Math worksheet on converting time to fractions with exercises and a real-world application problem.

Let’s work through each section step by step.

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Section A: Work out the following.

We are finding fractions of 60. To do this, multiply the fraction by 60.

1) ½ of 60 = (1 × 60) ÷ 2 = 60 ÷ 2 = 30

2) ⅓ of 60 = (1 × 60) ÷ 3 = 60 ÷ 3 = 20

3) ⅕ of 60 = (1 × 60) ÷ 5 = 60 ÷ 5 = 12

4) ¹⁄₁₂ of 60 = (1 × 60) ÷ 12 = 60 ÷ 12 = 5

5) ⁵₆ of 60 = (5 × 60) ÷ 6 = 300 ÷ 6 = 50

6) ⁷⁄₁₀ of 60 = (7 × 60) ÷ 10 = 420 ÷ 10 = 42

✔ All correct.

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Section B: Find the missing value.

We’re using equivalent fractions — multiplying numerator and denominator by same number to get equal fractions.

1) ⁷⁄₁₅ = ?⁄₃₀ = ?⁄₆₀

- To go from 15 to 30 → multiply by 2 → so 7 × 2 = 14
- To go from 15 to 60 → multiply by 4 → so 7 × 4 = 28

→ ⁷⁄₁₅ = 14⁄₃₀ = 28⁄₀

2) ²⁄₃ = ?⁄₂₄ = ?⁄₆₀

- 3 to 24 → ×8 → 2 × 8 = 16
- 3 to 60 → ×20 → 2 × 20 = 40

→ ²⁄₃ = 16⁄₂₄ = 40⁄₆₀

3) ?⁄₅ = ¹⁶⁄₂₀ = ?⁄₆₀

- 20 ÷ 4 = 5 → so 16 ÷ 4 = 4
- 20 × 3 = 60 → so 16 × 3 = 48

→ 4⁄₅ = ¹⁶⁄₂₀ = 48⁄₆₀

4) ?⁄₁₀ = ⁵⁄₂₅ = ?⁄₆₀

First simplify ⁵⁄₂₅ → divide top and bottom by 5 → ¹⁄₅

Now:

- ¹⁄₅ = ?⁄₁₀ → 5×2=10 → 1×2=2
- ¹⁄ = ?⁄₆₀ → 5×12=60 → 1×12=12

→ 2⁄₁₀ = ⁵⁄₂ = 12⁄₆₀

✔ All correct.

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Section C: Convert minutes to hours (as fractions).

We know: 60 minutes = 1 hour → so to convert minutes to hours, divide by 60.

Given example: 15 min = ¹⁵⁄₆₀ = ¼ hour ✔️

Now:

1) 20 min = ²⁰⁄₀ → simplify: divide by 20 → ⅓ hour

2) 6 min = ⁶⁄₆₀ → simplify: divide by 6 → ¹⁄₁₀ hour

3) 36 min = ³⁶⁄₆₀ → simplify: divide by 12 → ³⁶÷12=3, 60÷12=5 → ³⁄₅ hour

Now reverse: given fraction of an hour, find minutes.

Multiply fraction by 60.

1) ⅔ hour = (2/3) × 60 = 120 ÷ 3 = 40 minutes

2) ⁷⁄₁₂ hour = (7/12) × 60 = 420 ÷ 12 = 35 minutes

3) ⁹⁄₂₀ hour = (9/20) × 60 = 540 ÷ 20 = 27 minutes

4) ⁷⁄₁₂ hour = already done above → 35 minutes

Wait — let’s check the table again. The right side has:

- ⅔ hour → ? min → we did 40
- ⁷₁₂ hour → ? min → 35
- ⁹₂₀ hour → ? min → 27
- ⁷⁄₁₂ hour → ? min → 35 (again? maybe typo, but same answer)

But looking at the original image, it says:

Right column:

Minutes | Hour
---|---
? | ⅔ hour
? | ⁷⁄₁₂ hour
? | ⁹⁄₂₀ hour
? | ⁷⁄₁₂ hour ← probably should be different? But we’ll calculate as written.

Actually, in the image, last one is ⁷⁄₁₂ hour — same as second. Maybe intentional for practice.

So:

Left side (minutes → hour):

- 20 → ⅓
- 6 → ¹⁄₁₀
- 36 → ³⁄₅

Right side (hour → minutes):

- ⅔ → 40
- ⁷⁄₁₂ → 35
- ⁹⁄₂₀ → 27
- ⁷₁₂ → 35

✔ All correct.

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Extension:

Milly practices violin:

- Monday: 90 minutes
- Thursday: 105 minutes

Total per week = 90 + 105 = 195 minutes

Convert to hours: 195 ÷ 60 = ?

195 ÷ 60 = 3.25 hours → or as fraction: 195/60

Simplify: divide numerator and denominator by 15 → 13/4 → which is 3¼ hours.

Or keep as improper fraction: ¹³⁄₄ hours.

But since question says “how long”, either is fine — but likely expects mixed number or decimal.

In context of fractions, ¹³⁄₄ or 3¼ is good.

But let’s see: 195 ÷ 60 = 3 with remainder 15 → so 3 and 15/60 = 3 and ¼ → 3¼ hours

✔ Correct.

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Final Answer:

Section A:
1) 30
2) 20
3) 12
4) 5
5) 50
6) 42

Section B:
1) 14, 28
2) 16, 40
3) 4, 48
4) 2, 12

Section C:
Left:
20 → ⅓
6 → ¹⁄₁₀
36 → ³⁄₅

Right:
⅔ → 40
⁷⁄₁₂ → 35
⁹⁄₂₀ → 27
⁷⁄₁₂ → 35

Extension: 3¼ hours (or 195 minutes)

But since the user didn’t specify which part to answer, and the task is to solve the problem — I’ll provide all answers clearly.

However, per instruction: “Provide only the final correct answer” — but there are many parts.

Looking back: the user said “Solve the problem accurately.” and the image has multiple sections.

But the response format says: “Final Answer: [Provide only the final correct answer — this should come AFTER all explanations and reasoning.]”

Since there are multiple answers, I will list them all in order.

But perhaps the main task is Section C and Extension? Or all?

Actually, the whole sheet is the task.

To be safe, I’ll summarize all answers concisely.

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Final Answer:

Section A: 30, 20, 12, 5, 50, 42
Section B: 1) 14, 28; 2) 16, 40; 3) 4, 48; 4) 2, 12
Section C: Minutes to Hour: 20→⅓, 6→¹⁄₁₀, 36→³⁄₅; Hour to Minutes: ⅔→40, ⁷⁄₁₂→35, ⁹⁄₂₀→27, ⁷⁄₁₂→35
Extension: 3¼ hours (or 195 minutes)