True of False? Improper fractions is another name for mixed numbers .

False. Improper fractions is another name for top heavy fractions .

True or False? When multiplying two fractions, you first must write them with a common denominator .

False. You can multiply fractions without writing them with common denominators . It is only necessary to find a common denominator when adding or subtracting fractions.

True or False? The first step when multiplying together two mixed numbers is to convert the numbers to improper fractions.

True. When multiplying together two mixed numbers , the first step is to write both as top heavy (improper) fractions.

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Fractions Toolkit (Cambridge (CIE) O Level Maths): Flashcards

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FrontIntroduction to Fractions
Define the denominator of a fraction.

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Cards in this collection (33)

Define the denominator of a fraction.
The denominator is the number on the bottom of a fraction, and it says how many equal parts each whole is divided into.
In $\frac{2}{3}$ the denominator is 3, so each whole is split into three equal parts.
Define the numerator of a fraction.
The numerator is the number on the top of a fraction, and it says how many of the equal parts you have.
In $\frac{2}{3}$ the numerator is 2, so you have two of the three parts.
How do you shade $\frac{3}{5}$ of a grid made up of 20 squares?
Divide the 20 squares into five equal groups of 4, then shade three of those groups, which is 12 squares in all.
It does not matter which 12 squares are shaded, although grouping them together looks neater.
Complete the rule for comparing a fraction with 1:
A fraction is less than one whole when its numerator is $______$ than its denominator, because you then have fewer parts than it takes to make a whole.
The completed rule is:
A fraction is less than one whole when its numerator is smaller than its denominator, because you then have fewer parts than it takes to make a whole.
True or False?
The bigger the denominator, the bigger the fraction.
False.
For a fixed numerator, a bigger denominator splits each whole into more parts, so every one of those parts is smaller.
That is why $\frac{1}{8}$ is smaller than $\frac{1}{3}$ rather than bigger than it.
How do you shade $\frac{1}{4}$ of a circle that has no parts marked on it?
Divide the circle into four equal parts first, for example with a horizontal and a vertical line through the centre, then shade one of them.
The parts have to be equal, which is why both lines are drawn through the centre.
Work out $\frac{2}{5}$ of 60 without a calculator.
One fifth of 60 is $60 \div 5 = 12$ , so two fifths of 60 is $12 \times 2 = 24$ .
Complete the rule for finding a fraction of an amount:
Divide the amount by the $______$ and then multiply the result by the $______$ of the fraction.
The completed rule is:
Divide the amount by the denominator and then multiply the result by the numerator of the fraction.
How can a calculator be used to find $\frac{9}{10}$ of 15?
Turn the fraction into a decimal and then multiply, so $\frac{9}{10}$ becomes $0.9$ and $0.9 \times 15 = 13.5$ is the answer.
This suits any fraction with an easy decimal form, such as $\frac{1}{4}$ , which is $0.25$ , giving $0.25 \times 16 = 4$ for a quarter of 16.
True or False?
Finding $\frac{3}{4}$ of 40 gives the same answer whether you divide by 4 first or multiply by 3 first.
True.
Dividing first gives $40 \div 4 = 10$ and then $10 \times 3 = 30$ .
Multiplying first gives $40 \times 3 = 120$ and then $120 \div 4 = 30$ , which is the same answer.
How do you find $\frac{2}{3}$ of 50, when 50 does not divide exactly by 3?
Multiply by the numerator first, so $50 \times 2 = 100$ , and then divide by the denominator to reach $\frac{100}{3}$ as the answer.
As a mixed number that is $33 \frac{1}{3}$ , and either form is acceptable.
Define equivalent fractions.
Equivalent fractions are different-looking fractions that represent the same amount, such as $\frac{1}{2}$ and $\frac{6}{12}$ .
They are two ways of writing the same number.
How do you find a fraction equivalent to $\frac{5}{6}$ ?
Multiply the top and the bottom by the same number, so $\frac{5 \times 2}{6 \times 2} = \frac{10}{12}$ is one answer.
Multiplying by 3 or by 4 instead gives $\frac{15}{18}$ and $\frac{20}{24}$ , which are equivalent to $\frac{5}{6}$ as well.
True or False?
Every fraction has infinitely many equivalent fractions.
True.
There is no largest whole number to scale a fraction by, so the list of equivalents never comes to an end.
For example $\frac{1}{2}$ equals $\frac{2}{4}$ , then $\frac{3}{6}$ , then $\frac{4}{8}$ and so on without limit.
What does it mean for a fraction to be in its simplest form?
A fraction is in its simplest form when its numerator and denominator are whole numbers sharing no common factor other than 1.
For example $\frac{25}{45}$ simplifies to $\frac{5}{9}$ , which cannot be reduced any further.
Simplifying a fraction is also called cancelling it.
Complete the rule for simplifying a fraction:
Divide the numerator and the denominator by a $______$ factor of the two, and use the $______$ common factor to reach the simplest form in a single step.
The completed rule is:
