Martin is an after-school math tutor. He noticed that 6 people still needed help and only Two-fifths of the tutoring session time was left. Since each person is to be given an equal amount of time, Martin wrote the expression below to find the fraction of the tutoring session each person who still needed help would be allotted.

Question

Two-fifths divided by 6

Which expression is equivalent to Martin’s expression?
StartFraction 6 Over 15 EndFraction divided by 6
StartFraction 6 Over 5 EndFraction divided by 2
Five-halves times 6
Two-fifths times 6

Answer 1

To find an equivalent expression to Martin's expression of "Two-fifths divided by 6," we can write it mathematically as:

\[ \frac{2}{5} \div 6 \]

Dividing by a number is the same as multiplying by its reciprocal. Therefore, we rewrite the expression:

\[ \frac{2}{5} \div 6 = \frac{2}{5} \times \frac{1}{6} = \frac{2 \times 1}{5 \times 6} = \frac{2}{30} = \frac{1}{15} \]

Now let's examine the provided options to see which one is equivalent to \(\frac{2}{5} \div 6\):

1. StartFraction 6 Over 15 EndFraction divided by 6: \[ \frac{6}{15} \div 6 = \frac{6}{15} \times \frac{1}{6} = \frac{6 \times 1}{15 \times 6} = \frac{1}{15} \] This is equivalent.

2. StartFraction 6 Over 5 EndFraction divided by 2: \[ \frac{6}{5} \div 2 = \frac{6}{5} \times \frac{1}{2} = \frac{6 \times 1}{5 \times 2} = \frac{6}{10} = \frac{3}{5} \] This is not equivalent.

3. Five-halves times 6: \[ \frac{5}{2} \times 6 = \frac{30}{2} = 15 \] This is not equivalent.

4. Two-fifths times 6: \[ \frac{2}{5} \times 6 = \frac{12}{5} \] This is not equivalent.

The only expression that is equivalent to Martin's expression of \(\frac{2}{5} \div 6\) is:

StartFraction 6 Over 15 EndFraction divided by 6.