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Lesson 3 of 18
  • Year 7

Checking and securing converting improper fractions to mixed numbers

I can use awareness that fractions of the form a/b, where a>b, are greater than one and so convert from improper fractions to mixed numbers.

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Lesson 3 of 18
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New
  • Year 7

Checking and securing converting improper fractions to mixed numbers

I can use awareness that fractions of the form a/b, where a>b, are greater than one and so convert from improper fractions to mixed numbers.

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Lesson details

Key learning points

  1. Fractions where the denominator and numerator are the same are equal to one.
  2. Fractions where the numerator is less than the denominator are less than one.
  3. Fractions where the numerator is greater than the denominator are greater than one.
  4. Improper fractions can be written as a whole number and a proper fraction.
  5. Improper fractions can be converted to mixed numbers.

Keywords

  • Proper - A proper fraction is a fraction where the numerator is less than the denominator.

  • Improper - An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

  • Mixed number - A mixed number is an improper fraction written as its integer part plus the fractional part where the fractional part is a proper fraction.

Common misconception

A mixed number can be confused with an integer multiplying by the proper fraction.

Emphasise the language eg. 3 and a 1/2 means 3 + 1/2.


To help you plan your year 7 maths lesson on: Checking and securing converting improper fractions to mixed numbers, download all teaching resources for free and adapt to suit your pupils' needs...

Play a game in class where the starting value is 2/5. The next pupil will add another 2/5. Once the number gets to an improper faction, the answer must be said as a mixed number. For a more challenging game, use 3/8 or 5/11.
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Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Prior knowledge starter quiz

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6 Questions

Q1.
Two fractions are equivalent if they have the same .

Correct Answer: value, decimal answer, answer

Q2.
Use the diagram to help you find two more fractions that are equivalent to $$4 \over 5$$.

An image in a quiz
$$4 \over 20$$
$$6 \over 10$$
Correct answer: $$8 \over 10$$
Correct answer: $$16 \over 20$$
$$18 \over 20$$

Q3.
Alex writes: $$\frac{3\times \square}{7\times \square} = \frac{12}{28}$$. What number should Alex write in each box?

Correct Answer: 4, four

Q4.
Select all the fractions that are equivalent to $$1 \over 4$$.

$$2 \over 5$$
Correct answer: $$2 \over 8$$
$$3 \over 9$$
Correct answer: $$3 \over 12$$
Correct answer: $$4 \over 16$$

Q5.
Select all the fractions that are equivalent to $$5 \over7$$.

Correct answer: $$10 \over 14$$
$$10 \over 12$$
Correct answer: $$15 \over 21$$
$$18 \over 24$$

Q6.
Match each fraction to an equivalent fraction.

Correct Answer:$$1 \over 6$$,$$3 \over 18$$

$$3 \over 18$$

Correct Answer:$$2 \over 9$$,$$6 \over 27$$

$$6 \over 27$$

Correct Answer:$$5 \over 11$$,$$25 \over 55$$

$$25 \over 55$$

Correct Answer:$$5 \over 8$$,$$20 \over 32$$

$$20 \over 32$$

Correct Answer:$$5 \over 7$$,$$20 \over 28$$

$$20 \over 28$$

Assessment exit quiz

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6 Questions

Q1.
Match together each type of fraction with an example of that fraction.

Correct Answer:improper fraction,$$\frac {8}{5}$$

$$\frac {8}{5}$$

Correct Answer:proper fraction,$$\frac {3}{5}$$

$$\frac {3}{5}$$

Correct Answer:mixed number,$$1 \frac {3}{5}$$

$$1 \frac {3}{5}$$

Q2.
Write the correct symbol (<, > or =) to complete the statement: 467 ÷ 466 1

Correct Answer: >

Q3.
Match each statement to the symbol that should go in the box.

Correct Answer:$$\frac{7} {8} \square 1$$,<

<

Correct Answer:$$\frac{7+8}{8+7} \square 1$$,=

=

Correct Answer:$$\frac{8} {7} \square 1$$,>

>

Q4.
Jun writes: $$\frac{12} {5} = \square \frac {2}{5}$$. Jun should write the number in the box.

Correct Answer: 2, two

Q5.
Izzy writes: $$\frac{19} {3} = 6 \frac {\square}{3}$$. Izzy should write the number in the box.

Correct Answer: 1, one

Q6.
Match each improper fraction to its equivalent mixed number.

Correct Answer:$$ \frac {7}{4}$$,$$1 \frac {3}{4}$$

$$1 \frac {3}{4}$$

Correct Answer:$$ \frac {5}{2}$$,$$2 \frac {1}{2}$$

$$2 \frac {1}{2}$$

Correct Answer:$$ \frac {10}{8}$$,$$1 \frac {1}{4}$$

$$1 \frac {1}{4}$$

Correct Answer:$$ \frac {11}{4}$$,$$2 \frac {3}{4}$$

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

Correct Answer:$$ \frac {12}{8}$$,$$1 \frac {1}{2}$$

$$1 \frac {1}{2}$$