Transcript 5-10 6th grade math

8-2
6th grade math
Proportions
Objective
• To solve proportions using equivalent ratios.
• Why? To use ratios to compare two quantities
when enlarging (increasing) or reducing
(decreasing) ratios. To solve for missing sides
of geometric shapes. To solve for ‘x’ in ratios
or proportions.
California State Standards
NS 1.3 : Use proportions to solve problems (e.g.,
determine the value of N if 4/7 = n/21)
NS 1.0 : Solve problems involving … proportions
…
MR 1.1: Analyze problems by identifying
relationships, …
Vocabulary
• Proportion
– An equation stating that two ratios are equivalent
• 35 = 105
23
69
• 1 = 16
2
32
How to Know if 2 Ratios are
Proportional
1) Solve as stated in the
previous lesson. Cross
multiply the numbers.
2) Write the numbers from
cross multiplying.
3) Compare the ‘numbers.’
If they are the same,
then the ratios are
proportional. If they are
not, the ratios are not
proportional.
3 ? 18
5
30
3 x 30 = 90
5 x 18 = 90
3 = 18
5
30
How to Solve Proportions- Solving for ‘x’
1. As in the previous
lesson, Cross multiply
2. Divide by the last
number
3. Check for
reasonableness.
15 = n
35 7
15 x 7 = 105
3
35 105
15 = 3
35 7
Another Way to Solve ProportionsSolving for ‘x’
18 = 9
1) Re-write as equivalent
fractions, if possible. Decide
how the known portions- the
numerators or denominatorswere able to change ‘into’ each
other. Did it get multiplied or
divided by a special number?
Pay attention to the order.
2) If traveling in the same motion,
multiply or divide the other
portion by the same number.
3) If traveling in the opposite
motion, use inverse
operations.
3) Check the results for
reasonableness.
12
x
18 ÷ 2 = 9 →
12 ÷ 2 = 6 →
or
9 x 2 = 18 ←
12 ÷ 2 = 6 →
18 = 9
12
6
Try It!
Are these equivalent?
1) 4 , 12
5 15
2) 3 , 9
8 21
3) 2 , 18
3 27
4) 5 , 40
8 64
60 60
1) 4 12 yes (or x 3)
5 15
63 72
2) 3 , 9 no <
8 21
54 54
3) 2 , 18 yes (or x 9)
3 27
320 320
4) 5 , 40 yes (or x8)
8 64
Objective Review
• To solve proportions using
equivalent ratios.
• Why? You can now use ratios to
compare two quantities when enlarging
(increasing) or reducing (decreasing)
ratios. You can solve for missing sides
of geometric shapes.
• You can solve proportions by finding
equivalent ratios.
• You can solve for x in a proportion or
ratio problem.
Independent Practice
• Complete problems 615
– 10-13 = solving for x
• Copy original problem
first.
• Show all work!
• If time, complete Mixed
Review: 16-22
• If still more time, work
on Accelerated Math.