Question Solve the proportion equation $1: 4(1/2) = x: 2(3/4)$ for the unknown value of $x$ .

Studdy Solution

STEP 1

1. The given expression represents a proportion, where $1: 4(1 / 2)$ is equivalent to $x: 2(3 / 4)$ .
2. To solve for $x$ , we can set up a ratio and solve the resulting equation.
3. The numbers involved are mixed numbers and can be converted to improper fractions for ease of calculation.

STEP 2

1. Convert mixed numbers to improper fractions.
2. Set up the proportion as an equation.
3. Solve the equation for $x$ .
4. Convert the solution back to a mixed number if necessary.

STEP 3

Convert the mixed number $4(1 / 2)$ to an improper fraction.
$4(1 / 2) = 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2}$

STEP 4

Convert the mixed number $2(3 / 4)$ to an improper fraction.
$2(3 / 4) = 2 + \frac{3}{4} = \frac{8}{4} + \frac{3}{4} = \frac{11}{4}$

STEP 5

Set up the proportion as an equation using the improper fractions.
$\frac{1}{\frac{9}{2}} = \frac{x}{\frac{11}{4}}$

STEP 6

Cross-multiply to solve for $x$ .
$1 \cdot \frac{11}{4} = x \cdot \frac{9}{2}$

STEP 7

Simplify the equation to isolate $x$ .
$\frac{11}{4} = \frac{9}{2}x$

STEP 8

Multiply both sides of the equation by the reciprocal of $\frac{9}{2}$ to solve for $x$ .
$x = \frac{11}{4} \cdot \frac{2}{9}$

STEP 9

Simplify the right side of the equation to find the value of $x$ .
$x = \frac{11 \cdot 2}{4 \cdot 9}$

STEP 10

Further simplify the fraction by multiplying the numerators and denominators.
$x = \frac{22}{36}$

STEP 11

Reduce the fraction to its simplest form.
$x = \frac{22 \div 2}{36 \div 2} = \frac{11}{18}$

STEP 12

Since the solution is already in simplest form and does not require conversion back to a mixed number, we can state the final solution.
$x = \frac{11}{18}$

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Question Solve the proportion equation $1: 4(1/2) = x: 2(3/4)$ for the unknown value of $x$ .

Studdy Solution

STEP 1

1. The given expression represents a proportion, where $1: 4(1 / 2)$ is equivalent to $x: 2(3 / 4)$ .
2. To solve for $x$ , we can set up a ratio and solve the resulting equation.
3. The numbers involved are mixed numbers and can be converted to improper fractions for ease of calculation.

STEP 2

1. Convert mixed numbers to improper fractions.
2. Set up the proportion as an equation.
3. Solve the equation for $x$ .
4. Convert the solution back to a mixed number if necessary.

STEP 3

Convert the mixed number $4(1 / 2)$ to an improper fraction.
$4(1 / 2) = 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2}$

STEP 4

Convert the mixed number $2(3 / 4)$ to an improper fraction.
$2(3 / 4) = 2 + \frac{3}{4} = \frac{8}{4} + \frac{3}{4} = \frac{11}{4}$

STEP 5

Set up the proportion as an equation using the improper fractions.
$\frac{1}{\frac{9}{2}} = \frac{x}{\frac{11}{4}}$

STEP 6

Cross-multiply to solve for $x$ .
$1 \cdot \frac{11}{4} = x \cdot \frac{9}{2}$

STEP 7

Simplify the equation to isolate $x$ .
$\frac{11}{4} = \frac{9}{2}x$

STEP 8

Multiply both sides of the equation by the reciprocal of $\frac{9}{2}$ to solve for $x$ .
$x = \frac{11}{4} \cdot \frac{2}{9}$

STEP 9

Simplify the right side of the equation to find the value of $x$ .
$x = \frac{11 \cdot 2}{4 \cdot 9}$

STEP 10

Further simplify the fraction by multiplying the numerators and denominators.
$x = \frac{22}{36}$

STEP 11

Reduce the fraction to its simplest form.
$x = \frac{22 \div 2}{36 \div 2} = \frac{11}{18}$

STEP 12

Since the solution is already in simplest form and does not require conversion back to a mixed number, we can state the final solution.
$x = \frac{11}{18}$

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Question Solve the proportion equation 1:4(1/2)=x:2(3/4)1: 4(1/2) = x: 2(3/4)1:4(1/2)=x:2(3/4) for the unknown value of xxx.

