Question Evaluate $\frac{1}{6}b + \frac{11}{24}$ when $b = \frac{1}{4}$ , and simplify the expression.

Studdy Solution

STEP 1

Assumptions
1. We are given that $b=\frac{1}{4}$ .
2. We need to evaluate the expression $\frac{1}{6} b+\frac{11}{24}$ .
3. We will substitute the value of $b$ into the expression and simplify.

STEP 2

Substitute the value of $b$ into the expression.
$\frac{1}{6} b+\frac{11}{24} = \frac{1}{6} \left(\frac{1}{4}\right) + \frac{11}{24}$

STEP 3

To simplify the expression, we first multiply $\frac{1}{6}$ by $\frac{1}{4}$ .
$\frac{1}{6} \times \frac{1}{4} = \frac{1}{24}$

STEP 4

Now we can rewrite the expression with the calculated value.
$\frac{1}{24} + \frac{11}{24}$

STEP 5

Since both terms have the same denominator, we can add the numerators directly.
$\frac{1 + 11}{24}$

STEP 6

Add the numerators.
$\frac{12}{24}$

STEP 7

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 12.
$\frac{12 \div 12}{24 \div 12}$

STEP 8

Calculate the simplified fraction.
$\frac{1}{2}$
The evaluated expression $\frac{1}{6} b+\frac{11}{24}$ when $b=\frac{1}{4}$ is $\frac{1}{2}$ .

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Question Evaluate $\frac{1}{6}b + \frac{11}{24}$ when $b = \frac{1}{4}$ , and simplify the expression.

Studdy Solution

STEP 1

Assumptions
1. We are given that $b=\frac{1}{4}$ .
2. We need to evaluate the expression $\frac{1}{6} b+\frac{11}{24}$ .
3. We will substitute the value of $b$ into the expression and simplify.

STEP 2

Substitute the value of $b$ into the expression.
$\frac{1}{6} b+\frac{11}{24} = \frac{1}{6} \left(\frac{1}{4}\right) + \frac{11}{24}$

STEP 3

To simplify the expression, we first multiply $\frac{1}{6}$ by $\frac{1}{4}$ .
$\frac{1}{6} \times \frac{1}{4} = \frac{1}{24}$

STEP 4

Now we can rewrite the expression with the calculated value.
$\frac{1}{24} + \frac{11}{24}$

STEP 5

Since both terms have the same denominator, we can add the numerators directly.
$\frac{1 + 11}{24}$

STEP 6

Add the numerators.
$\frac{12}{24}$

STEP 7

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 12.
$\frac{12 \div 12}{24 \div 12}$

STEP 8

Calculate the simplified fraction.
$\frac{1}{2}$
The evaluated expression $\frac{1}{6} b+\frac{11}{24}$ when $b=\frac{1}{4}$ is $\frac{1}{2}$ .

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Question Evaluate 16b+1124\frac{1}{6}b + \frac{11}{24}61​b+2411​ when b=14b = \frac{1}{4}b=41​, and simplify the expression.

Studdy Solution

STEP 1

Assumptions1. We are given that b=14b=\frac{1}{4}b=41​.2. We need to evaluate the expression 16b+1124\frac{1}{6} b+\frac{11}{24}61​b+2411​.3. We will substitute the value of bbb into the expression and simplify.

STEP 2

Substitute the value of bbb into the expression.16b+1124=16(14)+1124\frac{1}{6} b+\frac{11}{24} = \frac{1}{6} \left(\frac{1}{4}\right) + \frac{11}{24}61​b+2411​=61​(41​)+2411​

STEP 3

To simplify the expression, we first multiply 16\frac{1}{6}61​ by 14\frac{1}{4}41​.16×14=124\frac{1}{6} \times \frac{1}{4} = \frac{1}{24}61​×41​=241​

STEP 4

Now we can rewrite the expression with the calculated value.124+1124\frac{1}{24} + \frac{11}{24}241​+2411​

STEP 5

Since both terms have the same denominator, we can add the numerators directly.1+1124\frac{1 + 11}{24}241+11​

STEP 6

Add the numerators.1224\frac{12}{24}2412​

STEP 7

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 12.12÷1224÷12\frac{12 \div 12}{24 \div 12}24÷1212÷12​

STEP 8

Calculate the simplified fraction.12\frac{1}{2}21​The evaluated expression 16b+1124\frac{1}{6} b+\frac{11}{24}61​b+2411​ when b=14b=\frac{1}{4}b=41​ is 12\frac{1}{2}21​.

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Question Evaluate $\frac{1}{6}b + \frac{11}{24}$ when $b = \frac{1}{4}$ , and simplify the expression.

Assumptions
1. We are given that $b=\frac{1}{4}$ .
2. We need to evaluate the expression $\frac{1}{6} b+\frac{11}{24}$ .
3. We will substitute the value of $b$ into the expression and simplify.

Substitute the value of $b$ into the expression.
$\frac{1}{6} b+\frac{11}{24} = \frac{1}{6} \left(\frac{1}{4}\right) + \frac{11}{24}$

To simplify the expression, we first multiply $\frac{1}{6}$ by $\frac{1}{4}$ .
$\frac{1}{6} \times \frac{1}{4} = \frac{1}{24}$

Now we can rewrite the expression with the calculated value.
$\frac{1}{24} + \frac{11}{24}$

Since both terms have the same denominator, we can add the numerators directly.
$\frac{1 + 11}{24}$

Add the numerators.
$\frac{12}{24}$

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 12.
$\frac{12 \div 12}{24 \div 12}$

Calculate the simplified fraction.
$\frac{1}{2}$
The evaluated expression $\frac{1}{6} b+\frac{11}{24}$ when $b=\frac{1}{4}$ is $\frac{1}{2}$ .