Transcript Lesson 8-3a

8-3
6th grade math
Solving Proportions
Using
Cross Products
Objective
• To solve proportions using cross products
• Why? To know how to find the missing
number in a proportion- especially when the
ratios are not easily ‘convertible.’
California State Standards
NS 1.3 : Use proportions to solve problems …
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.
NS 1.2 : Interpret and use ratios in different
contexts … to show the relative size of two
quantities, using appropriate notations (x/y, x to
y, x : y)
AF 1.1 : Write and solve one-step linear
equations in one variable.
Vocabulary
• Cross products
– In a proportion, the product of a numerator of one
ratio with the denominator of the other ratio.
bc (b x c)
• a=c
b d
ad (a x d)
– This is similar to solving an equation with fractions.
• a=c
b d
• a (b) = c (b) = bc (b x c)
b (a) d (a) = ad (a x d)
How to Solve Proportions Using Cross
7 = n
Products
1)Multiply the numerator
and the denominator of
two known numbers
2) Divide by the last used
number.
3) Check your answer for
reasonableness. You
could also recheck the
final proportion by
dividing the fractions.
1.2
3
7 x 3 = 21
21 ÷ 1.2 = 17.5
7 = 17.5
1.2
3
7 ≈ 5.8
1.2
17.5 ≈ 5.8
3
Try It!
1) n = 12
1) 6 = 8
9
n
2) n = 6
2) 9 = n
15
10
3) n = 21.25
3) 8.5 = n
3.2
8
4) n = 3.12
4) 2.6 = 4
n
4.8
Try Some More!
Proportional?
5) 4 , 6
10 15
5) Yes (60)
6) No (72, 81)
6) 6 , 9
9 12
7) Yes (72)
7) 6 , 9
8 12
8) Yes (90)
8) 6 , 9
10 15
Objective Review
• To solve proportions
using cross products
• Why? You now know how to
find the missing number in a
proportion- especially when the
ratios are not easily
‘convertible.’
• You can use cross products to
solve for the unknown value in
a proportion.
Independent Practice
• Complete problems 1018
• Copy original problem
first.
• Show all work!
• If time, complete Mixed
Review: 19-25
• If still more time, work
on Accelerated Math.