Using the correct order of operations (BODMAS), work out the value of the expression: 24 / 3 + 2 × 5 − 4.

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5. Using the correct order of operations (BODMAS), work out the value of the expression: $24 \div 3 + 2 \times 5 - 4$ .

Perform division.
$24 \div 3 = 8$
The expression becomes: $8 + 2 \times 5 - 4$ .
Perform multiplication.
$2 \times 5 = 10$
The expression becomes: $8 + 10 - 4$ .
Perform addition.
$8 + 10 = 18$
The expression becomes: $18 - 4$ .
Perform subtraction.
$18 - 4 = 14$
The final answer is $\boxed{\text{B. 14}}$ .

6. In a mathematics test, a student was asked to express the fraction $\frac{3}{8}$ as a decimal. Which of the following is correct?
Divide the numerator by the denominator.
$\frac{3}{8} = 3 \div 8$
Perform the division.
$3 \div 8 = 0.375$
The final answer is $\boxed{\text{A. 0.375}}$ .

7. What is the final result when you calculate the square root of the mixed fraction $\sqrt{(6 \frac{1}{4})}$ ?
Convert the mixed fraction to an improper fraction.
$6 \frac{1}{4} = \frac{(6 \times 4) + 1}{4} = \frac{24 + 1}{4} = \frac{25}{4}$
Calculate the square root of the improper fraction.
$\sqrt{\frac{25}{4}} = \frac{\sqrt{25}}{\sqrt{4}}$
Find the square roots of the numerator and the denominator.
$\frac{\sqrt{25}}{\sqrt{4}} = \frac{5}{2}$
Convert the improper fraction back to a mixed number.
$\frac{5}{2} = 2 \frac{1}{2}$
The final answer is $\boxed{\text{A. } 2 \frac{1}{2}}$ .

8. A farmer has $n$ cows and $m$ goats in his farm. If he sells 5 of his cows, which algebraic expression represents the total remaining animals?
Identify the initial number of each type of animal.
Number of cows = $n$
Number of goats = $m$
Determine the number of cows remaining after selling 5.
Remaining cows = $n - 5$
Write the expression for the total remaining animals by adding the remaining cows and the goats.
Total remaining animals = (Remaining cows) + (Number of goats)
Total remaining animals = $(n - 5) + m$
Total remaining animals = $n - 5 + m$

The final answer is $\boxed{\text{B. } n - 5 + m}$ .

9. Convert the decimal number 0.45 into a fraction and then reduce it to its simplest form.
Convert the decimal to a fraction.
The decimal 0.45 means 45 hundredths.
$0.45 = \frac{45}{100}$
Reduce the fraction to its simplest form by finding the greatest common divisor (GCD) of the numerator and the denominator.
The GCD of 45 and 100 is 5.
Divide both the numerator and the denominator by their GCD.
$\frac{45 \div 5}{100 \div 5} = \frac{9}{20}$
The final answer is $\boxed{\text{B. } \frac{9}{20}}$ .

Using the correct order of operations (BODMAS), work out the value of the expression: 24 / 3 + 2 x 5 - 4.

Step-by-step solution

Perform division.

Perform multiplication.

Perform addition.

Perform subtraction.

Divide the numerator by the denominator.

Perform the division.

Convert the mixed fraction to an improper fraction.

Calculate the square root of the improper fraction.

Find the square roots of the numerator and the denominator.

Convert the improper fraction back to a mixed number.

Identify the initial number of each type of animal.

Determine the number of cows remaining after selling 5.

Write the expression for the total remaining animals by adding the remaining cows and the goats.

Convert the decimal to a fraction.

Reduce the fraction to its simplest form by finding the greatest common divisor (GCD) of the numerator and the denominator.

Divide both the numerator and the denominator by their GCD.

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