Which fractions are equivalent to 0.4{8}? Select all that apply. Multi-select Choices: (A)48/100 (B)48/99 (C)44/90 (D)66/135

Convert to Fraction: Convert the repeating decimal 0.4{8} to a fraction. Let x = 0.4{8}. Then 10x = 4.8{8}. Subtracting the original x from this equation, 10x - x = 4.8{8} - 0.4{8}, results in 9x = 4.4. Solving for x gives x = 4.4 / 9. Simplify Fraction: Simplify the fraction 4.4/9. Since 4.4 can be written as 44/10, the fraction becomes (44/10) / 9 = 44 / (10*9) = 44 / 90. Check Equivalency: Check if the simplified fraction 44/90 is equivalent to any of the given choices. Simplify 44/90 by dividing the numerator and denominator by their greatest common divisor, which is 2. This gives 44/90 = 22/45, which is not listed in the choices.

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Which fractions are equivalent to $0.4\overline{8}$ ? Select all that apply. $\newline$ Multi-select Choices: $\newline$ (A) $\frac{48}{100}$ $\newline$ (B) $\frac{48}{99}$ $\newline$ (C) $\frac{44}{90}$ $\newline$ (D) $\frac{66}{135}$

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Math Problems

Grade 8

Checkpoint: Rational and irrational numbers

Full solution

Q. Which fractions are equivalent to

0.4\overline{8}

? Select all that apply.

\newline

Multi-select Choices:

\newline

(A)

\frac{48}{100}

\newline

(B)

\frac{48}{99}

\newline

(C)

\frac{44}{90}

\newline

(D)

\frac{66}{135}

Convert to Fraction: Convert the repeating decimal $0.4\overline{8}$ to a fraction. Let $x = 0.4\overline{8}$ . Then $10x = 4.8\overline{8}$ . Subtracting the original $x$ from this equation, $10x - x = 4.8\overline{8} - 0.4\overline{8}$ , results in $9x = 4.4$ . Solving for $x$ gives $x = \frac{4.4}{9}$ .
Simplify Fraction: Simplify the fraction $4.4/9$ . Since $4.4$ can be written as $44/10$ , the fraction becomes $(44/10) / 9 = 44 / (10*9) = 44 / 90$ .
Check Equivalency: Check if the simplified fraction $\frac{44}{90}$ is equivalent to any of the given choices. Simplify $\frac{44}{90}$ by dividing the numerator and denominator by their greatest common divisor, which is $2$ . This gives $\frac{44}{90} = \frac{22}{45}$ , which is not listed in the choices.