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Which of the following expressions is equivalent to
0.8 ×12.4 ?
Choose 1 answer:
(A)
8×124÷100
(B)
8×124÷1,000
(C)
8×124÷10,000
(D)
8×124÷100,000

Which of the following expressions is equivalent to $\newline$ $0.8 \times 12.4$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $\newline$ $8\times124\div100$ $\newline$ (B) $\newline$ $8\times124\div1,000$ $\newline$ (C) $\newline$ $8\times124\div10,000$ $\newline$ (D) $\newline$ $8\times124\div100,000$

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Division patterns with zeros

Full solution

Q. Which of the following expressions is equivalent to

\newline

0.8 \times 12.4

?

\newline

Choose

1

answer:

\newline

(A)

\newline

8\times124\div100

\newline

(B)

\newline

8\times124\div1,000

\newline

(C)

\newline

8\times124\div10,000

\newline

(D)

\newline

8\times124\div100,000

Convert to Fractions: First, let's express $0.8$ as a fraction in terms of its decimal place value. $\newline$ $0.8$ can be written as $\frac{8}{10}$ or $\frac{80}{100}$ since moving the decimal point two places to the right turns it into $80$ , and we must divide by $100$ to compensate for the shift.
Express $12$ . $4$ : Now, let's express $12.4$ in a similar way. $\newline$ $12.4$ can be written as $\frac{124}{10}$ because moving the decimal point one place to the right turns it into $124$ , and we must divide by $10$ to compensate for the shift.
Multiply Fractions: Next, we multiply the two fractions we have obtained. $\newline$ $(\frac{80}{100}) \times (\frac{124}{10}) = (\frac{80 \times 124}{100 \times 10})$
Perform Multiplication: Now, we perform the multiplication and division. $\newline$ $(80 \times 124) / (100 \times 10) = 9,920 / 1,000$
Simplify Expression: We simplify the expression by dividing both the numerator and the denominator by $10$ to make the numbers more manageable. $9,920 / 1,000 = 992 / 100$
Final Result: Finally, we can see that the expression $992 / 100$ is equivalent to $8 \times 124 \div 100$ , which corresponds to option (A).

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