CROSS-MULTIPLYING

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

Suppose we have an equation that looks like this: What should be done in order to eliminate the 5 that is dividing the a? “In order to eliminate the 5, we should _________ because __________.” Use the vocabulary term “inverse operation” in your answer.

Now suppose we have an equation that looks like this: What should be done in order to eliminate the b that is dividing the a? “In order to eliminate the b, we should _________ because __________.” Use the vocabulary term “inverse operation” in your answer.

What should be done in order to eliminate the d that is dividing the bc? “In order to eliminate the d, we should _________ because __________.” Use the vocabulary term “inverse operation” in your answer.

We have now changed the equation into

What is cross- multiplying? Why is cross- multiplying useful? This is ONLY used for equations! If the products of the diagonals are equal, then the fractions/ratios are equivalent.

Are the fractions equivalent? Cross-multiply 4×15 =? 6×10 60 = 60 The fractions are equivalent.

Store A: 7 toys, 4 books Store B: 5 toys, 3 books Do the stores have equivalent ratios of toys to books? Cross-multiply 7×3 =? 4×5 21 ≠ 20 The ratios are NOT equivalent.

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 two 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 about real-life situations that involve proportions.

Collaborative Station: Four High Schools You will receive information about Four High Schools and various descriptions. Your job is to figure out which high school each description is talking about. Example: High School E has 5 teachers and 50 students. The description “The ratio of teachers to students is 1:10” would match High School E since The description “The ratio of teachers to students is 1:2” would not match High School E because

Independent Station We are continuing ST Math’s unit on Ratios. Write down proportions to represent each problem you do. For example, if each plant eats 4 bananas and there are 5 plants, you would would write down