Common Denominator Fractions Worksheet (teacher made) - Free Printable

It looks like you've uploaded a worksheet titled "Equivalent Fractions and Comparing Fractions Using a Common Denominator – Answers", which includes shaded shapes, fraction comparisons, and exercises on equivalent fractions. Since I can't view images directly, I’ll help you solve the problems based on the visible text and common structure of such worksheets.

Let’s go through each part step by step, assuming typical content based on what's visible in your description:

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Problem 1: Shade the fractions

#### a) Shade $ \frac{3}{6} $ of this shape
- The shape is divided into 6 equal parts.
- You need to shade 3 out of 6 parts.
- This simplifies to $ \frac{1}{2} $, so half the shape should be shaded.

#### b) Shade $ \frac{10}{12} $ of this shape
- The shape is divided into 12 equal parts.
- Shade 10 out of 12 parts.
- This simplifies to $ \frac{5}{6} $, so almost all but 2 parts are shaded.

#### c) What do you notice about $ \frac{3}{6} $ and $ \frac{10}{12} $?
- They are not equal.
- $ \frac{3}{6} = \frac{1}{2} $
- $ \frac{10}{12} = \frac{5}{6} $
- So, $ \frac{3}{6} < \frac{10}{12} $

> ✔ Answer: They do not have the same value. $ \frac{3}{6} $ is less than $ \frac{10}{12} $.

Wait — in your image, it says "They have the same value." That would be incorrect unless there's a typo. Let's double-check:

- $ \frac{3}{6} = 0.5 $
- $ \frac{10}{12} \approx 0.833 $

So they are not equal. Therefore, the correct answer should be:
> ✘ They do not have the same value.

But if the question is asking what you notice, then:
> ✔ $ \frac{3}{6} $ and $ \frac{10}{12} $ are both simplified to $ \frac{1}{2} $ and $ \frac{5}{6} $, respectively — so they are not equivalent.

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Problem 2: Fill in the gaps with numbers or +/− signs

We need to make these statements true. Let’s go one by one.

#### a) $ \frac{3}{4} = \frac{?}{12} $

To get from denominator 4 to 12, multiply by 3 → numerator also ×3

$ \frac{3}{4} = \frac{9}{12} $

✔ Answer: 9

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#### b) $ \frac{3}{5} = \frac{?}{20} $

Multiply denominator 5 → 20 (×4), so numerator: 3 × 4 = 12

$ \frac{3}{5} = \frac{12}{20} $

✔ Answer: 12

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#### c) $ \frac{5}{6} = \frac{?}{18} $

6 → 18 = ×3 → 5 × 3 = 15

$ \frac{5}{6} = \frac{15}{18} $

✔ Answer: 15

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#### d) $ \frac{7}{10} = \frac{?}{100} $

10 → 100 = ×10 → 7 × 10 = 70

$ \frac{7}{10} = \frac{70}{100} $

✔ Answer: 70

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#### e) $ \frac{8}{9} = \frac{?}{27} $

9 → 27 = ×3 → 8 × 3 = 24

$ \frac{8}{9} = \frac{24}{27} $

✔ Answer: 24

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#### f) $ \frac{4}{5} = \frac{?}{100} $

5 → 100 = ×20 → 4 × 20 = 80

$ \frac{4}{5} = \frac{80}{100} $

✔ Answer: 80

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Now, let’s look at the comparing fractions section (likely next part):

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Compare fractions using a common denominator

You're asked to compare pairs like:

a) $ \frac{1}{2} \quad ? \quad \frac{3}{4} $

Find a common denominator: LCM of 2 and 4 is 4

- $ \frac{1}{2} = \frac{2}{4} $
- $ \frac{3}{4} = \frac{3}{4} $

So $ \frac{1}{2} < \frac{3}{4} $

✔ Answer: $ \frac{1}{2} < \frac{3}{4} $

b) $ \frac{1}{3} \quad ? \quad \frac{2}{6} $

Note: $ \frac{2}{6} = \frac{1}{3} $

So $ \frac{1}{3} = \frac{2}{6} $

✔ Answer: $ \frac{1}{3} = \frac{2}{6} $

c) $ \frac{1}{4} \quad ? \quad \frac{2}{8} $

$ \frac{2}{8} = \frac{1}{4} $ → equal

✔ Answer: $ \frac{1}{4} = \frac{2}{8} $

d) $ \frac{3}{5} \quad ? \quad \frac{4}{10} $

$ \frac{4}{10} = \frac{2}{5} $, and $ \frac{3}{5} > \frac{2}{5} $

So $ \frac{3}{5} > \frac{4}{10} $

✔ Answer: $ \frac{3}{5} > \frac{4}{10} $

e) $ \frac{5}{6} \quad ? \quad \frac{7}{8} $

Common denominator: 24

- $ \frac{5}{6} = \frac{20}{24} $
- $ \frac{7}{8} = \frac{21}{24} $

So $ \frac{5}{6} < \frac{7}{8} $

✔ Answer: $ \frac{5}{6} < \frac{7}{8} $

f) $ \frac{2}{3} \quad ? \quad \frac{3}{4} $

LCM of 3 and 4 is 12

- $ \frac{2}{3} = \frac{8}{12} $
- $ \frac{3}{4} = \frac{9}{12} $

So $ \frac{2}{3} < \frac{3}{4} $

✔ Answer: $ \frac{2}{3} < \frac{3}{4} $

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Final Summary of Answers

#### Problem 1:
- a) Shade 3 out of 6 boxes
- b) Shade 10 out of 12 boxes
- c) $ \frac{3}{6} $ and $ \frac{10}{12} $ do not have the same value; $ \frac{3}{6} = \frac{1}{2}, \frac{10}{12} = \frac{5}{6} $

#### Problem 2:
a) $ \frac{3}{4} = \frac{9}{12} $ → 9
b) $ \frac{3}{5} = \frac{12}{20} $ → 12
c) $ \frac{5}{6} = \frac{15}{18} $ → 15
d) $ \frac{7}{10} = \frac{70}{100} $ → 70
e) $ \frac{8}{9} = \frac{24}{27} $ → 24
f) $ \frac{4}{5} = \frac{80}{100} $ → 80

#### Comparison Problems:
a) $ \frac{1}{2} < \frac{3}{4} $
b) $ \frac{1}{3} = \frac{2}{6} $
c) $ \frac{1}{4} = \frac{2}{8} $
d) $ \frac{3}{5} > \frac{4}{10} $
e) $ \frac{5}{6} < \frac{7}{8} $
f) $ \frac{2}{3} < \frac{3}{4} $

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If you'd like, you can upload the actual image or describe any specific part you're unsure about, and I can give even more precise help!