ratio 3 : 7. 0 40 1 2 34 5 6 78 9 4 8 12 16 20 24 28 32 36 010 if we write the pairs of numbers as...
TRANSCRIPT
Ratio
3 : 7
0 40
1 2 3 4 5 6 7 8 9
4 8 12 16 20 24 28 32 36
0 10
If we write the pairs of numbers as fractions we get the following:
4
1
8
2
12
3
16
4
20
5
24
6
28
7
32
8
36
9
40
10== == == == =
1
4
2
8
3
12
4
16
5
20
6
24
7
28
8
32
9
36
10
40== == == == =
20
2 3 5
4 6 10
10
What do YOU notice?
40
6 9 15
8 12 20
30
2 + 3 + 5 = 10
4 + 6 + 10 = 20
6 + 9 + 15 = 30
8 + 12 + 20 = 40
Top line x 2
Top line x 3
Top line x 4
20
2 3 5
4 6 10
10
What is in a ratio of 2:3:5
40
6 9 15
8 12 20
30
Question:
20 sweets are split up in a ratio of 2:3:5 between 3 friends Bill, Ben & Jerry. How many did Ben get?
WHY?
How do you know you are right?
20
2 3 5
4 6 10
10
What is in a ratio of 2:3:5
40
6 9 15
8 12 20
30
Question:
30 pounds is split up in a ratio of 2:3:5 between 3 friends Bill, Ben & Jerry. How many did Ben get?
WHY?
How do you know you are right?
20
2 3 5
4 6 10
10
What is in a ratio of 2:3:5
40
6 9 15
8 12 20
30
Question:
50 marbles are split up in a ratio of 2:3:5 between 3 friends Bill, Ben & Jerry. How many did Ben get?
WHY?
How do you know you are right?
20
2 3 5
4 6 10
10
What is in a ratio of 2:3:5
40
6 9 15
8 12 20
30
Question:
What is 50 in a ratio of 2:3:5?
What is 60 in a ratio of 2:3:5?
WHY?
How do you know you are right?
Card activity
• Split into two groups • Find the odd one out in your groups card set• Discuss why this is the case• Elect someone to feedback
• Look at the other card set that the other group had discuss what the differences and similarities
Which one is the odd one out?
32
64
3020
332210
62718
128
1510
Which one is the odd one out?
32
64
3020
332210
62718
128
1510
WHY?
Which is the odd one out?
8:12
20:30 4:6
22:33 10:15 2:3
14:21 6:9
6:10 18:27
Which is the odd one out?
8:12
20:30 4:6
22:33 10:15 2:3
14:21 6:9
6:10 18:27
WHY?
Ratios can be simplified in the same way fractions can be simplified
Ratios9:12
= 6:8 = 3:4
Fractions
4
3
8
6
12
9
These are know as equivalent fractions.
These can be described as equivalent ratios.
Ratios can also be written as fractions
Strategy
Add the ratios together – get the total
Write each of the ratios in fraction form over the total
E.g. the ratio 3:4
Add the ratios 3+4 = 7
The ratio can be written in fraction form as: and
7
3
7
4
Ratios describe some thing else. Example of what they can be used for
Draw two lines of equal length, label one ratio and the other what ever it is describing
Use the lines as scales and add the information that you know.
Ratio
DegreesIn a triangle
180
The angles of a triangle are in a ratio of 2:3:4
2 3 4
? ? ?
9 Total
0 40
1 2 3 4 5 6 7 8 9
4 8 12 16 20 24 28 32 36
0 10
What we get are equivalent fractions
4
1
8
2
12
3
16
4
20
5
24
6
28
7
32
8
36
9
40
10== == == == =
1
4
2
8
3
12
4
16
5
20
6
24
7
28
8
32
9
36
10
40== == == == =
The angles of a triangle are in a ratio of 2:3:4 What are they?
DegreesIn a triangle
180
2 3 4
? ? ?
9 TotalRatio
therefore9
180
2
?
9
180
3
?
9
180
4
?
Multiply both sides by the number that divides the ? 40220?
29
180?
60320?
39
180?
80420?
49
180?
1. Read the Question2. Extract the information (ratios are on the same line)3. Write the calculation (use equivalent fractions)4. Write the answer in context to the question
Strategy
58
?
385
Lines to extract information
Answer – in context to the question.
Calculation
Lines to extract informationQuestionIn a shop the ratio of oranges to
apples is 2:5. If there are 84 pieces of fruit altogether, how
many oranges are there?
ratio
fruit2
?
8
84?
5
Equivalent fraction is 8
84
2
?
8
84
2
?
2122
212
8
84?
There are 21 oranges in the shop.
What do you remember about ratio
• 3:4 is read 3 to 4
• Ratio can be simplified in the same way fractions are
• Ratios can be written as fractions
• Ratios describe the make up of some group of objects
• Ratios can be used to find actual quantities