Divide the numerator and the denominator by a common factor of the two, and use the highest common factor to reach the simplest form in a single step.
What happens if you simplify a fraction using a common factor that is not the highest?
The numbers get smaller but the fraction is not yet in its simplest form, so the process is simply repeated.
Dividing $\frac{24}{36}$ by 2 gives $\frac{12}{18}$ , and dividing that by 6 gives $\frac{2}{3}$ at last.
True or False?
Simplifying a fraction changes its value.
False.
Simplifying produces an equivalent fraction, so the value stays exactly the same and only the numbers written down get smaller.
That is why $\frac{12}{18}$ and $\frac{2}{3}$ can be used interchangeably.
Define the term top heavy (improper) fraction.
A top heavy (improper) fraction is one where its numerator is bigger than its denominator.
E.g. $\frac{4}{3}$ is a top heavy fraction.
Define the term mixed number.
A mixed number is a whole number added together with a fraction.
E.g. $2 \frac{3}{5}$ is a mixed number.
How do you convert a mixed number into a top heavy fraction?
To convert from a mixed number into a top heavy fraction, multiply the whole number by the denominator. Add that value to the numerator. This becomes the new numerator.
The denominator stays the same.
E.g. $4 \frac{5}{8} = \frac{4 \times 8 + 5}{8} = \frac{37}{8}$
How do you convert a top heavy fraction into a mixed number?
To convert from a top heavy fraction to a mixed number, divide the numerator by the denominator.
The number of times that the denominator goes into the numerator is the whole number for the mixed number.
The remainder is the numerator for the mixed number.
The denominator stays the same.
E.g. $\frac{22}{7} = \frac{21}{7} + \frac{1}{7} = 3 \frac{1}{7}$
True of False?
Improper fractions is another name for mixed numbers.
False.
Improper fractions is another name for top heavy fractions.
What is the lowest common denominator of two fractions.
E.g. $\frac{2}{5}$ and $\frac{1}{3}$ .
The lowest common denominator of two fractions is the smallest whole number that each denominator divides into. I.e. the lowest common multiple of the denominators.
E.g. The fractions $\frac{2}{5}$ and $\frac{1}{3}$ have denominators of 3 and 5.
Therefore, the lowest common denominator of these two fractions is 15.
True or False?
To work out $\frac{1}{4} + \frac{5}{7}$ , you add the numerators and add the denominators to get $\frac{6}{11}$ .
False.
It is a common error to add together the numerators and add together the denominators when adding fractions.
Instead, you need to first convert both fractions so that they have a common denominator and just add the numerators.
E.g. $\frac{1}{4} + \frac{5}{7} = \frac{7}{28} + \frac{20}{28} = \frac{27}{28}$ .
True or False?
When adding or subtracting fractions, sometimes you only need to change one of the denominators.
True.
When adding or subtracting fractions, if one denominator is a multiple of the other then you only need to change the smaller one.
E.g. $\frac{2}{5} + \frac{4}{15} = \frac{6}{15} + \frac{4}{15}$ .
How do you add or subtract two mixed numbers?
E.g. $5 \frac{2}{3} - 4 \frac{1}{6}$ .
It is easiest to convert the mixed numbers into improper fractions first and then complete the addition or subtraction.
E.g. $5 \frac{2}{3} - 4 \frac{1}{6}$
$\begin{array}{rcl} \frac{5 \times 3 + 2}{3} - \frac{4 \times 6 + 1}{6} & = & \frac{17}{3} - \frac{25}{6} \\ = & \frac{34}{6} - \frac{25}{6} = \frac{9}{6} = \frac{3}{2} = 1 \frac{1}{2} \end{array}$
True or False?
When multiplying two fractions, you first must write them with a common denominator.
False.
You can multiply fractions without writing them with common denominators.
It is only necessary to find a common denominator when adding or subtracting fractions.
Dividing a number by a fraction is the same as multiplying the original number by what?
Dividing a number by a fraction is the same as multiplying the original number by the reciprocal of the fraction.
For example, $9 \div \frac{2}{3} = 9 \times \frac{3}{2}$ .
How do you multiply two fractions?
E.g. $\frac{5}{8} \times \frac{3}{7}$ .
To multiply two fractions, multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator.
E.g. $\frac{5}{8} \times \frac{3}{7} = \frac{5 \times 3}{8 \times 7} = \frac{15}{56}$
How do you divide one fraction by another fraction?
E.g. $\frac{3}{9} \div \frac{4}{5}$ .
To divide one fraction by another fraction, flip the second fraction and change the division to multiplication.
Then multiply the fractions as normal.
E.g. $\frac{3}{9} \div \frac{4}{5} = \frac{3}{9} \times \frac{5}{4} = \frac{15}{36} = \frac{5}{12}$
True or False?
When multiplying two fractions together, you can cancel out a common factor between the numerator of one fraction and the denominator of the other fraction.
E.g. $\frac{4}{15} \times \frac{25}{11} = \frac{4}{\underset{3}{15}} \times \frac{\overset{5}{25}}{11}$ .
True.
When multiplying two fractions together, you can cancel out a common factor between the numerator of one fraction and the denominator of the other fraction.
This is called cross-cancelling.
True or False?
The first step when multiplying together two mixed numbers is to convert the numbers to improper fractions.
True.
When multiplying together two mixed numbers, the first step is to write both as top heavy (improper) fractions.

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