Ratios.notebook March 10, 2016
Ratios.notebook
March 10, 2016
Would you rather be in a classroom that has 20 iPads or 10 iPads?
Why?
Ratios.notebook
Class A
March 10, 2016
How about now?
Class B
Ratios.notebook
Ratios What are they? A ratio is a statement that compares numbers *Each number in a ratio is called a term Example:
How many different ratios can you create with the visual above?
March 10, 2016
Ratios.notebook
March 10, 2016
Ways we can express ratios
When comparing stars to triangles, we can express our answer as: 2:3 (using ":" to separate numbers) 2 to 3 (words) 2/3 (like a fraction) ***What makes this fraction representation different than we would normally represent fractions?
Ratios.notebook
Types of Ratios
ParttoPart: hearts:arrows = 3:2, arrows: hearts = 2:3 **Ratios can be expressed in any order, but pay attention to the language ParttoWhole: hearts:total figures = 3:5, arrows:total figures = 2:5
March 10, 2016
Ratios.notebook
March 10, 2016
Using Ratios During the next few days, you will have a chance to find equivalent ratios, compare ratios, and use your knowledge of ratios to solve realworld problems (recipes, scale drawings, etc.) *Most of what you need to know, you have already learned when we worked with fractions (a little bit of algebra knowledge helps, too)
Ratios.notebook
March 10, 2016
Equivalent Ratios
Let's start with the fraction 3/5. Name three equivalent fractions to 3/5 and explain how you got them.
t/15 = 2/5; how would you solve for "t"?
Ratios.notebook
March 10, 2016
Equivalent Ratios The same rules that work for equivalent fractions work for equivalent ratios. To find equivalent fractions, we would multiply (or divide) the numerator and the denominator by the same number Examples: 1(x4)/7(x4) = 4/28, 25(÷25) /100(÷25) = 1/4 **To find equivalent ratios, you multiply or divide the first term and the second term by the same number. Examples: A cookie recipe calls for 2 cups of flour and 3 cups of sugar. How many cups of each would you need if you wanted to triple the recipe? c:12 = 5:6; c =
Ratios.notebook
March 10, 2016
Comparing Ratios Let's think back to comparing fractions. Before we could compare two fractions, we would need to convert our fractions to equivalent fractions that have a common denominator. Example: compare 4/7 to 5/8 77, 14, 21, 28, 35, 42, 49, 56 8 8, 16, 24, 32, 40, 48, 56 4/7 (x 8) = 32/56 5/8 (x 7) = 35/56 Soooo, 5/8 > 4/7 We can do the same thing when comparing ratios. Find the LCM or either the first term or the second term, then find equivalent ratios that use the LCM. Compare the term that is not the same.
Ratios.notebook
March 10, 2016
Comparing Ratios Both Jayden and Yousif buy some Mio at the store. Jayden adds 4 squirts of Mio to 6 cups of water. Yousif adds 3 squirts of Mio to 5 cups of water. Whose drink is stronger?
Ratios.notebook
March 10, 2016
Comparing Ratios Jayden
Yousif
3:5 x 6 Find the LCM of 6 and 5 so we can make the second = 20:30 = 18:30 terms the same 4:6
x 5
6: 6, 12, 18, 24, 30 5: 5, 10, 15, 20, 25, 30 The LCM for 6 and 5 is 30. *To make equivalent ratios, find out what you needed to multiply the second term by Jayden's mix will be stronger because he would use 20 to make it 30. Do the same squirts of Mio for 30 cups of water. This is two more to the first term squirts than Yousif would use for 30 cups.
*When you have found your equivalent ratios with the same second term, compare first terms.
Ratios.notebook
March 10, 2016
Tips for working with ratios **Remember your fractions work (equivalent, comparing) **Read the questions carefully. Ratios can be expressed in any order, but they MUST match the words in the question to be correct
Ratios.notebook
March 10, 2016
Ratios Homework Questions Review Questions 1. Use the numbers in the box to write each ratio. a) odd numbers to even numbers
25
16
13
38
b) numbers less than 20 to all numbers
17
30
49
3
24
45
7
14
c) multiples of 5 to multiples of 7 d) prime numbers to composite numbers
2. What is being compared in each ratio? a) 1 to 2 b) 2:6 c) 2:3 d) 1/6 e) 3/6
Level 2 Questions 1. Write each ratio in simplest form. a) 10:4
b) 14:28
c) 25:10 l = 90 cm
2. The lengthtowidth ratio of a poster is 3:2. The poster is 90 cm long. How wide is it?
w = ?
3. The ratio of iPads to students in our class is 3:5. The ratio of iPads to students in Mr. Court's class is 2:3. Both classes have the same number of students. Which class has more iPads? Show your work.
Level 3 Questions 1. Find each missing term. a) f/10 = 4/5
b) x:16 = 5:4
c) x:6 = 12:9
2. An ad stated that 7 out of 10 teenagers ate cereal for breakfast. Suppose 140 teenagers were interviewed How many did not eat cereal for breakfast?
3. The scale on a map of Canada is 1:8 000 000. The distance from Prince George, B.C., to Fredericton, N.B. is 5320 km. What is the distance between these 2 places on the map?
