True or False? The denominator is the number on the bottom of a fraction.

True. The denominator is the number on the bottom of a fraction. The numerator is the number of the top of a fraction.

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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The denominator is the number on the bottom of a fraction.

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True or False?
The denominator is the number on the bottom of a fraction.
True.
The denominator is the number on the bottom of a fraction.
The numerator is the number of the top of a fraction.
Define the term equivalent fractions.
E.g. Find an equivalent fraction to $\frac{2}{5}$ .
Equivalent fractions are two fractions that represent the same amount.
If two fractions are equivalent, you can multiply both parts of one fraction by the same value in order to get the second fraction.
E.g. $\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}$
How do you simplify a fraction?
E.g. Simplify $\frac{18}{24}$ .
To simplify a fraction, divide both parts of the fraction by their highest common factor.
Alternatively, you can also keep dividing both parts of the fraction by common factors until the two parts have no common factors.
E.g. $\frac{18}{24} = \frac{18 \div 6}{24 \div 6} = \frac{3}{4}$
How do you find a fraction of an amount?
E.g. What is $\frac{2}{5}$ of 35?
To find a fraction of an amount, multiply the amount by the fraction.
This is the same as dividing the amount by the denominator of the fraction and then multiplying by the numerator of the fraction.
E.g. $\frac{2}{5}$ of 35
$\begin{array}{rcl} \frac{2}{5} \times 35 & = & \frac{35}{5} \times 2 \\ = & 7 \times 2 \\ = & 14 \end{array}$
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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