Flashcards · J560 · Topic 2

Fractions, decimals and percentages flashcards

19 cards on Topic 2, subtopics 2.01 to 2.04. Pick a subtopic or study them all.

Study mode needs JavaScript. Every card is listed below, so you can still cover the answers and test yourself.

All 19 cards

For a quick read-through or printing. Cover the right-hand side to test yourself. Cards marked Higher are Higher tier content only.

Convert a mixed number to an improper fraction: 5 2/3: (whole × bottom + top)/bottom = (5 × 3 + 2)/3 = 17/3
How do you add or subtract fractions?: Convert mixed numbers to improper fractions, rewrite over the lowest common denominator, combine the numerators only, then simplify. Example: 1/6 + 7/10 = 5/30 + 21/30 = 26/30 = 13/15.
How do you divide by a fraction?: Keep the first fraction, change ÷ to ×, flip the second fraction. Example: −4/5 ÷ 2/15 = −4/5 × 15/2 = −6.
Find 5/6 of £4.20: Divide by the bottom, multiply by the top: £4.20 ÷ 6 = £0.70, × 5 = £3.50.
Write 18 minutes as a fraction of 1 hour 30 minutes: Same units first: 18/90 = 1/5.

How do you multiply decimals by hand? Example: 1.2 × (−0.07): Multiply as whole numbers, then give the answer as many decimal places as the two factors have in total. 12 × 7 = 84; 3 decimal places → 0.084; different signs → −0.084.
How do you divide by a decimal? Example: 0.195 ÷ 0.15: Multiply both numbers by the same power of 10 so the divisor is a whole number: 19.5 ÷ 15 = 1.3.
Which fractions give terminating decimals?: In its simplest form, a fraction terminates only if its denominator has no prime factors other than 2 and 5. Otherwise the decimal recurs.
Write 0.545454… as a fractionHigher: x = 0.5454…, 100x = 54.5454… 100x − x = 99x = 54 x = 54/99 = 6/11
Shortcut for a pure recurring decimalHigher: Write the repeating block over the same number of 9s, then simplify: one digit over 9, two digits over 99, three over 999. So 0.2525… = 25/99.

Percentage change: (new − original) ÷ original × 100. Divide by the original, not the new value. Example: 150 → 135 is −15/150 × 100 = a 10% decrease.
After a 12% decrease a price is £74.80. Find the original price.: Multiplier 0.88. Original = 74.80 ÷ 0.88 = £85. Check: 85 × 0.88 = 74.80.
Multipliers for +150% and −6%: +150%: × 2.5 (1 + 1.5). −6%: × 0.94 (1 − 0.06).
Simple interest on £600 at 4% per year for 3 years: Per year: 600 × 4 ÷ 100 = £24. For 3 years: £72. Total: £672. The same amount is added each year.
Find 24% of 150 without a calculator: 10% = 15, so 20% = 30. 1% = 1.5, so 4% = 6. 24% = 30 + 6 = 36.

How do you order fractions, decimals and percentages?: 1. Convert every value to a decimal. 2. Pad to the same number of decimal places. 3. Put negatives first, the most negative smallest. 4. Write the answer in the original forms.
Order smallest first: 0.4, 3/8, 38%, −1/2: As decimals: 0.400, 0.375, 0.380, −0.500. Order: −1/2, 3/8, 38%, 0.4
Which inequality symbols include the end value?: ≤ (less than or equal to) and ≥ (greater than or equal to) include it. < and > do not.
List the integers n with −1 < n ≤ 3: 0, 1, 2, 3 (−1 is excluded, 3 is included).