Define a simplified fraction .

A simplified fraction is one written using the smallest possible whole numbers on the top and bottom. Simplifying a fraction is also called cancelling it.

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 (Edexcel GCSE Maths: Foundation): Flashcards

Exam code: 1MA1

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FrontIntroduction to Fractions
Define the denominator of a fraction.

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Cards in this collection (32)

Define the denominator of a fraction.
The denominator is the number on the bottom of a fraction, and it tells you how many equal parts each whole is split into.
In $\frac{2}{3}$ the denominator is $3$ , so each whole is split into three equal parts.
True or False?
To shade $\frac{5}{7}$ of a grid of $21$ equal squares, the shaded squares must be next to each other.
False.
What matters is how many of the equal parts are shaded, not which ones, so any $15$ of the $21$ squares shows $\frac{5}{7}$ .
Define the numerator of a fraction.
The numerator is the number on the top of a fraction, and it tells you how many of the equal parts you have.
In $\frac{2}{3}$ the numerator is $2$ , so you have two of the three equal parts.
How can you tell straight away whether a fraction is less than $1$ ?
A fraction is less than $1$ when the numerator is smaller than the denominator, because you have fewer parts than it takes to make a whole.
So $\frac{2}{3}$ is less than $1$ , and $\frac{7}{5}$ is greater than $1$ .
True or False?
$\frac{6}{6}$ is equal to $1$ .
True.
The whole has been split into six equal parts and you have all six of them, so together they make one whole.
How do you find $\frac{2}{5}$ of $60$ ?
Divide by the denominator, then multiply by the numerator.
Here $60 \div 5 = 12$ , and then $12 \times 2 = 24$ .
Complete the working, which finds $\frac{9}{10}$ of $15$ by first writing the fraction as a decimal:
$\frac{9}{10} of 15 =______\times 15 =______$
The completed working is:
$\frac{9}{10} of 15 = 0.9 \times 15 = 13.5$
Writing the fraction as a decimal turns the whole thing into a single multiplication.
How do you turn " $\frac{2}{3}$ of $60$ " into a multiplication of two fractions?
The word of means multiply, and a whole number can be written as a fraction over $1$ :
$\frac{2}{3} of 60 = \frac{2}{3} \times \frac{60}{1} = \frac{120}{3} = 40$
True or False?
You can find a fraction of another fraction, such as $\frac{5}{6}$ of $\frac{8}{3}$ .
True.
The amount does not have to be a whole number, and $\frac{5}{6}$ of $\frac{8}{3}$ comes to $\frac{40}{18}$ , which simplifies to $\frac{20}{9}$ .
Why does finding $\frac{1}{3}$ of $90$ by turning the fraction into a decimal give only an approximate answer?
$\frac{1}{3}$ has no exact decimal form, since $\frac{1}{3} = 0.333 \dots$ , so whatever decimal you multiply by has already been rounded.
One of the other methods gives the exact value instead.
Define equivalent fractions.
Equivalent fractions are fractions that represent the same amount, written in different ways.
For example, $\frac{1}{2}$ and $\frac{6}{12}$ are equivalent fractions.
How do you find a fraction that is equivalent to $\frac{5}{6}$ ?
Multiply the top and bottom by the same number.
For example, $\frac{5 \times 2}{6 \times 2} = \frac{10}{12}$ and $\frac{5 \times 3}{6 \times 3} = \frac{15}{18}$ .
True or False?
There are infinitely many fractions equivalent to $\frac{5}{6}$ .
True.
The list never ends: $\frac{10}{12}$ , $\frac{15}{18}$ and $\frac{20}{24}$ all equal $\frac{5}{6}$ , and there is always another one after them.
Define a simplified fraction.
A simplified fraction is one written using the smallest possible whole numbers on the top and bottom.
Simplifying a fraction is also called cancelling it.
Complete the working by filling in the number that has been divided by on the top and on the bottom:
$\frac{12}{18} = \frac{12 \div______}{18 \div______} = \frac{2}{3}$
The completed working is:
$\frac{12}{18} = \frac{12 \div 6}{18 \div 6} = \frac{2}{3}$
The same number goes in both gaps, because the top and the bottom must be divided by a common factor.
How can you tell that a fraction cannot be simplified any further?
There is no whole number greater than $1$ that divides into both the top and the bottom.
For example, $\frac{5}{9}$ cannot be simplified, but $\frac{25}{45}$ can, because $5$ divides into both.
True or False?
Simplifying a fraction makes it smaller.
False.
Only the two numbers get smaller, and the fraction is still worth exactly the same: $\frac{12}{18}$ and $\frac{2}{3}$ are the same amount.
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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