Chapter 3 Test on Fractions and Mixed Numbers, Form A.

Let's solve each question from the test step by step.

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Question 1: Which fraction has the same value as $ 1\frac{1}{4} $?

We are given a mixed number:
$$
1\frac{1}{4}
$$

To convert this to an improper fraction:

- Multiply the whole number (1) by the denominator (4):
$$
1 \times 4 = 4
$$
- Add the numerator (1):
$$
4 + 1 = 5
$$
- Place over the original denominator:
$$
\frac{5}{4}
$$

So, $ 1\frac{1}{4} = \frac{5}{4} $

Now check the options:
a. $ \frac{2}{4} $ → No
b. $ \frac{5}{4} $ → ✔ Yes
c. $ \frac{11}{4} $ → No
d. $ \frac{1}{4} $ → No

✔ Answer: b. $ \frac{5}{4} $

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Question 2: What is the value of $ \frac{3}{8} \div \frac{2}{5} $?

To divide fractions, we multiply by the reciprocal:

$$
\frac{3}{8} \div \frac{2}{5} = \frac{3}{8} \times \frac{5}{2}
$$

Now multiply numerators and denominators:

- Numerator: $ 3 \times 5 = 15 $
- Denominator: $ 8 \times 2 = 16 $

So,
$$
\frac{15}{16}
$$

Check the options:
a. $ \frac{6}{40} $ → simplify: $ \frac{3}{20} $ → No
b. $ \frac{15}{16} $ → ✔ Yes
c. $ \frac{1}{16} $ → No
d. $ \frac{10}{16} $ → $ \frac{5}{8} $ → No

✔ Answer: b. $ \frac{15}{16} $

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Question 3: What is $ 32 \div 7 $ expressed as a mixed number?

Divide 32 by 7:

- $ 7 \times 4 = 28 $
- $ 32 - 28 = 4 $

So,
$$
32 \div 7 = 4 \frac{4}{7}
$$

Check the options:
a. $ \frac{4}{7} $ → No
b. $ 4\frac{4}{7} $ → ✔ Yes
c. $ \frac{7}{4} $ → No
d. $ \frac{32}{7} $ → This is the improper fraction, not mixed → Not correct format

✔ Answer: b. $ 4\frac{4}{7} $

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Question 4: Which fraction has the same value as $ 0.42 $?

Convert decimal $ 0.42 $ to a fraction:

- $ 0.42 = \frac{42}{100} $
- Simplify: Divide numerator and denominator by 2:
$$
\frac{42 \div 2}{100 \div 2} = \frac{21}{50}
$$

Now check the options:
a. $ \frac{42}{100} $ → Equal but not simplified → Not best answer
b. $ \frac{21}{50} $ → ✔ Yes
c. $ \frac{2}{5} $ → $ 0.4 $ → No
d. $ \frac{42}{10} $ → $ 4.2 $ → No

✔ Answer: b. $ \frac{21}{50} $

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✔ Final Answers:

1. b. $ \frac{5}{4} $
2. b. $ \frac{15}{16} $
3. b. $ 4\frac{4}{7} $
4. b. $ \frac{21}{50} $

Let me know if you'd like these explained in another way or need help with more questions!