Options 1, 3, and, 5 are true.
The statements given are,
1.) The product of reciprocals is 1.
Let the fraction be [tex]\dfrac{a}{b}[/tex], and reciprocal be [tex]\dfrac{b}{a}[/tex],
The product of the two will be [tex]\dfrac{a}{b} \times \dfrac{b}{a} = 1[/tex].
Hence, the statement is true.
2.) To divide fractions, multiply the divisor by the reciprocal of the dividend.
Let the fraction be [tex]\dfrac{a}{b}[/tex], now,
[tex]\dfrac{a}{b\times \dfrac{1}{a} } = \dfrac{a^2}{b}[/tex],
Hence, the statement is false.
3.) The reciprocal of a whole number is 1 over the number.
Let the number be 3, now,
The reciprocal of number 3 is [tex]\dfrac{1}{3}[/tex].
Hence, the statement is true.
4.) Reciprocals are used to multiply fractions.
The statement is false, Reciprocals are not used to multiply fractions.
5.) To find the reciprocal of a fraction, switch the numerator and denominator.
Let the fraction be [tex]\dfrac{a}{b}[/tex], then the reciprocal will be [tex]\dfrac{b}{a}[/tex].
Hence, the statement is true.
Therefore, Options 1, 3, and, 5 are true.
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