Year 6 Maths Worksheets - Printable Maths Worksheets Year 6 ... - Free Printable

Let's solve each question step by step, ensuring the fractions are in ascending order (from smallest to largest), and that all fractions are in simplest form.

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Question 1:

$$
\frac{\square}{3} \quad \frac{1}{2} \quad \frac{\square}{4}
$$

We need to fill in the blanks so that the three fractions are in order.

Let’s compare:
- $\frac{1}{2} = 0.5$
- We need a fraction less than $0.5$ with denominator 3 → Try $\frac{1}{3} \approx 0.333$
- A fraction greater than $0.5$ with denominator 4 → Try $\frac{3}{4} = 0.75$

So the order is:
$$
\frac{1}{3} < \frac{1}{2} < \frac{3}{4}
$$

✔ All in simplest form.

Answer:
$$
\frac{1}{3} \quad \frac{1}{2} \quad \frac{3}{4}
$$

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Question 2:

$$
\frac{\square}{4} \quad \frac{3}{8} \quad \frac{1}{\square}
$$

We need:
- One fraction with denominator 4 (so numerator is blank)
- One fraction with numerator 1 and unknown denominator

We know:
- $\frac{3}{8} = 0.375$

Try possible values:

Let’s test $\frac{1}{4} = 0.25$, which is less than $0.375$.
Then we need something greater than $0.375$ for $\frac{1}{\square}$ → So $\frac{1}{\square} > 0.375$ → $\square < \frac{1}{0.375} = 2.666...$, so $\square = 2$ → $\frac{1}{2} = 0.5$

Now check order:
- $\frac{1}{4} = 0.25$
- $\frac{3}{8} = 0.375$
- $\frac{1}{2} = 0.5$

Yes! Ascending order.

So:
- First blank: numerator = 1 (for $\frac{1}{4}$)
- Last blank: denominator = 2 (for $\frac{1}{2}$)

Answer:
$$
\frac{1}{4} \quad \frac{3}{8} \quad \frac{1}{2}
$$

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Question 3:

$$
\frac{3}{7} \quad \frac{\square}{2} \quad \frac{2}{\square} \quad \frac{\square}{8}
$$

We have:
- $\frac{3}{7} \approx 0.4286$

We need to find numbers such that all fractions are in order.

Let’s analyze:
- $\frac{3}{7} \approx 0.4286$
- Next is $\frac{\square}{2}$ — try $\frac{1}{2} = 0.5$ → good
- Then $\frac{2}{\square}$ — needs to be > 0.5 → so $\frac{2}{x} > 0.5$ → $x < 4$ → possible x = 3 → $\frac{2}{3} \approx 0.666$
- Then $\frac{\square}{8}$ → needs to be > $\frac{2}{3} \approx 0.666$ → try $\frac{6}{8} = 0.75$ → but $\frac{6}{8} = \frac{3}{4}$, not simplest form → invalid

Wait: All fractions must be in simplest form.

So $\frac{6}{8}$ is not simplest → reduce to $\frac{3}{4}$, but then it would be written as $\frac{3}{4}$, not $\frac{6}{8}$.

So can’t use $\frac{6}{8}$. What about $\frac{5}{8} = 0.625$? That’s less than $\frac{2}{3} \approx 0.666$, so no.

$\frac{7}{8} = 0.875$ → greater than $\frac{2}{3}$, and already in simplest form.

So let’s go:
- $\frac{3}{7} \approx 0.4286$
- $\frac{1}{2} = 0.5$
- $\frac{2}{3} \approx 0.666$
- $\frac{7}{8} = 0.875$

All in simplest form.

Now check:
- $\frac{3}{7} < \frac{1}{2} < \frac{2}{3} < \frac{7}{8}$ → yes!

So:
- $\frac{\square}{2}$ → numerator = 1
- $\frac{2}{\square}$ → denominator = 3
- $\frac{\square}{8}$ → numerator = 7

Answer:
$$
\frac{3}{7} \quad \frac{1}{2} \quad \frac{2}{3} \quad \frac{7}{8}
$$

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Question 4:

$$
\frac{1}{3} \quad \frac{\square}{7} \quad \frac{1}{2} \quad \frac{3}{\square} \quad \frac{2}{\square}
$$

We have:
- $\frac{1}{3} \approx 0.333$
- $\frac{1}{2} = 0.5$

Need to fill:
- $\frac{x}{7}$ → between $\frac{1}{3}$ and $\frac{1}{2}$
- $\frac{3}{y}$ → after $\frac{1}{2}$
- $\frac{2}{z}$ → last

Let’s find:
- $\frac{x}{7}$: what value of $x$ makes $\frac{x}{7}$ between $0.333$ and $0.5$?

Try $x = 2$: $\frac{2}{7} \approx 0.2857$ → too small
$x = 3$: $\frac{3}{7} \approx 0.4286$ → good
$x = 4$: $\frac{4}{7} \approx 0.571$ → bigger than 0.5 → maybe later

But we want $\frac{x}{7}$ just after $\frac{1}{3}$, before $\frac{1}{2}$ → so $x = 3$ → $\frac{3}{7} \approx 0.4286$

So far:
- $\frac{1}{3} \approx 0.333$
- $\frac{3}{7} \approx 0.4286$
- $\frac{1}{2} = 0.5$

Now next: $\frac{3}{y}$ > $0.5$ → so $\frac{3}{y} > 0.5$ → $y < 6$

Possible values: $y = 5$ → $\frac{3}{5} = 0.6$ → good
$y = 4$ → $\frac{3}{4} = 0.75$ → also good
But we want increasing order.

