Fractions Unit 1 worksheet with various fraction exercises for students.

Let's solve each problem step by step and explain the reasoning.

---

1. Write as a fraction:

a) Two-thirds
This is written as:
$$
\frac{2}{3}
$$

b) One and five tenths
This is a mixed number: $1 \frac{5}{10}$
We can write it as an improper fraction or keep it as a mixed number. But since it says "write as a fraction," we’ll convert to an improper fraction:
$$
1 \frac{5}{10} = \frac{10}{10} + \frac{5}{10} = \frac{15}{10}
$$
But this can be simplified (we'll do that in Q2). For now, the answer is:
$$
\frac{15}{10}
$$
Or you could leave it as $1 \frac{5}{10}$, but since it says “fraction,” improper is acceptable.

✔ Final answers:
a) $\boxed{\frac{2}{3}}$
b) $\boxed{\frac{15}{10}}$

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2. Reduce each fraction to lowest terms:

We reduce by dividing numerator and denominator by their greatest common divisor (GCD).

a) $\frac{21}{28}$
Find GCD of 21 and 28 → both divisible by 7:
$$
\frac{21 \div 7}{28 \div 7} = \frac{3}{4}
$$

b) $\frac{150}{300}$
Both divisible by 150:
$$
\frac{150 \div 150}{300 \div 150} = \frac{1}{2}
$$
Alternatively, divide both by 10 first: $\frac{15}{30}$, then by 15 → $\frac{1}{2}$

c) $\frac{36}{63}$
GCD of 36 and 63 is 9:
$$
\frac{36 \div 9}{63 \div 9} = \frac{4}{7}
$$

✔ Answers:
a) $\boxed{\frac{3}{4}}$
b) $\boxed{\frac{1}{2}}$
c) $\boxed{\frac{4}{7}}$

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3. Make the following fraction equivalent:

We need to find missing numerators or denominators so fractions are equal.

a) $\frac{9}{10} = \frac{?}{30}$
We want to scale up from 10 to 30 → multiply by 3:
So, $9 \times 3 = 27$
$$
\frac{9}{10} = \frac{27}{30}
$$

b) $\frac{5}{8} = \frac{?}{16}$
From 8 to 16 → multiply by 2 → $5 \times 2 = 10$
$$
\frac{5}{8} = \frac{10}{16}
$$

c) $\frac{45}{60} = \frac{3}{?}$
We simplify $\frac{45}{60}$: divide numerator and denominator by 15 → $\frac{3}{4}$
So, $\frac{45}{60} = \frac{3}{4}$, therefore the missing denominator is 4

✔ Answers:
a) $\boxed{27}$
b) $\boxed{10}$
c) $\boxed{4}$

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4. Change each fraction to a whole or mixed number:

Divide numerator by denominator.

a) $\frac{24}{6}$
$24 \div 6 = 4$ → whole number
$$
\boxed{4}
$$

b) $\frac{71}{8}$
Divide 71 by 8:
8 × 8 = 64 → remainder 7
So: $8 \frac{7}{8}$
$$
\boxed{8 \frac{7}{8}}
$$

c) $\frac{45}{7}$
7 × 6 = 42 → remainder 3
So: $6 \frac{3}{7}$
$$
\boxed{6 \frac{3}{7}}
$$

✔ Answers:
a) $\boxed{4}$
b) $\boxed{8 \frac{7}{8}}$
c) $\boxed{6 \frac{3}{7}}$

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5. Change each mixed number to an improper fraction:

Use formula:
$$
\text{Improper} = \left(\text{whole} \times \text{denominator}\right) + \text{numerator} \quad \text{over denominator}
$$

a) $4 \frac{1}{6}$
$(4 \times 6) + 1 = 24 + 1 = 25$ → $\frac{25}{6}$
$$
\boxed{\frac{25}{6}}
$$

b) $1 \frac{5}{8}$
$(1 \times 8) + 5 = 8 + 5 = 13$ → $\frac{13}{8}$
$$
\boxed{\frac{13}{8}}
$$

c) $5 \frac{2}{12}$
First simplify $\frac{2}{12} = \frac{1}{6}$, but let’s keep it for now:
$(5 \times 12) + 2 = 60 + 2 = 62$ → $\frac{62}{12}$
But we should reduce: GCD of 62 and 12 is 2 → $\frac{31}{6}$
So final answer: $\boxed{\frac{31}{6}}$ (or $\frac{62}{12}$ if not reduced)

But typically, we reduce:
$$
\boxed{\frac{31}{6}}
$$

✔ Answers:
a) $\boxed{\frac{25}{6}}$
b) $\boxed{\frac{13}{8}}$
c) $\boxed{\frac{31}{6}}$

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6. Word Problem:

There are 24 bottles in a full case.
17 bottles were given away.

a) How many were left?
$$
24 - 17 = 7 \quad \Rightarrow \boxed{7}
$$

b) What fraction of the case:

i) Was given away?
$$
\frac{17}{24}
$$
(Already in lowest terms — GCD of 17 and 24 is 1)
→ $\boxed{\frac{17}{24}}$

ii) Remained?
$$
\frac{7}{24}
$$
Also already reduced → $\boxed{\frac{7}{24}}$

✔ Answers:
a) $\boxed{7}$
b) i) $\boxed{\frac{17}{24}}$
ii) $\boxed{\frac{7}{24}}$

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✔ Final Answer Summary:

1.
a) $\frac{2}{3}$
b) $\frac{15}{10}$

2.
a) $\frac{3}{4}$
b) $\frac{1}{2}$
c) $\frac{4}{7}$

3.
a) 27
b) 10
c) 4

4.
a) 4
b) $8 \frac{7}{8}$
c) $6 \frac{3}{7}$

5.
a) $\frac{25}{6}$
b) $\frac{13}{8}$
c) $\frac{31}{6}$

6.
a) 7
b) i) $\frac{17}{24}$
ii) $\frac{7}{24}$

Let me know if you'd like this formatted as a printable worksheet!