Maths Revision: Converting Improper Fractions to Mixed Numbers and Vice Versa, Study notes of Calculus

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Maths Revision: Converting an Improper Fraction to a

Mixed Number

An improper fraction is one where the numerator (top value) is bigger than the denominator (bottom value)

I know that 1 whole is shared into 6 parts as 6 is my denominator. I know that there are 17 parts altogether as 17 is mu numerator. I know that this fraction must be greater than 1 whole because 17 (the numerator) is greater than 6 (the denominator)

1. Look at the denominator. This tells you how many parts make up the whole. In this example, we know that a group of 6 parts is equal to 1 whole.
2. Divide the numerator by the denominator so 17 ÷ 6. To do this, ask yourself ‘how many groups of 6 can I make out of 17?’ Count up in sixes. How many complete groups of 6 can you make? What do you have leftover as a remainder?

17 ÷ 6 = 2 r 5

3. The amount of completed groups you could make tells you the number of wholes your mixed number has.
4. Your remainder becomes your numerator for your fraction. Your denominator always stays the same as it was in the improper fraction.

A mixed number contains whole numbers and parts of a whole (a fraction)

Is equal to

Each whole is split into 6 equal parts. 17 parts are shaded.

Maths Revision: Converting Mixed Numbers to an

Improper Fraction

An improper fraction is one where the numerator (top value) is bigger than the denominator (bottom value)

I know that there are 2 wholes and 5/6 which represents a part of a whole. I know that this mixed number is greater than 2 but is less than 3.

1. Multiply your whole number (2) by the denominator (6). This will tell you the value of the numerator when the whole is represented in its fraction form.

2 x 6 = 12

2 wholes =

2. Once you have converted your whole number to an improper fraction, you need to add together your whole number (in its fraction form) to the fraction already in the mixed number. When adding fractions, remember to only add together your numerators providing that the denominators of both fractions are the same.

A mixed number contains whole numbers and parts of a whole (a fraction)

Is equal to

As you can see, the denominator stays the same as the fraction.

2 wholes

TASK 2: Converting Improper Fractions and Mixed

Numbers Reasoning

1. Decide if each statement true or false? #ProveIt using conversion calculations and/or a fraction diagram.

A) 3 >

This statement is ___________ because...

B) 2 <

This statement is ___________ because...

C) > 6

This statement is ___________ because...

D) = 4

This statement is ___________ because...

2. Give three improper fractions that could replace the to make this statement true.

Prove that each possibility is plausible.

Possibility 1. = Possibility 2. = Possibility 3. =

TASK 3: Converting Improper Fractions and Mixed

Numbers Problem Solving Investigation 1

In this statement, B is double the value of A.

What could the values of A , B and C be? How many possibilities can you find? Explain how you know you have found all of the possibilities.