CROSS-MULTIPLYING WITH PROPORTIONS

• NS 1.3 Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse.

• Today’s objective: learn a second method (cross-multiplication) for solving proportions

•Bill has 14 shirts. If his ratio of pants to shirts is 6:4, how many pants does he have?

•4 does not go evenly into 14. Use a variable, such as x, for the unknown amount.

•Cross multiply•6 × 14 = 4 × x• 84 = 4x • ÷4 ÷4• 21 pants = x

•Cross multiply• 3 × x = 9 × 5• 3x = 45 • ÷3 ÷3• x = 15 miles

•3 inches on a map represents 9 miles in real life. If cities are 5 inches away on a map, how far apart are they in real life?

Direct Station• We will work together on word problems that can be

solved using proportions

Collaborative Station: Create Your Own Proportion Problem• One partner will create their own proportion problem.

Then all partners, including the one who made the problem, solve for the value of the variable by doing cross-multiplication.

• Remember, proportions look like Choose numbers from 1-12 for 3 of the variables and then calculate the value of the remaining letter.

• All proportions can be solved! However, sometimes the answer will be a decimal. You may stop after 2 decimal digits if the long division keeps going.

Independent Station• We are switching to ST Math’s unit on equations, which

we will review next week