Solved on Feb 12, 2024

Find the expression equivalent to $5.8 \div 1.15$ .

STEP 1

Assumptions
1. We are given the expression $5.8 \div 1.15$ .
2. We need to find which of the given options is equivalent to the given expression.
3. The options are $0.58 \div 115$ , $5.8 \div 115$ , and $58 \div 115$ .

STEP 2

To determine which expression is equivalent to $5.8 \div 1.15$ , we need to understand how division by a number is related to division by a power of 10 of that number.

STEP 3

Dividing by a number is the same as multiplying by its reciprocal. The reciprocal of a number $a$ is $\frac{1}{a}$ .

STEP 4

Let's write the reciprocal of $1.15$ .
$Reciprocal\, of\, 1.15 = \frac{1}{1.15}$

STEP 5

To make the division easier, we can multiply the numerator and denominator by 100 to remove the decimal.
$\frac{1}{1.15} \times \frac{100}{100} = \frac{100}{115}$

STEP 6

Now, let's multiply $5.8$ by the reciprocal of $1.15$ .
$5.8 \times \frac{100}{115}$

STEP 7

To simplify the multiplication, we can also multiply $5.8$ by 10 to remove the decimal, and then divide by 10 to compensate.
$\left(5.8 \times 10\right) \times \frac{100}{115} \div 10$

STEP 8

Now, calculate the multiplication before division.
$\left(58 \times \frac{100}{115}\right) \div 10$

STEP 9

We can simplify the expression by canceling out the common factor of 10.
$\frac{58 \times 10}{115} \div 10 = \frac{58}{115}$

STEP 10

Now, we have the simplified expression $\frac{58}{115}$ , which is equivalent to $5.8 \div 1.15$ .

STEP 11

Comparing the simplified expression with the given options, we can see that $\frac{58}{115}$ matches one of the options.
The expression equivalent to $5.8 \div 1.15$ is $58 \div 115$ .

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Find the expression equivalent to $5.8 \div 1.15$ .

STEP 1

Assumptions
1. We are given the expression $5.8 \div 1.15$ .
2. We need to find which of the given options is equivalent to the given expression.
3. The options are $0.58 \div 115$ , $5.8 \div 115$ , and $58 \div 115$ .

STEP 2

To determine which expression is equivalent to $5.8 \div 1.15$ , we need to understand how division by a number is related to division by a power of 10 of that number.

STEP 3

Dividing by a number is the same as multiplying by its reciprocal. The reciprocal of a number $a$ is $\frac{1}{a}$ .

STEP 4

Let's write the reciprocal of $1.15$ .
$Reciprocal\, of\, 1.15 = \frac{1}{1.15}$

STEP 5

To make the division easier, we can multiply the numerator and denominator by 100 to remove the decimal.
$\frac{1}{1.15} \times \frac{100}{100} = \frac{100}{115}$

STEP 6

Now, let's multiply $5.8$ by the reciprocal of $1.15$ .
$5.8 \times \frac{100}{115}$

STEP 7

To simplify the multiplication, we can also multiply $5.8$ by 10 to remove the decimal, and then divide by 10 to compensate.
$\left(5.8 \times 10\right) \times \frac{100}{115} \div 10$

STEP 8

Now, calculate the multiplication before division.
$\left(58 \times \frac{100}{115}\right) \div 10$

STEP 9

We can simplify the expression by canceling out the common factor of 10.
$\frac{58 \times 10}{115} \div 10 = \frac{58}{115}$

STEP 10

Now, we have the simplified expression $\frac{58}{115}$ , which is equivalent to $5.8 \div 1.15$ .

STEP 11

Comparing the simplified expression with the given options, we can see that $\frac{58}{115}$ matches one of the options.
The expression equivalent to $5.8 \div 1.15$ is $58 \div 115$ .

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Find the expression equivalent to 5.8÷1.155.8 \div 1.155.8÷1.15.

