Final answer:
The equivalent fractions to 0.58 are both 29/50 and 58/100. The correct options are a) 29/50 and b) 58/100, as these both represent the decimal 0.58 in fractional form.
Step-by-step explanation:
The student asked which value is equivalent to 0.58. To find a fraction equivalent to a decimal, we can write the decimal as a fraction with a denominator of 1 and then multiply the numerator and denominator by a power of 10 that makes the numerator a whole number. For 0.58, we can express it as 58/100 since 0.58 = 58/1 × 1/100 = 58/100.
Answer a) 29/50 can be checked by cross-multiplying: if 58/100 is equivalent to 29/50, then 58×50 should equal 100×29. After calculating, we have 58×50 = 2900 and 100×29 = 2900, which means these fractions are equivalent, so a) 29/50 is correct.
Answer b) 58/100 is simply the decimal 0.58 written as a fraction, so it is directly equivalent and correct.
Answer c) 145/250 and d) 116/200 can both be checked through simplification or cross-multiplication. Simplifying 145/250 and 116/200 does not yield the fraction 58/100, making both incorrect.
The equivalent fractions to 0.58 are 29/50 and 58/100, which correspond to options a) and b).