NF Test worksheet focusing on fractions and operations.

Let's solve each problem on the "Number & Operations - Fractions Test" step by step and explain the solutions.

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1. Which letter shows 10/7?

We are given a number line from 0 to 2, marked in increments of 1/7.

- The number line is divided into 7 equal parts between 0 and 1, so each tick represents 1/7.
- So:
- 1 = 7/7
- 2 = 14/7
- We need to find where 10/7 is located.

Since:
- 7/7 = 1
- 8/7 = 1 + 1/7
- 9/7 = 1 + 2/7
- 10/7 = 1 + 3/7

So, 10/7 is 3/7 past 1, which is three ticks after 1.

Looking at the number line:
- Letter C is located at 10/7 (since it’s three ticks after 1).

✔ Answer: C

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2. Using the number lines, what fraction is equivalent to 1/4?

We are given two number lines:

- First number line: from 0 to 1, divided into 4 equal parts → each part is 1/4
- Second number line: from 0 to 1, divided into 8 equal parts → each part is 1/8

We are to find a fraction on the second number line that is equivalent to 1/4.

- 1/4 = ?/8
- Multiply numerator and denominator by 2:
$$
\frac{1}{4} = \frac{2}{8}
$$

So, 2/8 is equivalent to 1/4.

✔ Answer: 2/8

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3. Scale figure B to make it equivalent with figure A.

We have two rectangles:

- Figure A: Shaded area = 3 out of 6 parts → $ \frac{3}{6} $
- Figure B: 2 out of 4 parts → $ \frac{2}{4} $

But we are to scale Figure B so it matches Figure A.

Wait — let's clarify: both figures represent fractions.

- $ \frac{3}{6} = \frac{1}{2} $
- $ \frac{2}{4} = \frac{1}{2} $

They are already equivalent!

But the instruction says: "Scale figure B to make it equivalent with figure A."

This likely means: how many parts should Figure B be divided into to match the size of Figure A?

Alternatively, maybe it's asking: what scale factor would make the shaded portion of Figure B match Figure A?

But since both are already $ \frac{1}{2} $, they're equivalent.

Wait — perhaps Figure B has only 2 shaded out of 4, but we want to scale it so it matches Figure A’s shading pattern.

Alternatively, maybe the task is to shade Figure B so that it has the same proportion as Figure A, which is $ \frac{3}{6} = \frac{1}{2} $.

So if Figure B has 4 parts, then $ \frac{1}{2} $ of 4 is 2 parts shaded — which it already has.

So no change needed?

But the question says “Scale figure B” — perhaps it's asking for the scaling factor.

Let’s suppose Figure A has 6 parts, Figure B has 4 parts.

To make them comparable, we can scale up or down.

But since both represent $ \frac{1}{2} $, they’re already equivalent.

Maybe the student is supposed to draw or shade Figure B so that it matches Figure A’s fraction.

But since both are $ \frac{1}{2} $, it's already correct.

✔ Conclusion: Figure B is already equivalent to Figure A. No scaling needed.

But if the task is to write the fraction or explain, then:

- $ \frac{3}{6} = \frac{2}{4} = \frac{1}{2} $

✔ Answer: Figure B is already equivalent to Figure A.

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4. List one equivalent fraction for each.

Given:

1. $ \frac{1}{2} $ → Equivalent: $ \frac{2}{4}, \frac{3}{6}, \frac{4}{8}, \dots $
✔ Example: $ \frac{2}{4} $

2. $ \frac{2}{3} $ → Multiply numerator and denominator by 2: $ \frac{4}{6} $
✔ Example: $ \frac{4}{6} $

3. $ \frac{1}{3} $ → $ \frac{2}{6} $
✔ Example: $ \frac{2}{6} $

4. $ \frac{4}{5} $ → $ \frac{8}{10} $
✔ Example: $ \frac{8}{10} $

✔ Answers:
- $ \frac{1}{2} $ → $ \frac{2}{4} $
- $ \frac{2}{3} $ → $ \frac{4}{6} $
- $ \frac{1}{3} $ → $ \frac{2}{6} $
- $ \frac{4}{5} $ → $ \frac{8}{10} $

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5. Solve each problem using <, >, or =

Compare:

1. $ \frac{4}{5} \quad \text{vs} \quad \frac{5}{6} $

Find common denominator: LCM of 5 and 6 is 30.

- $ \frac{4}{5} = \frac{24}{30} $
- $ \frac{5}{6} = \frac{25}{30} $

Since $ 24 < 25 $, $ \frac{4}{5} < \frac{5}{6} $

✔ Answer: $ \frac{4}{5} < \frac{5}{6} $

2. $ \frac{5}{8} \quad \text{vs} \quad \frac{5}{6} $

Same numerator, compare denominators.

- Larger denominator → smaller fraction.

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

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

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6. Write each as a whole number

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

2. $ \frac{12}{3} $ → $ 12 ÷ 3 = 4 $
✔ Answer: 4

3. $ \frac{18}{6} $ → $ 18 ÷ 6 = 3 $
✔ Answer: 3

4. $ \frac{14}{2} $ → $ 14 ÷ 2 = 7 $
✔ Answer: 7

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✔ Final Answers Summary:

1. Which letter shows 10/7? → C
2. Fraction equivalent to 1/4 on second number line? → 2/8
3. Scale Figure B to match Figure A? → Already equivalent; both represent $ \frac{1}{2} $.
4. Equivalent fractions:
- $ \frac{1}{2} $ → $ \frac{2}{4} $
- $ \frac{2}{3} $ → $ \frac{4}{6} $
- $ \frac{1}{3} $ → $ \frac{2}{6} $
- $ \frac{4}{5} $ → $ \frac{8}{10} $
5. Compare:
- $ \frac{4}{5} < \frac{5}{6} $
- $ \frac{5}{8} < \frac{5}{6} $
6. Write as whole numbers:
- $ \frac{8}{4} = 2 $
- $ \frac{12}{3} = 4 $
- $ \frac{18}{6} = 3 $
- $ \frac{14}{2} = 7 $

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