Ratios.notebook
March 10, 2016
March 10, 2016
Would you rather be in a classroom that has 20 iPads or 10 iPads?
Why?
Ratios.notebook
Class A
March 10, 2016
How about now?
Class B
Ratios.notebook
Ratios What are they? A ratio is a statement that compares numbers *Each number in a ratio is called a term Example:
How many different ratios can you create with the visual above?
March 10, 2016
Ratios.notebook
March 10, 2016
Ways we can express ratios
When comparing stars to triangles, we can express our answer as: 2:3 (using ":" to separate numbers) 2 to 3 (words) 2/3 (like a fraction) ***What makes this fraction representation different than we would normally represent fractions?
Ratios.notebook
Types of Ratios
ParttoPart: hearts:arrows = 3:2, arrows: hearts = 2:3 **Ratios can be expressed in any order, but pay attention to the language ParttoWhole: hearts:total figures = 3:5, arrows:total figures = 2:5
March 10, 2016
Ratios.notebook
March 10, 2016
Using Ratios During the next few days, you will have a chance to find equivalent ratios, compare ratios, and use your knowledge of ratios to solve realworld problems (recipes, scale drawings, etc.) *Most of what you need to know, you have already learned when we worked with fractions (a little bit of algebra knowledge helps, too)
Ratios.notebook
March 10, 2016
Equivalent Ratios
Let's start with the fraction 3/5. Name three equivalent fractions to 3/5 and explain how you got them.
t/15 = 2/5; how would you solve for "t"?
Ratios.notebook
March 10, 2016
Equivalent Ratios The same rules that work for equivalent fractions work for equivalent ratios. To find equivalent fractions, we would multiply (or divide) the numerator and the denominator by the same number Examples: 1(x4)/7(x4) = 4/28, 25(÷25) /100(÷25) = 1/4 **To find equivalent ratios, you multiply or divide the first term and the second term by the same number. Examples: A cookie recipe calls for 2 cups of flour and 3 cups of sugar. How many cups of each would you need if you wanted to triple the recipe? c:12 = 5:6; c =
Ratios.notebook
March 10, 2016
Comparing Ratios Let's think back to comparing fractions. Before we could compare two fractions, we would need to convert our fractions to equivalent fractions that have a common denominator. Example: compare 4/7 to 5/8 77, 14, 21, 28, 35, 42, 49, 56 8 8, 16, 24, 32, 40, 48, 56 4/7 (x 8) = 32/56 5/8 (x 7) = 35/56 Soooo, 5/8 > 4/7 We can do the same thing when comparing ratios. Find the LCM or either the first term or the second term, then find equivalent ratios that use the LCM. Compare the term that is not the same.
Ratios.notebook
March 10, 2016
Comparing Ratios Both Jayden and Yousif buy some Mio at the store. Jayden adds 4 squirts of Mio to 6 cups of water. Yousif adds 3 squirts of Mio to 5 cups of water. Whose drink is stronger?
Ratios.notebook
March 10, 2016
Comparing Ratios Jayden
Yousif
3:5 x 6 Find the LCM of 6 and 5 so we can make the second = 20:30 = 18:30 terms the same 4:6
x 5
6: 6, 12, 18, 24, 30 5: 5, 10, 15, 20, 25, 30 The LCM for 6 and 5 is 30. *To make equivalent ratios, find out what you needed to multiply the second term by Jayden's mix will be stronger because he would use 20 to make it 30. Do the same squirts of Mio for 30 cups of water. This is two more to the first term squirts than Yousif would use for 30 cups.
*When you have found your equivalent ratios with the same second term, compare first terms.
Ratios.notebook
March 10, 2016
Tips for working with ratios **Remember your fractions work (equivalent, comparing) **Read the questions carefully. Ratios can be expressed in any order, but they MUST match the words in the question to be correct
Ratios.notebook
March 10, 2016
Ratios Homework Questions Review Questions 1. Use the numbers in the box to write each ratio. a) odd numbers to even numbers
25
16
13
38
b) numbers less than 20 to all numbers
17
30
49
3
24
45
7
14
c) multiples of 5 to multiples of 7 d) prime numbers to composite numbers
2. What is being compared in each ratio? a) 1 to 2 b) 2:6 c) 2:3 d) 1/6 e) 3/6
Level 2 Questions 1. Write each ratio in simplest form. a) 10:4
b) 14:28
c) 25:10 l = 90 cm
2. The lengthtowidth ratio of a poster is 3:2. The poster is 90 cm long. How wide is it?
w = ?
3. The ratio of iPads to students in our class is 3:5. The ratio of iPads to students in Mr. Court's class is 2:3. Both classes have the same number of students. Which class has more iPads? Show your work.
Level 3 Questions 1. Find each missing term. a) f/10 = 4/5
b) x:16 = 5:4
c) x:6 = 12:9
2. An ad stated that 7 out of 10 teenagers ate cereal for breakfast. Suppose 140 teenagers were interviewed How many did not eat cereal for breakfast?
3. The scale on a map of Canada is 1:8 000 000. The distance from Prince George, B.C., to Fredericton, N.B. is 5320 km. What is the distance between these 2 places on the map?
Ratios.notebook
March 10, 2016
