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READING MATERIAL
Read About Ratios
WHAT ARE RATIOS?
A ratio describes the relationship between different amounts. A ratio can describe the relationship between two parts of a group, or between one part and the whole group. To better understand ratios…
LET’S BREAK IT DOWN!
A ratio shows a relationship between two amounts.
A bunny has 2 eyes and 1 nose. That’s a ratio of 2 to 1. You can also write it as 2 : 1. If there are two bunnies, the ratio of eyes to noses becomes 4 to 2, or 4 : 2. For three bunnies, the ratio is 6 to 3, or 6 : 3, and for four bunnies, the ratio is 8 to 4, or 8 : 4. Like with equivalent fractions, you can multiply both numbers in a ratio to get another, equivalent ratio. Multiply 2 : 1 by 3 to get 6 : 3, or 6 eyes on 3 bunnies. Try this one yourself: A sign has 5 parts red for every 1 part white. With the same color ratio, a larger sign hasA sign has 5 parts red for every 1 part white. With the same color ratio, a larger sign has 20 parts red. How many parts white does the larger sign have?20 parts red. How many parts white does the larger sign have?
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Part-to-whole ratios are related to fractions.
A pack of 5 markers contains 1 blue marker. This is a part-to-whole ratio. We can represent part-to-whole ratios with fractions. Write this ratio
as 51. We can use equivalent
fractions to represent the number of blue markers in more packs. Two packs of markers have 2 blue
markers out of 10 total, or 102. This is
the same as multiplying the original numerator, 1, by 2 and multiplying the original denominator, 5, by 2. Try this one yourself: Find the part-to-whole ratio that describes the number of blueFind the part-to-whole ratio that describes the number of blue markers in 10 packs of markers.markers in 10 packs of markers.
Part-to-part ratios don’t show the whole.
A fish tank contains 20 fish: 14 blue
and 6 yellow. The ratio 2014 describes
the number of blue fish out of the
total. The ratio 206 describes the
number of yellow fish out of the total. These are both part-to-whole ratios. You can also use 'part-to-part' ratios to show this information. The ratio 14 : 6 compares the number of blue fish to the number of yellow fish. Similarly, the ratio 6 : 14 compares the number of yellow fish to the number of blue fish. Try this one yourself: A bag ofA bag of marbles has 8 red marbles out of 15 total. The marbles that aren’t red are purple. Find the part-marbles has 8 red marbles out of 15 total. The marbles that aren’t red are purple. Find the part- to-part ratio that compares the number of red marbles to the number of purple marbles. Thento-part ratio that compares the number of red marbles to the number of purple marbles. Then find the part-to-part ratio that compares the number of purple marbles to the number of redfind the part-to-part ratio that compares the number of purple marbles to the number of red marbles.marbles.
Graphing ratios shows patterns more visually.
A carnival game involves a basketball hoop. For each basket you make, you win 3 tickets. This is a ratio of 3 : 1. You can use multiplication to make a set of equivalent ratios: 6 : 2, 9 : 3, 12 : 4, 15 : 5. These ratios can be displayed on a coordinate grid. The number of baskets goes on the x-axis, and the number of tickets goes on the y-axis. Then the ratios also represent coordinate pairs: (3, 1), (6, 2), (9, 3), (12, 4), (15, 5). Each point is 3 right and 1 up from the previous point. To predict the number of tickets more easily, draw a straight line through these points and keep going up and to the right. Try this one yourself:To get into a carnival, each child admission ticket is $5. Graph the cost of 1,To get into a carnival, each child admission ticket is $5. Graph the cost of 1, 2, 3, 4, and 5 admission tickets on a coordinate grid. Draw a line through these points to find the2, 3, 4, and 5 admission tickets on a coordinate grid. Draw a line through these points to find the cost of 8 admission tickets.cost of 8 admission tickets.
Many careers use ratios.
Chefs use ratios to calculate the right amount of ingredients to use in a recipe. Florists use ratios to determine how many flowers are needed in each arrangement at a banquet. One of the responsibilities of a doctor is prescribing medication. Doctors often use ratios based on body weight to determine the proper dosages their patients should take.
RATIOS VOCABULARY
Ratio A comparison of two amounts.
Colon The math symbol used for the word “to.”
Fraction A numerator over a denominator, separated by a fraction bar.
Equivalent fractions Fractions that have the same value even though they contain different numbers.
Part-to-part ratio A comparison of two parts from the same whole.
Part-to-whole ratio A comparison of one of the parts of a whole to the total amount in the whole.
RATIOS DISCUSSION QUESTIONS
Give an example of a part-to-whole ratio in words and in symbols.
Orange juice is 2 parts fruit concentrate out of 5 parts total. 25 of the juice is fruit concentrate.
Give an example of a part-to-part ratio in words and in symbols.
There are 3 pink carnations for every 2 red roses. 3 : 2
Let’s say there are 8 teachers in a group of 40 teachers and students. Without
simplifying or making the numbers bigger, what ratios describe this
situation?
8 40 are teachers. 8 teachers : 32 students. 32 students : 8 teachers.^
32 40 are students.
Without doubling or halving, name some ratios that are equivalent to 100 :
10 : 20. 25 : 50. 300 : 600. 1,000 : 2,000. (The goal is to get past multiplying and dividing by 2.)
How can you display ratios from a table on a graph?
Use one row of data for the x-coordinates and the other row for the y-coordinates. Place a point for each ratio and draw a line between the points.
