Ten members of Balin’s soccer team ran warm ups for practice. Each member ran the same distance. Their combined distance was StartFraction 5 Over 6 EndFraction of a mile. To find the distance that each member ran, Balin wrote the expression below.

Question

StartFraction 5 Over 6 EndFraction divided by 10

Which expression is equivalent to Balin’s expression?
StartFraction 10 Over 12 EndFraction divided by 10
StartFraction 10 Over 6 EndFraction divided by 5
StartFraction 6 Over 5 EndFraction times 10
StartFraction 5 Over 6 EndFraction times 10

Answer 1

Balin's expression to find the distance that each member ran is \(\frac{5}{6} \div 10\).

To find an equivalent expression, we can make use of the properties of division and multiplication:

1. The expression \(\frac{5}{6} \div 10\) can be rewritten as \(\frac{5}{6} \times \frac{1}{10}\).

2. This further simplifies to \(\frac{5}{60}\), which is \(\frac{1}{12}\).

Now let's analyze the options to see which one is equivalent to \(\frac{5}{6} \div 10\):

1. \(\frac{10}{12} \div 10\) simplifies to \(\frac{10}{120} = \frac{1}{12}\) (equivalent).

2. \(\frac{10}{6} \div 5\) simplifies to \(\frac{10}{30} = \frac{1}{3}\) (not equivalent).

3. \(\frac{6}{5} \times 10\) simplifies to \(\frac{60}{5} = 12\) (not equivalent).

4. \(\frac{5}{6} \times 10\) simplifies to \(\frac{50}{6} = \frac{25}{3}\) (not equivalent).

Thus, the expression that is equivalent to Balin’s expression is:

\(\frac{10}{12} \div 10\).