by subtracting the number of students who failed from the total number of students.
$\text{Number of students who passed} = \text{Total number of students} - \text{Number of students who failed}$

STEP 3

Now, plug in the given values for the total number of students and the number of students who failed to calculate the number of students who passed.
$\text{Number of students who passed} = 258 - 16$

STEP 4

Calculate the number of students who passed the test.
$\text{Number of students who passed} = 258 - 16 = 242$

STEP 5

To find the fraction of students who passed the test, we need to divide the number of students who passed by the total number of students.
$\text{Fraction of students who passed} = \frac{\text{Number of students who passed}}{\text{Total number of students}}$

STEP 6

Plug in the values for the number of students who passed and the total number of students to calculate the fraction.
$\text{Fraction of students who passed} = \frac{242}{258}$

STEP 7

To express the fraction in its lowest terms, we need to find the greatest common divisor (GCD) of the numerator and the denominator.

STEP 8

Find the GCD of 242 and 258.

STEP 9

Since both numbers are even, we know that 2 is a common divisor. We can divide both the numerator and the denominator by 2 to simplify the fraction.
$\frac{242}{258} = \frac{242 \div 2}{258 \div 2} = \frac{121}{129}$

STEP 10

Check if 121 and 129 have any common divisors other than 1. Since 121 is a prime number, the only divisors it has are 1 and itself. Therefore, 121 and 129 do not have any common divisors other than 1.

STEP 11

The fraction $\frac{121}{129}$ is already in its lowest terms, as there are no common divisors greater than 1.
The fraction of students who passed the test is $\frac{121}{129}$ , which corresponds to option (A).

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What fraction of students in a class of 258 passed a term test if 16 students failed? Express the answer in lowest terms.
$\frac{242}{258}$

STEP 1

Assumptions
1. The total number of students in the class is 258.
2. The number of students who failed the term test is 16.
3. We want to find the fraction of students who passed the test.
4. The fraction should be expressed in its lowest terms.

STEP 2

First, we need to calculate the number of students who passed the test. We can do this by subtracting the number of students who failed from the total number of students.
$\text{Number of students who passed} = \text{Total number of students} - \text{Number of students who failed}$

STEP 3

Now, plug in the given values for the total number of students and the number of students who failed to calculate the number of students who passed.
$\text{Number of students who passed} = 258 - 16$

STEP 4

Calculate the number of students who passed the test.
$\text{Number of students who passed} = 258 - 16 = 242$

STEP 5

To find the fraction of students who passed the test, we need to divide the number of students who passed by the total number of students.
$\text{Fraction of students who passed} = \frac{\text{Number of students who passed}}{\text{Total number of students}}$

STEP 6

Plug in the values for the number of students who passed and the total number of students to calculate the fraction.
$\text{Fraction of students who passed} = \frac{242}{258}$

STEP 7

To express the fraction in its lowest terms, we need to find the greatest common divisor (GCD) of the numerator and the denominator.

STEP 8

Find the GCD of 242 and 258.

STEP 9

Since both numbers are even, we know that 2 is a common divisor. We can divide both the numerator and the denominator by 2 to simplify the fraction.
$\frac{242}{258} = \frac{242 \div 2}{258 \div 2} = \frac{121}{129}$

STEP 10

Check if 121 and 129 have any common divisors other than 1. Since 121 is a prime number, the only divisors it has are 1 and itself. Therefore, 121 and 129 do not have any common divisors other than 1.

STEP 11

The fraction $\frac{121}{129}$ is already in its lowest terms, as there are no common divisors greater than 1.
The fraction of students who passed the test is $\frac{121}{129}$ , which corresponds to option (A).

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What fraction of students in a class of 258 passed a term test if 16 students failed? Express the answer in lowest terms.242258\frac{242}{258}258242​

STEP 1

Assumptions1. The total number of students in the class is 258.2. The number of students who failed the term test is 16.3. We want to find the fraction of students who passed the test.4. The fraction should be expressed in its lowest terms.

STEP 2

STEP 3

Now, plug in the given values for the total number of students and the number of students who failed to calculate the number of students who passed.Number of students who passed=258−16\text{Number of students who passed} = 258 - 16Number of students who passed=258−16

STEP 4

Calculate the number of students who passed the test.Number of students who passed=258−16=242\text{Number of students who passed} = 258 - 16 = 242Number of students who passed=258−16=242

STEP 5

STEP 6

Plug in the values for the number of students who passed and the total number of students to calculate the fraction.Fraction of students who passed=242258\text{Fraction of students who passed} = \frac{242}{258}Fraction of students who passed=258242​

STEP 7

To express the fraction in its lowest terms, we need to find the greatest common divisor (GCD) of the numerator and the denominator.

STEP 8

Find the GCD of 242 and 258.

STEP 9

Since both numbers are even, we know that 2 is a common divisor. We can divide both the numerator and the denominator by 2 to simplify the fraction.242258=242÷2258÷2=121129\frac{242}{258} = \frac{242 \div 2}{258 \div 2} = \frac{121}{129}258242​=258÷2242÷2​=129121​

STEP 10

Check if 121 and 129 have any common divisors other than 1. Since 121 is a prime number, the only divisors it has are 1 and itself. Therefore, 121 and 129 do not have any common divisors other than 1.

STEP 11

The fraction 121129\frac{121}{129}129121​ is already in its lowest terms, as there are no common divisors greater than 1.The fraction of students who passed the test is 121129\frac{121}{129}129121​, which corresponds to option (A).

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What fraction of students in a class of 258 passed a term test if 16 students failed? Express the answer in lowest terms.
$\frac{242}{258}$

Assumptions
1. The total number of students in the class is 258.
2. The number of students who failed the term test is 16.
3. We want to find the fraction of students who passed the test.
4. The fraction should be expressed in its lowest terms.

Now, plug in the given values for the total number of students and the number of students who failed to calculate the number of students who passed.
$\text{Number of students who passed} = 258 - 16$

Calculate the number of students who passed the test.
$\text{Number of students who passed} = 258 - 16 = 242$

Plug in the values for the number of students who passed and the total number of students to calculate the fraction.
$\text{Fraction of students who passed} = \frac{242}{258}$

Since both numbers are even, we know that 2 is a common divisor. We can divide both the numerator and the denominator by 2 to simplify the fraction.
$\frac{242}{258} = \frac{242 \div 2}{258 \div 2} = \frac{121}{129}$

The fraction $\frac{121}{129}$ is already in its lowest terms, as there are no common divisors greater than 1.
The fraction of students who passed the test is $\frac{121}{129}$ , which corresponds to option (A).