Functional Skills Qualifications Functional Skills Maths — Number and the Number System Flashcards

24 sample cards from the Functional Skills Maths — Number and the Number System deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. How do you convert the improper fraction $\frac{17}{5}$ to a mixed number?

   Divide $17$ by $5$: $17 \div 5 = 3$ remainder $2$, so $\frac{17}{5} = 3\frac{2}{5}$.

2. What does each digit after the decimal point represent in 4.276?

   After the point the places are tenths, hundredths and thousandths: $4.276 = 4 + \frac{2}{10} + \frac{7}{100} + \frac{6}{1000}$.

3. How do you add or subtract decimals correctly?

   Line up the decimal points (and the place-value columns) one under the other, fill empty places with zeros if needed, then add or subtract as with whole numbers, keeping the decimal point in line.

4. How do you multiply $0.3 \times 0.4$ using whole-number multiplication?

   Ignore the points: $3 \times 4 = 12$. The two factors have $2$ decimal places in total, so the answer has $2$ decimal places: $0.3 \times 0.4 = 0.12$.

5. How do you divide a number by a decimal, e.g. $4.8 \div 0.6$?

   Multiply both numbers by a power of $10$ so the divisor becomes a whole number: $\frac{4.8}{0.6}=\frac{48}{6}=8$.

6. What happens to a decimal when you multiply or divide by 10, 100 or 1000?

   Multiplying moves the digits to the left (the point appears to move right): $3.5 \times 100 = 350$. Dividing moves the digits to the right: $3.5 \div 100 = 0.035$.

7. What does 'per cent' mean, and what is 1% as a fraction and decimal?

   'Per cent' means 'out of 100'. So $1\% = \frac{1}{100} = 0.01$.

8. How do you find a percentage of an amount, e.g. 15% of £80?

   Convert the percentage to a decimal and multiply: $0.15 \times 80 = 12$, so $15\%$ of £80 is £12. (Or find $10\% = 8$ and $5\% = 4$, then add to get $12$.)

9. How do you write one quantity as a percentage of another, e.g. 18 out of 24?

   Write it as a fraction, divide, then multiply by 100: $\frac{18}{24}\times 100 = 75\%$.

10. How do you increase £200 by 12%?

    Find $12\%$ of $200$: $0.12 \times 200 = 24$, then add it on: $200 + 24 = 224$. (Or multiply by the factor $1.12$: $200 \times 1.12 = 224$.)

11. What is a percentage decrease, and decrease £50 by 20%.

    It reduces an amount by a given percentage. $20\%$ of $50$ is $10$, so $50 - 10 = 40$. (Or multiply by $0.80$: $50 \times 0.80 = 40$.)

12. How do you convert a fraction to a decimal, e.g. $\frac{3}{8}$?

    Divide the numerator by the denominator: $3 \div 8 = 0.375$.

13. How do you convert a decimal to a percentage and a percentage to a decimal?

    To get a percentage, multiply the decimal by $100$ (e.g. $0.45 \to 45\%$). To get a decimal, divide the percentage by $100$ (e.g. $45\% \to 0.45$).

14. How do you convert a percentage to a fraction in simplest form, e.g. 40%?

    Write it over $100$ then simplify: $40\% = \frac{40}{100} = \frac{2}{5}$.

15. List the common equivalences for $\frac{1}{2}$, $\frac{1}{4}$, $\frac{3}{4}$, $\frac{1}{10}$ and $\frac{1}{5}$ as decimals and percentages.

    $\frac{1}{2}=0.5=50\%$, $\frac{1}{4}=0.25=25\%$, $\frac{3}{4}=0.75=75\%$, $\frac{1}{10}=0.1=10\%$, $\frac{1}{5}=0.2=20\%$.

16. What is a ratio, and what does the ratio $2:3$ mean?

    A ratio compares quantities of the same kind. $2:3$ means that for every $2$ parts of the first quantity there are $3$ parts of the second, giving $5$ parts in total.

17. How do you simplify the ratio $12:18$?

    Divide both parts by their highest common factor. The HCF of $12$ and $18$ is $6$, so $12:18 = 2:3$.

18. How do you share £40 in the ratio $3:5$?

    Add the parts: $3 + 5 = 8$. One part is $40 \div 8 = 5$. So the shares are $3 \times 5 = £15$ and $5 \times 5 = £25$.

19. What is direct proportion?

    Two quantities are in direct proportion if they increase or decrease at the same rate, so doubling one doubles the other. Their ratio (or $\frac{y}{x}$) stays constant.

20. Using the unitary method, if 5 pens cost £2.00, what do 8 pens cost?

    Find the cost of one: $£2.00 \div 5 = £0.40$. Then multiply: $8 \times £0.40 = £3.20$.

21. What does a map scale of $1:50{,}000$ mean, and how far is $4\,\mathrm{cm}$ on the map in real life?

    It means $1\,\mathrm{cm}$ on the map represents $50{,}000\,\mathrm{cm}$ in reality. So $4\,\mathrm{cm}$ represents $4 \times 50{,}000 = 200{,}000\,\mathrm{cm} = 2\,\mathrm{km}$.

22. On a scale drawing with scale $1:20$, a real wall is $5\,\mathrm{m}$ long. How long is it on the drawing?

    Convert and divide by the scale: real length $= 500\,\mathrm{cm}$, drawing length $= 500 \div 20 = 25\,\mathrm{cm}$.

23. If the exchange rate is £1 = $1.25, how many dollars do you get for £80, and how many pounds for $50?

    To convert pounds to dollars multiply: $80 \times 1.25 = \$100$. To convert dollars to pounds divide: $50 \div 1.25 = £40$.

24. State the metric conversions between mm, cm, m and km, and between g and kg, ml and litres.

    $10\,\mathrm{mm}=1\,\mathrm{cm}$, $100\,\mathrm{cm}=1\,\mathrm{m}$, $1000\,\mathrm{m}=1\,\mathrm{km}$; $1000\,\mathrm{g}=1\,\mathrm{kg}$; $1000\,\mathrm{ml}=1\,\mathrm{litre}$. To convert to a larger unit divide; to a smaller unit multiply.

What this deck covers

Functional Skills Maths — Number and the Number System flashcards FAQ