Two types of ratios — know which one a question is asking for
Two Types of Ratios
Part-to-Part: Compares one part of a group to another part. Part-to-Whole: Compares one part to the entire group (the total).
A class has 12 boys and 8 girls (20 total)
Part-to-Part: Boys to girls = 12:8
Part-to-Whole: Boys to total students = 12:20
Part-to-Whole: Girls to total students = 8:20
How to Tell Which Type
Look at what's being compared. If both numbers are subgroups of the same total, it's part-to-part. If one number is a subgroup and the other is the total, it's part-to-whole.
"Ratio of boys to girls" → part-to-part (two subgroups).
"Ratio of boys to all students" → part-to-whole (subgroup to total).
"What fraction of students are boys?" → part-to-whole (12 out of 20).
Converting Between Them
If you know the part-to-part ratio, you can find the part-to-whole ratio by adding the parts to get the total.
Boys to girls = 3:2
Total parts: 3 + 2 = 5
Boys to total: 3:5
Girls to total: 2:5
💡 Connection to fractions and percents: Part-to-whole ratios translate directly to fractions. Boys are 3/5 of the class = 60%. Part-to-part ratios don't convert to fractions as directly.
🎯 Practice Problems
1. A bag has 6 red and 4 blue marbles. What is the part-to-part ratio of red to blue?
A) 6:10
B) 4:6
C) 6:4
D) 10:6
2. Same bag (6 red, 4 blue). What is the part-to-whole ratio of blue marbles?
A) 4:6
B) 4:10
C) 6:10
D) 10:4
3. 'What fraction of the team are seniors?' — is this part-to-part or part-to-whole?
A) Part-to-part
B) Part-to-whole
C) Neither
D) Both
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🎯 Bonus Practice
1. The ratio of cats to dogs is 5:3. What is the ratio of cats to total animals?
A) 5:3
B) 3:8
C) 5:8
D) 8:5
2. A survey found 30 yes and 20 no. What is the part-to-whole ratio of yes responses?
A) 30:20
B) 20:50
C) 30:50
D) 50:30
3. 'The ratio of wins to losses is 7:3.' Is this part-to-part or part-to-whole?
A) Part-to-whole
B) Part-to-part
C) Neither
D) Cannot tell
4. If the ratio of adults to children is 2:5, what fraction of the group are children?
A) 2/5
B) 5/2
C) 5/7
D) 2/7
5. A smoothie uses 3 parts fruit and 1 part yogurt. What part-to-whole ratio is yogurt?