QuestionCalculate $\frac{5}{4}-\frac{5}{12}$ and express the answer as a mixed number.

Studdy Solution

STEP 1

Assumptions1. We are adding two fractions $\frac{5}{4}$ and $-\frac{5}{12}$ . We are not using a calculator3. The solution should be in the form of a mixed number4. Negative numbers should be written with no space between the negative sign and the number

STEP 2

First, we need to find a common denominator for the two fractions. The common denominator of4 and12 is12.

STEP 3

Convert the fractions to have the common denominator.To convert $\frac{5}{}$ to a fraction with denominator12, we multiply both the numerator and the denominator by3.
$\frac{5}{} = \frac{5 \times3}{ \times3} = \frac{15}{12}$

STEP 4

Now, we can subtract the two fractions since they have the same denominator.
$\frac{15}{12} - \frac{}{12}$

STEP 5

Subtract the numerators and keep the denominator.
$\frac{15 -5}{12} = \frac{10}{12}$

STEP 6

implify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is2.
$\frac{10}{12} = \frac{10 \div2}{12 \div2} = \frac{5}{6}$

STEP 7

Convert the improper fraction to a mixed number. Since the numerator is less than the denominator, the fraction is already in its simplest form and there is no whole number part. So, the mixed number is $\frac{5}{6}$ .
The result of adding $\frac{5}{4}$ and $-\frac{5}{12}$ is $\frac{5}{6}$ .

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QuestionCalculate $\frac{5}{4}-\frac{5}{12}$ and express the answer as a mixed number.

Studdy Solution

STEP 1

Assumptions1. We are adding two fractions $\frac{5}{4}$ and $-\frac{5}{12}$ . We are not using a calculator3. The solution should be in the form of a mixed number4. Negative numbers should be written with no space between the negative sign and the number

STEP 2

First, we need to find a common denominator for the two fractions. The common denominator of4 and12 is12.

STEP 3

Convert the fractions to have the common denominator.To convert $\frac{5}{}$ to a fraction with denominator12, we multiply both the numerator and the denominator by3.
$\frac{5}{} = \frac{5 \times3}{ \times3} = \frac{15}{12}$

STEP 4

Now, we can subtract the two fractions since they have the same denominator.
$\frac{15}{12} - \frac{}{12}$

STEP 5

Subtract the numerators and keep the denominator.
$\frac{15 -5}{12} = \frac{10}{12}$

STEP 6

implify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is2.
$\frac{10}{12} = \frac{10 \div2}{12 \div2} = \frac{5}{6}$

STEP 7

Convert the improper fraction to a mixed number. Since the numerator is less than the denominator, the fraction is already in its simplest form and there is no whole number part. So, the mixed number is $\frac{5}{6}$ .
The result of adding $\frac{5}{4}$ and $-\frac{5}{12}$ is $\frac{5}{6}$ .

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QuestionCalculate 54−512\frac{5}{4}-\frac{5}{12}45​−125​ and express the answer as a mixed number.

Studdy Solution

STEP 1

Assumptions1. We are adding two fractions 54\frac{5}{4}45​ and −512-\frac{5}{12}−125​ . We are not using a calculator3. The solution should be in the form of a mixed number4. Negative numbers should be written with no space between the negative sign and the number

STEP 2

First, we need to find a common denominator for the two fractions. The common denominator of4 and12 is12.

STEP 3

Convert the fractions to have the common denominator.To convert 5\frac{5}{}5​ to a fraction with denominator12, we multiply both the numerator and the denominator by3.5=5×3×3=1512\frac{5}{} = \frac{5 \times3}{ \times3} = \frac{15}{12}5​=×35×3​=1215​

STEP 4

Now, we can subtract the two fractions since they have the same denominator.1512−12\frac{15}{12} - \frac{}{12}1215​−12​

STEP 5

Subtract the numerators and keep the denominator.15−512=1012\frac{15 -5}{12} = \frac{10}{12}1215−5​=1210​

STEP 6

implify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is2.1012=10÷212÷2=56\frac{10}{12} = \frac{10 \div2}{12 \div2} = \frac{5}{6}1210​=12÷210÷2​=65​

STEP 7

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QuestionCalculate $\frac{5}{4}-\frac{5}{12}$ and express the answer as a mixed number.

Assumptions1. We are adding two fractions $\frac{5}{4}$ and $-\frac{5}{12}$ . We are not using a calculator3. The solution should be in the form of a mixed number4. Negative numbers should be written with no space between the negative sign and the number

Convert the fractions to have the common denominator.To convert $\frac{5}{}$ to a fraction with denominator12, we multiply both the numerator and the denominator by3.
$\frac{5}{} = \frac{5 \times3}{ \times3} = \frac{15}{12}$

Now, we can subtract the two fractions since they have the same denominator.
$\frac{15}{12} - \frac{}{12}$

Subtract the numerators and keep the denominator.
$\frac{15 -5}{12} = \frac{10}{12}$

implify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is2.
$\frac{10}{12} = \frac{10 \div2}{12 \div2} = \frac{5}{6}$