Math / Numbers & Operations

QuestionSimplify: $7.5 \cdot\left(\frac{1}{3}\right)^{2}$ $\square$

Studdy Solution

STEP 1

1. We are given the expression $7.5 \cdot \left(\frac{1}{3}\right)^2$ .
2. We need to simplify this expression by performing arithmetic operations.

STEP 2

1. Simplify the exponent.
2. Multiply the simplified exponent by 7.5.

STEP 3

Calculate the square of $\frac{1}{3}$ .
$\left(\frac{1}{3}\right)^2 = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}$

STEP 4

Multiply $7.5$ by the result from Step 1.
$7.5 \cdot \frac{1}{9} = \frac{7.5}{9}$

STEP 5

Simplify $\frac{7.5}{9}$ .
Convert $7.5$ to a fraction:
$7.5 = \frac{75}{10}$
Now simplify $\frac{75}{90}$ :
$\frac{75}{90} = \frac{5}{6}$
The simplified expression is:
$\boxed{\frac{5}{6}}$

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QuestionSimplify: $7.5 \cdot\left(\frac{1}{3}\right)^{2}$ $\square$

Studdy Solution

STEP 1

1. We are given the expression $7.5 \cdot \left(\frac{1}{3}\right)^2$ .
2. We need to simplify this expression by performing arithmetic operations.

STEP 2

1. Simplify the exponent.
2. Multiply the simplified exponent by 7.5.

STEP 3

Calculate the square of $\frac{1}{3}$ .
$\left(\frac{1}{3}\right)^2 = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}$

STEP 4

Multiply $7.5$ by the result from Step 1.
$7.5 \cdot \frac{1}{9} = \frac{7.5}{9}$

STEP 5

Simplify $\frac{7.5}{9}$ .
Convert $7.5$ to a fraction:
$7.5 = \frac{75}{10}$
Now simplify $\frac{75}{90}$ :
$\frac{75}{90} = \frac{5}{6}$
The simplified expression is:
$\boxed{\frac{5}{6}}$

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QuestionSimplify: 7.5⋅(13)27.5 \cdot\left(\frac{1}{3}\right)^{2}7.5⋅(31​)2 □\square□

Studdy Solution

STEP 1

1. We are given the expression 7.5⋅(13)2 7.5 \cdot \left(\frac{1}{3}\right)^2 7.5⋅(31​)2.2. We need to simplify this expression by performing arithmetic operations.

STEP 2

1. Simplify the exponent.2. Multiply the simplified exponent by 7.5.

STEP 3

Calculate the square of 13\frac{1}{3}31​.(13)2=13×13=19\left(\frac{1}{3}\right)^2 = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}(31​)2=31​×31​=91​

STEP 4

Multiply 7.5 7.5 7.5 by the result from Step 1.7.5⋅19=7.597.5 \cdot \frac{1}{9} = \frac{7.5}{9}7.5⋅91​=97.5​

STEP 5

Simplify 7.59\frac{7.5}{9}97.5​.Convert 7.5 7.5 7.5 to a fraction:7.5=75107.5 = \frac{75}{10}7.5=1075​Now simplify 7590\frac{75}{90}9075​:7590=56\frac{75}{90} = \frac{5}{6}9075​=65​ The simplified expression is:56\boxed{\frac{5}{6}}65​​

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QuestionSimplify: $7.5 \cdot\left(\frac{1}{3}\right)^{2}$ $\square$

1. We are given the expression $7.5 \cdot \left(\frac{1}{3}\right)^2$ .
2. We need to simplify this expression by performing arithmetic operations.

1. Simplify the exponent.
2. Multiply the simplified exponent by 7.5.

Calculate the square of $\frac{1}{3}$ .
$\left(\frac{1}{3}\right)^2 = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}$

Multiply $7.5$ by the result from Step 1.
$7.5 \cdot \frac{1}{9} = \frac{7.5}{9}$

Simplify $\frac{7.5}{9}$ .
Convert $7.5$ to a fraction:
$7.5 = \frac{75}{10}$
Now simplify $\frac{75}{90}$ :
$\frac{75}{90} = \frac{5}{6}$
The simplified expression is:
$\boxed{\frac{5}{6}}$