Fractions flashcards

Key points

• Multiply or divide the top and the bottom by the same number.
• It is the same amount cut into more, or fewer, equal pieces: $\frac{2}{3}$ = $\frac{8}{12}$.
• Multiplying by $\frac{4}{4}$ is multiplying by 1, so the value does not change.

Fill the gap: $\frac{3}{5}$ = ?/40

Key points

• Divide the top and the bottom by their highest common factor (HCF).
• Check that no number bigger than 1 still divides both.
• Answers are usually left in their simplest form: $\frac{3}{4}$, not $\frac{6}{8}$.

Simplify $\frac{18}{24}$

Key points

• An improper fraction has a top bigger than its bottom, like $\frac{9}{4}$.
• Improper to mixed: divide, and the remainder goes over the same bottom.
• Mixed to improper: whole × bottom + top, all over the bottom.

Example

Key points

• Write them over a common denominator, then compare the tops.
• The lowest common multiple of the bottoms is the quickest common denominator.
• Changing each one to a decimal works too.

Which is bigger, $\frac{3}{7}$ or $\frac{2}{5}$?

Key points

• Make the denominators the same first.
• Then add or subtract the tops only: the bottom stays the same.
• Simplify the answer at the end.

$\frac{2}{3}$ + $\frac{1}{4}$

Key points

• Change both to improper fractions over the same denominator.
• Subtract the tops, then change the answer back to a mixed number.
• That way the fraction parts can never be taken away the wrong way round.

4 $\frac{1}{3}$ − 1 $\frac{3}{4}$

Key points

• Multiply the tops, then multiply the bottoms.
• No common denominator is needed to multiply.
• Change mixed numbers to improper fractions before you start.

2 $\frac{1}{2}$ × 1 $\frac{1}{2}$

Key points

• Keep the first fraction, change ÷ to ×, and flip the second.
• The flipped fraction is the reciprocal: $\frac{2}{5}$ becomes $\frac{5}{2}$.
• Dividing by $\frac{1}{2}$ doubles: 6 ÷ $\frac{1}{2}$ = 12, because two halves fit in each whole.

$\frac{3}{4}$ ÷ $\frac{2}{5}$

Key points

• A fraction of an amount: divide by the bottom, then multiply by the top.
• One amount as a fraction of another: the first over the second, then simplify.
• Put both amounts in the same units first.

Example