Government Grants

$2\frac12$

Explanation

To find how much each city would receive, we will express \(12\frac12\) and 5 as fractions and then use the rule for dividing two fractions.

Write \(12\frac12\) as an improper fraction, and write 5 as a fraction.

$12\frac12 ÷ 5 = \frac{25}{2} ÷ \frac51$

Multiply by the reciprocal of \(frac51\), which is \(\frac15\)

$= \frac{25}{2} \cdot \frac15$

Multiply the numerators.  Multiply the denominators.

$= \frac{25 \cdot 1}{2 \cdot 5}$

To simplify, factor 25 as 5 • 5.  Then remove the common factor of 5 from the numerator and denominator.

$\require{cancel} = \frac{\cancel{5}^1 \cdot 5 \cdot 1}{2 \cdot \cancel{5}_1}$

Multiply the remaining factors in the numerator.  Multiply the remaining factors in the denominator.

$= \frac52$

Write the improper fraction \(\frac52\) as a mixed number by dividing 5 by 2.  The units are in millions of dollars.

$2\frac12$

So, each city will receive \(2\frac12\) million in grant money.