How a Bill Becomes Law

Explanation

Analyze

• It takes \(\frac23\) of those voting to override a veto (Given)
• All 435 members of the House cast a vote (Given)
• How many votes does it take to override a Presidential veto? (Find)

Form

The key phrase \(\frac23\) of suggests that we are to find a part of the 435 possible notes using multiplication.

We translate the words of the problem to numbers and symbols

(The number of notes needed in the house override a veto)  is equal to \(\frac23\)  (the number of House members that vote)

The number of votes needed in the House to override a veto = \(\frac23 \cdot 435\)

Solve

To find the product, we will express 435 as a fraction and then use the rule for multiplying two fractions

Write 435 as a fraction: 435 = \(\frac{435}{1}\)

$\frac23 \cdot 435 = \frac23 \cdot \frac{435}{1}$

Multiply the numerators.  Multiply the denominators

$= \frac{2 \cdot 435}{3 \cdot 1}$

To prepare to simplify, write 435 in prime-factored form: 3 • 5 • 29

$= \frac{2 \cdot 3 \cdot 5 \cdot 29}{3 \cdot 1}$

Remove the common factor of 3 from the numerator and denominator

$\require{cancel} = \frac{2 \cdot \cancel{3}^1 \cdot 5 \cdot 29}{\cancel{3}_1 \cdot 1}$

Multiply the remaining factors in the numerator: 2 • 1 • 5 • 29 = 290.  Multiply the remaining factors in the denominators: 1 • 1 = 1

$= \frac{290}{1}$

Any whole number divided by 1 is equal to that number

$= 290$

State

It would take 290 votes in the House to override a veto

Check

We can estimate to check the result.  We will use 440 to approximate the number of House members voting.  Since \(\frac12\) of 440 is 220, and since \(\frac23\) is a greater part than \(\frac12\), we would expect the number of votes needed to be more than 220.  The result of 290 seems reasonable.