Identify Place Value Grids as Fractions & Decimals - Math ... - Free Printable

Let's solve each problem step by step. The goal is to write the shaded portions as fractions and decimals based on the visual representations.

Each grid or bar represents a whole, and we need to determine what fraction (and decimal) of the total is shaded.

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🔹 Problem 1

Visuals:
- First square: Fully shaded → 100% = 1
- Second square: Mostly shaded, but missing a small part

Let’s count:
- Each square has 100 small squares (10×10)
- First square: 100 shaded → 1 whole
- Second square: Let's count unshaded squares
- Bottom row: 10 squares, 2 are white → so 8 shaded in that row?
- Wait — actually, look closely: the second square has a few white squares at the bottom right.
- Count white squares: It looks like 3 rows of 10, but only 1 row is fully white? No.

Wait — let’s re-express:

Actually, the second square appears to have:
- Top-left corner shaded
- A small white rectangle at the bottom-right.

Looking carefully: it seems like only 10 squares are unshaded (last row, last 10 columns). So:
- Shaded in second square: 100 − 10 = 90
- So total shaded: 100 + 90 = 190 out of 200?

But wait — are both squares equal in value? Yes — each represents 1 whole.

So:
- First square: 100/100 = 1
- Second square: 90/100 = 0.9
- Total shaded: 1 + 0.9 = 1.9

So:
- Fraction: $ \frac{190}{100} = \frac{19}{10} $
- Decimal: 1.9

✔ Answer 1:
- Fraction: $ \frac{19}{10} $
- Decimal: 1.9

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🔹 Problem 2

Three 10×10 grids.

- First two: Fully shaded → 100 each → 2 wholes
- Third: Partially shaded

Count shaded in third:
- Look at the bottom-right: some squares are white.
- It seems like the bottom row has 5 white squares (right side), so shaded = 100 − 5 = 95
- So total shaded: 100 + 100 + 95 = 295

Total parts: 300 (since each is 100)

So:
- Fraction: $ \frac{295}{100} = \frac{59}{20} $
- Decimal: 2.95

✔ Answer 2:
- Fraction: $ \frac{59}{20} $
- Decimal: 2.95

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🔹 Problem 3

Four rectangles, each divided into 10 vertical bars → each bar = 1/10

- First three: fully shaded → 3 wholes
- Fourth: 8 out of 10 bars shaded

So total shaded = 3 + 0.8 = 3.8

- Fraction: $ \frac{38}{10} = \frac{19}{5} $
- Decimal: 3.8

✔ Answer 3:
- Fraction: $ \frac{19}{5} $
- Decimal: 3.8

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🔹 Problem 4

Three rectangles, each with 10 vertical bars (each = 1/10)

- First two: fully shaded → 2 wholes
- Third: 2 out of 10 bars shaded → 0.2

Total: 2 + 0.2 = 2.2

- Fraction: $ \frac{22}{10} = \frac{11}{5} $
- Decimal: 2.2

✔ Answer 4:
- Fraction: $ \frac{11}{5} $
- Decimal: 2.2

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🔹 Problem 5

Four 10×10 grids (each = 100 squares)

- First three: fully shaded → 3 wholes
- Fourth: partially shaded

Look at fourth grid:
- Only 3 squares are white (top-left corner?)
- So shaded = 100 − 3 = 97

Total shaded: 3 + 0.97 = 3.97

- Fraction: $ \frac{397}{100} $
- Decimal: 3.97

✔ Answer 5:
- Fraction: $ \frac{397}{100} $
- Decimal: 3.97

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✔ Final Answers:

| Problem | Fraction | Decimal |
|--------|----------------|---------|
| 1 | $ \frac{19}{10} $ | 1.9 |
| 2 | $ \frac{59}{20} $ | 2.95 |
| 3 | $ \frac{19}{5} $ | 3.8 |
| 4 | $ \frac{11}{5} $ | 2.2 |
| 5 | $ \frac{397}{100} $ | 3.97 |

> 💡 Tip: Always check if the fraction can be simplified. For example, 19/10 and 397/100 are already in simplest form since 397 is prime.

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