Then $\frac{2}{z}$ > $\frac{3}{y}$

Try $y = 5$ → $\frac{3}{5} = 0.6$, then $\frac{2}{z} > 0.6$ → $z < \frac{2}{0.6} = 3.33$ → $z = 3$ → $\frac{2}{3} \approx 0.666$

Check:
- $\frac{1}{3} \approx 0.333$
- $\frac{3}{7} \approx 0.4286$
- $\frac{1}{2} = 0.5$
- $\frac{3}{5} = 0.6$
- $\frac{2}{3} \approx 0.666$

All increasing? Yes.

Are they in simplest form?
- $\frac{1}{3}$ → yes
- $\frac{3}{7}$ → yes
- $\frac{1}{2}$ → yes
- $\frac{3}{5}$ → yes
- $\frac{2}{3}$ → yes

Perfect.

So:
- $\frac{\square}{7}$ → numerator = 3
- $\frac{3}{\square}$ → denominator = 5
- $\frac{2}{\square}$ → denominator = 3

Answer:
$$
\frac{1}{3} \quad \frac{3}{7} \quad \frac{1}{2} \quad \frac{3}{5} \quad \frac{2}{3}
$$

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Question 5:

$$
\frac{5}{\square} \quad \frac{\square}{3} \quad \frac{5}{7} \quad \frac{\square}{11} \quad \frac{7}{\square}
$$

We need to fill:
- $\frac{5}{a}$
- $\frac{b}{3}$
- $\frac{5}{7} \approx 0.714$
- $\frac{c}{11}$
- $\frac{7}{d}$

Let’s assume ascending order.

Start from left to right.

We know $\frac{5}{7} \approx 0.714$, so:
- The first two fractions should be less than this
- The last two should be greater than this

Try:
- $\frac{5}{a}$: wants to be small → large denominator → say $a = 6$ → $\frac{5}{6} \approx 0.833$ → too big
→ try $a = 8$ → $\frac{5}{8} = 0.625$ → good
→ $a = 9$ → $\frac{5}{9} \approx 0.555$ → even smaller → better for early

Try $\frac{5}{9} \approx 0.555$

Then $\frac{b}{3}$: needs to be > 0.555 → so $b > 1.666$ → so $b = 2$ → $\frac{2}{3} \approx 0.666$

Then $\frac{5}{7} \approx 0.714$

Now need $\frac{c}{11} > 0.714$ → $c > 7.85$ → so $c = 8$ → $\frac{8}{11} \approx 0.727$ → good
$c = 9$ → $\frac{9}{11} \approx 0.818$ → also good

Then $\frac{7}{d} > \frac{c}{11}$

Try $c = 8$ → $\frac{8}{11} \approx 0.727$

Then $\frac{7}{d} > 0.727$ → $d < \frac{7}{0.727} \approx 9.63$ → so $d = 9$ → $\frac{7}{9} \approx 0.777$ → good
$d = 8$ → $\frac{7}{8} = 0.875$ → even better

Let’s pick:
- $\frac{5}{9} \approx 0.555$
- $\frac{2}{3} \approx 0.666$
- $\frac{5}{7} \approx 0.714$
- $\frac{8}{11} \approx 0.727$
- $\frac{7}{8} = 0.875$

Check order:
0.555 < 0.666 < 0.714 < 0.727 < 0.875 → yes!

All in simplest form?
- $\frac{5}{9}$ → yes
- $\frac{2}{3}$ → yes
- $\frac{5}{7}$ → yes
- $\frac{8}{11}$ → yes
- $\frac{7}{8}$ → yes

Perfect.

So:
- $\frac{5}{\square}$ → denominator = 9
- $\frac{\square}{3}$ → numerator = 2
- $\frac{\square}{11}$ → numerator = 8
- $\frac{7}{\square}$ → denominator = 8

Answer:
$$
\frac{5}{9} \quad \frac{2}{3} \quad \frac{5}{7} \quad \frac{8}{11} \quad \frac{7}{8}
$$

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✔ Final Answers:

#### Question 1:
$$
\frac{1}{3} \quad \frac{1}{2} \quad \frac{3}{4}
$$

#### Question 2:
$$
\frac{1}{4} \quad \frac{3}{8} \quad \frac{1}{2}
$$

#### Question 3:
$$
\frac{3}{7} \quad \frac{1}{2} \quad \frac{2}{3} \quad \frac{7}{8}
$$

#### Question 4:
$$
\frac{1}{3} \quad \frac{3}{7} \quad \frac{1}{2} \quad \frac{3}{5} \quad \frac{2}{3}
$$

#### Question 5:
$$
\frac{5}{9} \quad \frac{2}{3} \quad \frac{5}{7} \quad \frac{8}{11} \quad \frac{7}{8}
$$

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🟩 Summary of Boxed Numbers:

| Question | Left Blank | Middle Blank(s) | Right Blank |
|--------|------------|------------------|-------------|
| 1 | 1 | – | 3 |
| 2 | 1 | – | 2 |
| 3 | – | 1 (numerator), 3 (denominator), 7 (numerator) | – |
| 4 | 3 | 5, 3 | – |
| 5 | 9 | 2, 8 | 8 |

> Note: In Q3, there are three boxes: one above 2 (numerator), one below 2 (denominator), and one above 8 (numerator). So:
> - Above 2 → 1
> - Below 2 → 3
> - Above 8 → 7

In Q5:
- Below 5 → 9
- Above 3 → 2
- Above 11 → 8
- Below 7 → 8

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✔ All fractions are in simplest form and in ascending order.

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