Maths - fractions Flashcards
What is a fraction?
In maths a fraction is
A devision or part of a whole number
E.g. 1/2 or 3/4
What are fractions characterised by?
A numerator and a denominator
What is a numerator?
A numerator is the number on top of a fraction
E.g. 3/8 - 3 is the numerator
What is a denominator?
A denominator is the number at the bottom of a fraction
E.g. 3/8 - 8 is the denominator
What is an equivalent fraction?
An equivalent fraction is where the numerators and denominators are different but still equal to each other.
E.g. 1/2, 2/4 and 4/8
All represent the same amount
What is the fundamental rule associated with fractions?
If both the numerator and denominator are multiplied or divided by the same number the the value of the fraction remains the same
What is meant by the ‘simplest form’ in regards to fractions?
The simplest form is the one in which the numerator and denominator have the smallest possible value
E.g. 1/2, 2/3
Explain the term ‘cancellation’ in regards to fractions?
Cancellation is the process of dividing a nominator and a denominator by the same quantity.
How is the process ‘cancellation’ most commonly shown?
By striking through the numbers being divided and placing the new number beside it
5/15 - the numbers are striked through and besides the numbers 1/3 are written
Multiply 1/2 by 2
1/2 x 2 = 2/4
Multiply 2/4 by 2
2/4 x 2 = 4/8
Equivalent fractions
Multiply 1/2 by 3
1/2 x 3 = 3/6
Multiply 3/6 by 3
3/6 x 3 = 9/18
What is the simplest form of 9/18 and how did you get to this answer?
The simplest form of 9/18 is 1/2 this answer was found by dividing by 9
What is the simplest form of 4/8 and how did you get to that answer?
The simplest form of 4/8 is 1/2 this was achieved by dividing the numbers by 4
Find the simplest form of 6/9
2/3
This was found by dividing by 3
Find the simplest form of 8/12
The simplest form is 2/3 this was achieved by dividing by 4
Find the simplest form of 10/15
The simplest form is 2/3 this was achieved by dividing by 5
In order to add or subtract fractions what is it necessary for both fractions to have?
The same denominator
Fractions with the same denominator are said to have what?
A common denominator
What is a common denominator?
Fractions that have the same denominator
What is the lowest common denominator?
It is the smallest possible number for the denominator that two fractions can have
What could be the lowest common denominator in the calculation
3/4 + 7/16
The lowest common denominator is 16
This is found by multiplying 3/4 by 4
Explain briefly how you add/subtract fractions
1) you find a common denominator
2) it is convenient to find the lowest possible common denominator
3) you add the numerators together
4) this gives you your answer, unless you have not found the lowest common denominator in the beginning - then you may need to divide fractions
What is an improper fraction?
It is one where the numerator is higher than the denominator
What is a mixed number?
A mixed number is a combination of a whole number and a fraction
How could 19/16 be written as a mixed number?
1 3/16
19 can go in to 16 to make 1 whole, leaving 3 left over
For scientific reasons is it better to use improper fractions or mixed number?
It is best to leave it at improper fractions
E.g. 34/16
What could you do if the lowest common denominator is not easy to spot when adding/subtracting fractions?
It is acceptable to use any common denominator when adding/subtracting fractions. You could multiply the top and bottom of the first fraction to the denominator or the second fraction.
The simplest form should be expressed in the end calculation
What does the term evaluate mean in regards to maths?
It means calculate the value of
Evaluate the following expression, giving the answer in the simplest possible improper fraction
3/2+1/32
3/2x16 = 48/32
48/32+1/32=49/32
This is an improper fraction and can not be divided by anything to get an equal value, so this is its simplest form
Evaluate to the simplest form
2/3-1/6
2/3x2=4/6
4/6-1/6=3/6
3/6 divided by 3 =1/2
1/2 is the simplest form
Evaluate to the simplest form
1/3+1/2-2/5
1) 1/2x3=3/6
1/3x2=2/6
2/6+3/6=5/6
2)5/6-2/5
2/5x6=12/30
5/6x5=25/30
3)
25/30-12/30 =13/30
This is the simplest form
Evaluate 5/28 - 1/3
To the simplest form
1/3 x28= 28/84
5/28x3=15/84
15/84-28/84= -13/84
What is the definition of integer?
A whole number that can be positive, negative or zero
Positive and negative while numbers which can be zero
Which calculations to a fraction will not alter its value?
Multiplication and division
Which calculations will alter the value or a fraction?
All other operations carried out on a fraction except multiplication and division.
This rule may seem fairly obvious but it is the root cause of many errors in algebra
Evaluate 4/16 as a decimal
1/4 = 0.25
Evaluate 6/18 as a decimal
0.333
To three decimal places
Evaluate 2/14 as a decimal
0.143
To three decimal places
How do you multiply two or more fractions?
Multiply the numerators (top lines) together and multiply the denominators (bottom lines) together
How could you also write the 3 in this calculation?
3 x 4/5
3/1 x 4/5
How do you divide by a fraction?
2/3 divided by 4/5
Turn it up side down and multiply
2/3 x 5/4
Multiplying by 1/2 is equivalent to?
Dividing by two
Dividing by 1/2 is equivalent to?
Multiplying by two
Evaluate
4/3 divided by 5/9
4/3 x 9/5 = 36/15
36/15 divided by 3 =12/5
Evaluate
1/2 divided by 3
1/2 divided by 3/1
1/2 x 1/3
1/6
Evaluate 5/9 divided by 7
5/9 divided by 7/1
5/9 x 1/7 = 5/63
Express 25% as a fraction
1/4
How do you find ‘the power of’ on a scientific calculator?
E.g
5^4=625
How do you square a number on a scientific calculator?
X2
5x2 (smaller 2) =25
What is meant when you square a number?
Times it by itself
What is meant by the power of?
You time it by itself however many time it is to the power e.g.
4 (smaller)6 = 4x4x4x4x4x4
A number in which there is a decimal point is said to be written in ….?
Decimal notation
