Question

Compare -3.5 and -10/3 using symbols <, >, or =.

A. -3.5 < -10/3
B. -3.5 > -10/3
C. -10/3 = -3.5
D. -10/3 < -3.5

Answer 1

`\sf A. \quad -3.5 < -(10)/(3)`

Explanation:

Convert -3.5 into a fraction:

`\implies \sf -3.5=-(35)/(10)=-(\diagup\!\!\!\!5 * 7)/(\diagup\!\!\!\!5 * 2)=-(7)/(2)`

Rewrite both fractions so that they have the same denominator:

`\implies \sf -(7)/(2)=-(7 * 3)/(2 * 3)=-(21)/(6)`

`\implies \sf -(10)/(3)=-(10 * 2)/(3 * 2)=-(20)/(6)`

`\textsf{As }\: -(21)/(6) < -(20)/(6) \textsf{ then}:`

`\sf \implies -3.5 < -(10)/(3)`