Two-way tables worksheet | KS3-4 maths | Teachit - Free Printable

Let's solve each question step by step using the two-way tables provided.

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Problem 1: School Dinners vs. Packed Lunches

Table:
| | Boys | Girls |
|---------------|------|-------|
| School dinner | 24 | 16 |
| Packed lunch | 12 | 32 |

#### a. How many boys have a school dinner?
From the table: 24 boys have a school dinner.

✔ Answer: 24

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#### b. How many girls have a packed lunch?
From the table: 32 girls have a packed lunch.

✔ Answer: 32

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#### c. How many students stayed for a school dinner?
Add boys and girls who had school dinners:
- Boys: 24
- Girls: 16
Total = 24 + 16 = 40

✔ Answer: 40

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#### d. How many boys were there?
Boys with school dinner + boys with packed lunch:
- 24 + 12 = 36 boys

✔ Answer: 36

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#### e. How many students were there altogether?
Add all entries:
- Boys: 24 (dinner) + 12 (packed) = 36
- Girls: 16 (dinner) + 32 (packed) = 48
Total = 36 + 48 = 84 students

✔ Answer: 84

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#### f. What fraction of the students had a packed lunch?
Packed lunch total = 12 (boys) + 32 (girls) = 44
Total students = 84
Fraction = $ \frac{44}{84} $

Simplify: Divide numerator and denominator by 4 → $ \frac{11}{21} $

✔ Answer: $ \frac{11}{21} $

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Problem 2: Gender and Wearing Glasses

Table:
| | Boys | Girls |
|--------------|------|-------|
| Glasses | 24 | 16 |
| No glasses | 12 | 32 |

#### a. How many people wear glasses?
Glasses: 24 (boys) + 16 (girls) = 40

✔ Answer: 40

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#### b. How many girls were in the survey?
Girls with glasses + no glasses = 16 + 32 = 48

✔ Answer: 48

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#### c. What fraction of the girls wear glasses?
Girls who wear glasses = 16
Total girls = 48
Fraction = $ \frac{16}{48} = \frac{1}{3} $

✔ Answer: $ \frac{1}{3} $

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#### d. What fraction of the students do not wear glasses?
No glasses: 12 (boys) + 32 (girls) = 44
Total students = 24+16+12+32 = 84
Fraction = $ \frac{44}{84} = \frac{11}{21} $

✔ Answer: $ \frac{11}{21} $

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Problem 3: Left-handed vs. Right-handed Adults

Table:
| | Men | Women |
|-------------|-----|-------|
| Left-handed | 8 | 17 |
| Right-handed| 15 | 24 |

Total adults = 64 (given)

#### a. How many men are in the survey?
Men: left-handed (8) + right-handed (15) = 23

✔ Answer: 23

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#### b. How many of the 64 adults are right-handed?
Right-handed: 15 (men) + 24 (women) = 39

✔ Answer: 39

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#### c. What fraction of those asked were right-handed men?
Right-handed men = 15
Total adults = 64
Fraction = $ \frac{15}{64} $

✔ Answer: $ \frac{15}{64} $

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#### d. What fraction of the women are left-handed?
Left-handed women = 17
Total women = 17 + 24 = 41
Fraction = $ \frac{17}{41} $

✔ Answer: $ \frac{17}{41} $

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Problem 4: Pets and Gender

Table:
| | Cat | Dog |
|-------|-----|-----|
| Boy | 3 | 7 |
| Girl | 9 | 5 |

#### a. What fraction are cats?
Total cats = 3 (boys) + 9 (girls) = 12
Total pets = 3+7+9+5 = 24
Fraction = $ \frac{12}{24} = \frac{1}{2} $

✔ Answer: $ \frac{1}{2} $

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#### b. Of the boys, what fraction have dogs?
Boys: 3 (cats) + 7 (dogs) = 10
Dogs = 7
Fraction = $ \frac{7}{10} $

✔ Answer: $ \frac{7}{10} $

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#### c. Of cats, what fraction belong to boys?
Cats: 3 (boys), 9 (girls) → Total = 12
Fraction belonging to boys = $ \frac{3}{12} = \frac{1}{4} $

✔ Answer: $ \frac{1}{4} $

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#### d. What fraction of the owners are girls?
Total owners = total pets = 24
Girl owners: 9 (cats) + 5 (dogs) = 14
Fraction = $ \frac{14}{24} = \frac{7}{12} $

✔ Answer: $ \frac{7}{12} $

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✔ Final Answers Summary:

#### Problem 1
a. 24
b. 32
c. 40
d. 36
e. 84
f. $ \frac{11}{21} $

#### Problem 2
a. 40
b. 48
c. $ \frac{1}{3} $
d. $ \frac{11}{21} $

#### Problem 3
a. 23
b. 39
c. $ \frac{15}{64} $
d. $ \frac{17}{41} $

#### Problem 4
a. $ \frac{1}{2} $
b. $ \frac{7}{10} $
c. $ \frac{1}{4} $
d. $ \frac{7}{12} $

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