Math / Algebra

Question $1+\left(\frac{1}{4}+\frac{1}{2}\right)^{2}$

Studdy Solution

STEP 1

1. We are given an expression involving addition and exponentiation.
2. The expression inside the parentheses should be simplified first.
3. The result should be a single number.

STEP 2

1. Simplify the expression inside the parentheses: $\frac{1}{4} + \frac{1}{2}$ .
2. Square the result from Step 1.
3. Add 1 to the squared result.

STEP 3

Simplify the expression inside the parentheses:
$\frac{1}{4} + \frac{1}{2}$
To add these fractions, find a common denominator. The common denominator for 4 and 2 is 4.
Convert $\frac{1}{2}$ to $\frac{2}{4}$ :
$\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$

STEP 4

Square the result from Step 1:
$\left(\frac{3}{4}\right)^2 = \frac{3}{4} \times \frac{3}{4} = \frac{9}{16}$

STEP 5

Add 1 to the squared result:
Convert 1 to a fraction with a denominator of 16:
$1 = \frac{16}{16}$
Now add:
$\frac{16}{16} + \frac{9}{16} = \frac{25}{16}$
Convert $\frac{25}{16}$ to a mixed number:
$\frac{25}{16} = 1 \frac{9}{16}$
The equivalent number for the expression is:
$\boxed{1 \frac{9}{16}}$

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Question $1+\left(\frac{1}{4}+\frac{1}{2}\right)^{2}$

Studdy Solution

STEP 1

1. We are given an expression involving addition and exponentiation.
2. The expression inside the parentheses should be simplified first.
3. The result should be a single number.

STEP 2

1. Simplify the expression inside the parentheses: $\frac{1}{4} + \frac{1}{2}$ .
2. Square the result from Step 1.
3. Add 1 to the squared result.

STEP 3

Simplify the expression inside the parentheses:
$\frac{1}{4} + \frac{1}{2}$
To add these fractions, find a common denominator. The common denominator for 4 and 2 is 4.
Convert $\frac{1}{2}$ to $\frac{2}{4}$ :
$\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$

STEP 4

Square the result from Step 1:
$\left(\frac{3}{4}\right)^2 = \frac{3}{4} \times \frac{3}{4} = \frac{9}{16}$

STEP 5

Add 1 to the squared result:
Convert 1 to a fraction with a denominator of 16:
$1 = \frac{16}{16}$
Now add:
$\frac{16}{16} + \frac{9}{16} = \frac{25}{16}$
Convert $\frac{25}{16}$ to a mixed number:
$\frac{25}{16} = 1 \frac{9}{16}$
The equivalent number for the expression is:
$\boxed{1 \frac{9}{16}}$

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Question1+(14+12)21+\left(\frac{1}{4}+\frac{1}{2}\right)^{2}1+(41​+21​)2

Studdy Solution

STEP 1

1. We are given an expression involving addition and exponentiation.2. The expression inside the parentheses should be simplified first.3. The result should be a single number.

STEP 2

1. Simplify the expression inside the parentheses: 14+12\frac{1}{4} + \frac{1}{2}41​+21​.2. Square the result from Step 1.3. Add 1 to the squared result.

STEP 3

Simplify the expression inside the parentheses:14+12 \frac{1}{4} + \frac{1}{2} 41​+21​To add these fractions, find a common denominator. The common denominator for 4 and 2 is 4.Convert 12\frac{1}{2}21​ to 24\frac{2}{4}42​:14+24=34 \frac{1}{4} + \frac{2}{4} = \frac{3}{4} 41​+42​=43​

STEP 4

Square the result from Step 1:(34)2=34×34=916 \left(\frac{3}{4}\right)^2 = \frac{3}{4} \times \frac{3}{4} = \frac{9}{16} (43​)2=43​×43​=169​

STEP 5

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Question $1+\left(\frac{1}{4}+\frac{1}{2}\right)^{2}$

1. We are given an expression involving addition and exponentiation.
2. The expression inside the parentheses should be simplified first.
3. The result should be a single number.

1. Simplify the expression inside the parentheses: $\frac{1}{4} + \frac{1}{2}$ .
2. Square the result from Step 1.
3. Add 1 to the squared result.

Simplify the expression inside the parentheses:
$\frac{1}{4} + \frac{1}{2}$
To add these fractions, find a common denominator. The common denominator for 4 and 2 is 4.
Convert $\frac{1}{2}$ to $\frac{2}{4}$ :
$\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$

Square the result from Step 1:
$\left(\frac{3}{4}\right)^2 = \frac{3}{4} \times \frac{3}{4} = \frac{9}{16}$