Two lines have slopes or gradients of six-fifths and 12-10ths. Are these two lines parallel?
In order to answer this question, we need to understand the definition of parallel lines. Parallel lines are lines that never meet. As a result of this, they must have the same slope or the same gradient. In this particular question, we need to work out whether the six-fifths and 12-10ths are equivalent or equal to each other.
Equivalent fractions can be simplified or cancelled down to the same fraction. Two is a common factor of 10 and 12. Dividing 12 by two gives us six. Dividing 10 by two gives us five. Remember when you are simplifying fractions, whatever you do to the top number, the numerator you, must also do the same thing to the bottom, or the denominator.
As both of these fractions in their simplest form are six-fifths, or six over five, we can say that the two lines are parallel to each other because they have the same slope or gradient. Another quick way to check for equivalent fractions is to cross multiply. In this case, six multiplied by 10 is 60 and, also, five multiplied by 12 is 60. Therefore, these two fractions are definitely equivalent.