Math worksheet demonstrating fractions using shaded shapes and numerical examples.

Let’s solve this step by step.

We are given shapes divided into equal parts, and some of those parts are shaded. We need to find:

1. Unit Fraction — what fraction one small part is of the whole shape.
2. Total Number of Units Shaded — how many of those small parts are shaded in total (across all shapes shown).
3. Fraction Represented — multiply unit fraction × number of shaded units → that gives the total shaded amount as a fraction.

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Part b:

You have 2 big squares. Each square is divided into 8 equal triangles (like slicing a pizza into 8 slices). So each triangle is 1/8 of one square → that’s the unit fraction.

Now count how many triangles are shaded:
- First square: all 8 triangles are shaded.
- Second square: 7 triangles are shaded (one is white).
→ Total shaded = 8 + 7 = 15

So total shaded amount = 15 × (1/8) = 15/8

✔ Your answer for part b is correct!

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Part c:

You have 3 rectangles. Each rectangle is divided into 6 equal smaller rectangles (2 rows × 3 columns). So each small rectangle is 1/6 of one big rectangle → unit fraction = 1/6

Count shaded parts:
- First rectangle: 0 shaded
- Second rectangle: 0 shaded
- Third rectangle: 2 shaded (bottom right two)
→ Total shaded = 2

Total shaded amount = 2 × (1/6) = 2/6

But wait — we can simplify 2/6! Divide numerator and denominator by 2 → 1/3

However, looking at your work, you wrote 2/6, which is mathematically correct but not simplified. In most school settings, they want fractions simplified unless told otherwise.

BUT — let’s check the sample in part a:

In part a, they had 5 halves → wrote 5/2, which is an improper fraction and not simplified to mixed number. So maybe they don’t require simplifying here? Let’s see...

Actually, in part a, 5/2 is already in simplest form (can’t reduce it). But 2/6 can be reduced.

Still — since the problem doesn’t say “simplify”, and your teacher might accept 2/6, but ideally you should write 1/3.

Wait — look again at the image: in part c, you wrote “2/6” but then crossed out the 6 and wrote 5? That seems like a mistake.

Actually, no — looking closely, you wrote:

Unit Fraction: 1/6
Total shaded: 2
Then in last column: you wrote 2 over 6, but then changed the 6 to 5? That’s incorrect.

The third rectangle has 6 parts, 2 shaded → so 2/6.

There’s no reason to change denominator to 5.

So correct answer for part c is 2/6 or better yet 1/3.

But since the sample used unsimplified form only when necessary, and 2/6 reduces, I’d go with 1/3.

Wait — let me double-check the shading.

Looking at part c:

Three rectangles side by side.

Each is 2x3 grid → 6 cells.

First: all white → 0 shaded
Second: all white → 0 shaded
Third: bottom row, last two cells shaded → yes, 2 shaded.

So 2 out of 6 per rectangle? No — unit fraction is based on ONE whole rectangle. Since each small cell is 1/6 of one rectangle, and you have 2 shaded cells across all rectangles, total shaded = 2 × (1/6) = 2/6.

Yes.

So final answer for c: 2/6 or 1/3

But in the context of the worksheet, since part a kept 5/2 (which is fine), and part b has 15/8 (also fine), perhaps they expect unreduced forms? Actually 15/8 can’t be reduced, 5/2 can’t be reduced, but 2/6 can.

I think best practice is to reduce.

But let’s see what the student wrote: they wrote 2/6, then changed denominator to 5? That’s wrong. Probably a slip.

Correct value is 2/6 → simplify to 1/3.

But to match style of other answers, maybe leave as 2/6? Hmm.

Actually, in the sample, they didn’t have any reducible fractions. So perhaps for consistency, we leave as 2/6? Or reduce?

I think for accuracy, we should reduce.

But let’s hold on — maybe I miscounted.

Another way: total shaded area.

Each small rectangle is 1/6 of one big rectangle.

You have 2 shaded small rectangles → so total shaded = 2 * (1/6) = 2/6 = 1/3.

Yes.

So I’ll go with 1/3 for part c.

But the student wrote 2/6 then altered it — probably confused.

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Part d:

Two rectangles. Each is divided into 5 equal vertical strips. So each strip is 1/5 of one rectangle → unit fraction = 1/5

Count shaded strips:

First rectangle: 0 shaded
Second rectangle: 4 shaded (all except first one)

Total shaded = 4

Total shaded amount = 4 × (1/5) = 4/5

This is already simplified.

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Now, let’s summarize:

Part b:
Unit Fraction: 1/8
Total shaded: 15
Fraction: 15/8 ✔

Part c:
Unit Fraction: 1/6
Total shaded: 2
Fraction: 2/6 → simplify to 1/3

Part d:
Unit Fraction: 1/5
Total shaded: 4
Fraction: 4/5

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Final Answer:

b. Unit Fraction: \frac{1}{8}, Total Shaded: 15, Fraction: \frac{15}{8}
c. Unit Fraction: \frac{1}{6}, Total Shaded: 2, Fraction: \frac{1}{3}
d. Unit Fraction: \frac{1}{5}, Total Shaded: 4, Fraction: \frac{4}{5}