QuestionSolve: $7 \frac{1}{2} \div (4 \frac{1}{2} - 5 \frac{1}{8}) = \square$ with options: $-4 \frac{11}{16}$ , 12, $-12$ , $4 \frac{11}{16}$ .

Studdy Solution

STEP 1

Assumptions1. The operation order follows the BIDMAS/BODMAS rule (Brackets, Indices/Orders, Division and Multiplication (from left to right), Addition and Subtraction (from left to right)). . The fractions are proper fractions.

STEP 2

First, we need to convert the mixed numbers into improper fractions. The formula for converting a mixed number into an improper fraction is $\text{Improper Fraction} = \text{(Whole number)} \times \text{(Denominator)} + \text{(umerator)}$

STEP 3

Convert the mixed number $7 \frac{1}{2}$ into an improper fraction.
$\text{Improper Fraction} =7 \times2 +1 =15/2$

STEP 4

Convert the mixed number $4 \frac{1}{2}$ into an improper fraction.
$\text{Improper Fraction} =4 \times2 +1 =9/2$

STEP 5

Convert the mixed number $5 \frac{1}{8}$ into an improper fraction.
$\text{Improper Fraction} =5 \times8 +1 =41/8$

STEP 6

Now, we substitute these improper fractions back into the original equation.
$15/2 \div (9/2 -41/8)$

STEP 7

Next, we simplify the expression in the brackets. To subtract fractions, they must have the same denominator. We can convert $9/2$ to $36/$ to match the denominator of $41/$ .
$15/2 \div (36/ -41/)$

STEP 8

Now, we subtract the fractions in the brackets.
$15/2 \div (-5/8)$

STEP 9

We can simplify the division of fractions by multiplying the first fraction by the reciprocal of the second fraction.
$15/2 \times -8/5$

STEP 10

Multiply the fractions.
$\text{Result} = -24$ So, $7 \frac{}{2} \div\left(4 \frac{}{2}-5 \frac{}{8}\right) = -24$ .

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QuestionSolve: $7 \frac{1}{2} \div (4 \frac{1}{2} - 5 \frac{1}{8}) = \square$ with options: $-4 \frac{11}{16}$ , 12, $-12$ , $4 \frac{11}{16}$ .

Studdy Solution

STEP 1

Assumptions1. The operation order follows the BIDMAS/BODMAS rule (Brackets, Indices/Orders, Division and Multiplication (from left to right), Addition and Subtraction (from left to right)). . The fractions are proper fractions.

STEP 2

First, we need to convert the mixed numbers into improper fractions. The formula for converting a mixed number into an improper fraction is $\text{Improper Fraction} = \text{(Whole number)} \times \text{(Denominator)} + \text{(umerator)}$

STEP 3

Convert the mixed number $7 \frac{1}{2}$ into an improper fraction.
$\text{Improper Fraction} =7 \times2 +1 =15/2$

STEP 4

Convert the mixed number $4 \frac{1}{2}$ into an improper fraction.
$\text{Improper Fraction} =4 \times2 +1 =9/2$

STEP 5

Convert the mixed number $5 \frac{1}{8}$ into an improper fraction.
$\text{Improper Fraction} =5 \times8 +1 =41/8$

STEP 6

Now, we substitute these improper fractions back into the original equation.
$15/2 \div (9/2 -41/8)$

STEP 7

Next, we simplify the expression in the brackets. To subtract fractions, they must have the same denominator. We can convert $9/2$ to $36/$ to match the denominator of $41/$ .
$15/2 \div (36/ -41/)$

STEP 8

Now, we subtract the fractions in the brackets.
$15/2 \div (-5/8)$

STEP 9

We can simplify the division of fractions by multiplying the first fraction by the reciprocal of the second fraction.
$15/2 \times -8/5$

STEP 10

Multiply the fractions.
$\text{Result} = -24$ So, $7 \frac{}{2} \div\left(4 \frac{}{2}-5 \frac{}{8}\right) = -24$ .

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QuestionSolve: 712÷(412−518)=□7 \frac{1}{2} \div (4 \frac{1}{2} - 5 \frac{1}{8}) = \square721​÷(421​−581​)=□ with options: −41116-4 \frac{11}{16}−41611​, 12, −12-12−12, 411164 \frac{11}{16}41611​.

Studdy Solution

STEP 1

Assumptions1. The operation order follows the BIDMAS/BODMAS rule (Brackets, Indices/Orders, Division and Multiplication (from left to right), Addition and Subtraction (from left to right)). . The fractions are proper fractions.

STEP 2

STEP 3

Convert the mixed number 7127 \frac{1}{2}721​ into an improper fraction.Improper Fraction=7×2+1=15/2\text{Improper Fraction} =7 \times2 +1 =15/2Improper Fraction=7×2+1=15/2

STEP 4

Convert the mixed number 4124 \frac{1}{2}421​ into an improper fraction.Improper Fraction=4×2+1=9/2\text{Improper Fraction} =4 \times2 +1 =9/2Improper Fraction=4×2+1=9/2

STEP 5

Convert the mixed number 5185 \frac{1}{8}581​ into an improper fraction.Improper Fraction=5×8+1=41/8\text{Improper Fraction} =5 \times8 +1 =41/8Improper Fraction=5×8+1=41/8

STEP 6

Now, we substitute these improper fractions back into the original equation.15/2÷(9/2−41/8)15/2 \div (9/2 -41/8)15/2÷(9/2−41/8)

STEP 7

Next, we simplify the expression in the brackets. To subtract fractions, they must have the same denominator. We can convert 9/29/29/2 to 36/36/36/ to match the denominator of 41/41/41/.15/2÷(36/−41/)15/2 \div (36/ -41/)15/2÷(36/−41/)

STEP 8

Now, we subtract the fractions in the brackets.15/2÷(−5/8)15/2 \div (-5/8)15/2÷(−5/8)

STEP 9

We can simplify the division of fractions by multiplying the first fraction by the reciprocal of the second fraction.15/2×−8/515/2 \times -8/515/2×−8/5

STEP 10

Multiply the fractions.Result=−24\text{Result} = -24Result=−24So, 72÷(42−58)=−247 \frac{}{2} \div\left(4 \frac{}{2}-5 \frac{}{8}\right) = -2472​÷(42​−58​)=−24.

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QuestionSolve: $7 \frac{1}{2} \div (4 \frac{1}{2} - 5 \frac{1}{8}) = \square$ with options: $-4 \frac{11}{16}$ , 12, $-12$ , $4 \frac{11}{16}$ .

Convert the mixed number $7 \frac{1}{2}$ into an improper fraction.
$\text{Improper Fraction} =7 \times2 +1 =15/2$

Convert the mixed number $4 \frac{1}{2}$ into an improper fraction.
$\text{Improper Fraction} =4 \times2 +1 =9/2$

Convert the mixed number $5 \frac{1}{8}$ into an improper fraction.
$\text{Improper Fraction} =5 \times8 +1 =41/8$

Now, we substitute these improper fractions back into the original equation.
$15/2 \div (9/2 -41/8)$

Next, we simplify the expression in the brackets. To subtract fractions, they must have the same denominator. We can convert $9/2$ to $36/$ to match the denominator of $41/$ .
$15/2 \div (36/ -41/)$

Now, we subtract the fractions in the brackets.
$15/2 \div (-5/8)$

We can simplify the division of fractions by multiplying the first fraction by the reciprocal of the second fraction.
$15/2 \times -8/5$

Multiply the fractions.
$\text{Result} = -24$ So, $7 \frac{}{2} \div\left(4 \frac{}{2}-5 \frac{}{8}\right) = -24$ .