Studdy Solution

STEP 1

STEP 2

1. Convert mixed numbers to improper fractions.2. Set up the proportion as an equation.3. Solve the equation for xxx.4. Convert the solution back to a mixed number if necessary.

STEP 3

Convert the mixed number 4(1/2)4(1 / 2)4(1/2) to an improper fraction.4(1/2)=4+12=82+12=92 4(1 / 2) = 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2} 4(1/2)=4+21​=28​+21​=29​

STEP 4

Convert the mixed number 2(3/4)2(3 / 4)2(3/4) to an improper fraction.2(3/4)=2+34=84+34=114 2(3 / 4) = 2 + \frac{3}{4} = \frac{8}{4} + \frac{3}{4} = \frac{11}{4} 2(3/4)=2+43​=48​+43​=411​

STEP 5

Set up the proportion as an equation using the improper fractions.192=x114 \frac{1}{\frac{9}{2}} = \frac{x}{\frac{11}{4}} 29​1​=411​x​

STEP 6

Cross-multiply to solve for xxx.1⋅114=x⋅92 1 \cdot \frac{11}{4} = x \cdot \frac{9}{2} 1⋅411​=x⋅29​

STEP 7

Simplify the equation to isolate xxx.114=92x \frac{11}{4} = \frac{9}{2}x 411​=29​x

STEP 8

Multiply both sides of the equation by the reciprocal of 92\frac{9}{2}29​ to solve for xxx.x=114⋅29 x = \frac{11}{4} \cdot \frac{2}{9} x=411​⋅92​

STEP 9

Simplify the right side of the equation to find the value of xxx.x=11⋅24⋅9 x = \frac{11 \cdot 2}{4 \cdot 9} x=4⋅911⋅2​

STEP 10

Further simplify the fraction by multiplying the numerators and denominators.x=2236 x = \frac{22}{36} x=3622​

STEP 11

Reduce the fraction to its simplest form.x=22÷236÷2=1118 x = \frac{22 \div 2}{36 \div 2} = \frac{11}{18} x=36÷222÷2​=1811​

STEP 12

Since the solution is already in simplest form and does not require conversion back to a mixed number, we can state the final solution.x=1118 x = \frac{11}{18} x=1811​

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Question Solve the proportion equation $1: 4(1/2) = x: 2(3/4)$ for the unknown value of $x$ .

1. Convert mixed numbers to improper fractions.
2. Set up the proportion as an equation.
3. Solve the equation for $x$ .
4. Convert the solution back to a mixed number if necessary.

Convert the mixed number $4(1 / 2)$ to an improper fraction.
$4(1 / 2) = 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2}$

Convert the mixed number $2(3 / 4)$ to an improper fraction.
$2(3 / 4) = 2 + \frac{3}{4} = \frac{8}{4} + \frac{3}{4} = \frac{11}{4}$

Set up the proportion as an equation using the improper fractions.
$\frac{1}{\frac{9}{2}} = \frac{x}{\frac{11}{4}}$

Cross-multiply to solve for $x$ .
$1 \cdot \frac{11}{4} = x \cdot \frac{9}{2}$

Simplify the equation to isolate $x$ .
$\frac{11}{4} = \frac{9}{2}x$

Multiply both sides of the equation by the reciprocal of $\frac{9}{2}$ to solve for $x$ .
$x = \frac{11}{4} \cdot \frac{2}{9}$

Simplify the right side of the equation to find the value of $x$ .
$x = \frac{11 \cdot 2}{4 \cdot 9}$

Further simplify the fraction by multiplying the numerators and denominators.
$x = \frac{22}{36}$

Reduce the fraction to its simplest form.
$x = \frac{22 \div 2}{36 \div 2} = \frac{11}{18}$

Since the solution is already in simplest form and does not require conversion back to a mixed number, we can state the final solution.
$x = \frac{11}{18}$