STEP 1

Assumptions1. We are given the expression 5.8÷1.155.8 \div 1.155.8÷1.15.2. We need to find which of the given options is equivalent to the given expression.3. The options are 0.58÷1150.58 \div 1150.58÷115, 5.8÷1155.8 \div 1155.8÷115, and 58÷11558 \div 11558÷115.

STEP 2

To determine which expression is equivalent to 5.8÷1.155.8 \div 1.155.8÷1.15, we need to understand how division by a number is related to division by a power of 10 of that number.

STEP 3

Dividing by a number is the same as multiplying by its reciprocal. The reciprocal of a number aaa is 1a\frac{1}{a}a1​.

STEP 4

Let's write the reciprocal of 1.151.151.15.Reciprocal of 1.15=11.15Reciprocal\, of\, 1.15 = \frac{1}{1.15}Reciprocalof1.15=1.151​

STEP 5

To make the division easier, we can multiply the numerator and denominator by 100 to remove the decimal.11.15×100100=100115\frac{1}{1.15} \times \frac{100}{100} = \frac{100}{115}1.151​×100100​=115100​

STEP 6

Now, let's multiply 5.85.85.8 by the reciprocal of 1.151.151.15.5.8×1001155.8 \times \frac{100}{115}5.8×115100​

STEP 7

To simplify the multiplication, we can also multiply 5.85.85.8 by 10 to remove the decimal, and then divide by 10 to compensate.(5.8×10)×100115÷10\left(5.8 \times 10\right) \times \frac{100}{115} \div 10(5.8×10)×115100​÷10

STEP 8

Now, calculate the multiplication before division.(58×100115)÷10\left(58 \times \frac{100}{115}\right) \div 10(58×115100​)÷10

STEP 9

We can simplify the expression by canceling out the common factor of 10.58×10115÷10=58115\frac{58 \times 10}{115} \div 10 = \frac{58}{115}11558×10​÷10=11558​

STEP 10

Now, we have the simplified expression 58115\frac{58}{115}11558​, which is equivalent to 5.8÷1.155.8 \div 1.155.8÷1.15.

STEP 11

Comparing the simplified expression with the given options, we can see that 58115\frac{58}{115}11558​ matches one of the options.The expression equivalent to 5.8÷1.155.8 \div 1.155.8÷1.15 is 58÷11558 \div 11558÷115.

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

Find the expression equivalent to $5.8 \div 1.15$ .

Assumptions
1. We are given the expression $5.8 \div 1.15$ .
2. We need to find which of the given options is equivalent to the given expression.
3. The options are $0.58 \div 115$ , $5.8 \div 115$ , and $58 \div 115$ .

To determine which expression is equivalent to $5.8 \div 1.15$ , we need to understand how division by a number is related to division by a power of 10 of that number.

Dividing by a number is the same as multiplying by its reciprocal. The reciprocal of a number $a$ is $\frac{1}{a}$ .

Let's write the reciprocal of $1.15$ .
$Reciprocal\, of\, 1.15 = \frac{1}{1.15}$

To make the division easier, we can multiply the numerator and denominator by 100 to remove the decimal.
$\frac{1}{1.15} \times \frac{100}{100} = \frac{100}{115}$

Now, let's multiply $5.8$ by the reciprocal of $1.15$ .
$5.8 \times \frac{100}{115}$

To simplify the multiplication, we can also multiply $5.8$ by 10 to remove the decimal, and then divide by 10 to compensate.
$\left(5.8 \times 10\right) \times \frac{100}{115} \div 10$

Now, calculate the multiplication before division.
$\left(58 \times \frac{100}{115}\right) \div 10$

We can simplify the expression by canceling out the common factor of 10.
$\frac{58 \times 10}{115} \div 10 = \frac{58}{115}$

Now, we have the simplified expression $\frac{58}{115}$ , which is equivalent to $5.8 \div 1.15$ .

Comparing the simplified expression with the given options, we can see that $\frac{58}{115}$ matches one of the options.
The expression equivalent to $5.8 \div 1.15$ is $58 \div 115$ .