Percentages

Per cent means out of 100, so divide by 100.

$38 \div 100 = 0.38$

50% means half.

$240 \div 2 = 120$

Per cent means out of 100, so divide by 100.

$35\% = 35 \div 100 = 0.35$

Per cent means out of 100, so $37\% = \frac{37}{100}$.

Per cent means out of 100, so divide by 100.

$45 \div 100 = 0.45$

Per cent means out of 100, so divide by 100.

$15\% = 15 \div 100 = 0.15$

Per cent means out of 100, so $20\% = \frac{20}{100}$.

This simplifies to $\frac{1}{5}$.

To change a decimal to a percentage, multiply by 100.

$0.3 \times 100 = 30$, so the answer is $30\%$.

Multiply by 100 to change a decimal to a percentage.

$0.9 \times 100 = 90$%

$10\%$ of 80 is 8, so $20\%$ is $2 \times 8 = 16$.

Or: $80 \times 0.2 = 16$.

$10\%$ of £90 is £9

$70\% = 7 \times 9 = £63$

Interest per year $= 2.5\%$ of $3500 = 0.025 \times 3500 = £87.50$

Total interest $= 87.50 \times 6 = £525$

Children pay $100\% - 56\% = 44\%$

$0.44 \times 1800 = £792$

Each child pays $792 \div 66 = £12$

Children: $\frac{2}{5} \times 200 = 80$, adults: $200 - 80 = 120$

Vegetarian children: $0.35 \times 80 = 28$

Vegetarian adults: $0.45 \times 120 = 54$

Not vegetarian: $200 - 28 - 54 = 118$

$15\%$ of $88 = 0.15 \times 88 = 13.2$

$20\%$ of $62 = 0.2 \times 62 = 12.4$

$13.2 > 12.4$, so 15% of 88 is greater.

Yellow and green together: $200 - 38 - 52 = 110$

Yellow: $110 \div 2 = 55$

Percentage: $\frac{55}{200} \times 100 = 27.5\%$

(a) $0.68 \times 800 = 544$ people

$544 \times 2 = 1088$ cups

$1088 \times 10.6 = 11532.8$, so $11533$ g

(b) More people drink coffee, so he needs more than in (a).

(a) Swimming: $\frac{1}{6} \times 120 = 20$ minutes

Gym: $20\% \times 120 = 24$ minutes

Café: $120 - 50 - 20 - 24 = 26$ minutes

(b) $50 + 20 + 24 = 94$ minutes after 1.30 pm is 3.04 pm, so she was 4 minutes late.

Children: $214 - 14 = 200$

Not wearing a hat: $100\% - 35\% = 65\%$

$0.65 \times 200 = 130$

(a) $40\% = 56$, so $1\% = 1.4$ and $100\% = 140$

(b) $\frac{18}{56} \times 100 = 32.14... \approx 32\%$

One year: $4500 \times 0.018 = £81$

Three years: $81 \times 3 = £243$

Area of the garden: $90 \times 60 = 5400$ m²

Grass is $100\% - 40\% = 60\%$ of it.

$0.6 \times 5400 = 3240$ m²

10% of 160 $= 16$

5% $= 16 \div 2 = 8$

15% $= 16 + 8 = 24$ g

Adam: $0.3 \times 80 = £24$

Difference: $28 - 24 = £4$

Men are 30%, so women are $100 - 30 = 70\%$

$70\%$ is 28, so $10\%$ is $28 \div 7 = 4$

$100\%$ is $4 \times 10 = 40$ people.

VAT: $20\%$ of $14\,200 = 2840$

Total cost: $14\,200 + 2840 = £17\,040$

After deposit: $17\,040 - 5000 = £12\,040$

Each payment: $12\,040 \div 10 = £1204$

There are 20 squares in the grid.

Shaded: 10 whole squares and 5 halves, so $10 + 2.5 = 12.5$ squares.

$\frac{12.5}{20} \times 100 = 62.5\%$

One slice weighs $400 \div 10 = 40$ g.

Fibre is 5 g per 100 g, so in 40 g: $5 \times \frac{40}{100} = 2$ g.

Child tickets: $60\%$ of $180 = 108$.

Child income: $108 \times 8 = £864$.

Adult tickets: $180 - 108 = 72$; adult income: $1944 - 864 = £1080$.

Each adult ticket: $1080 \div 72 = £15$

Deposit: $25\%$ of £12 000 $= 12000 \div 4 = £3000$

Left to pay: $12000 - 3000 = £9000$

Each payment: $9000 \div 20 = £450$

Pass mark: $10\%$ of 60 is 6, so $70\%$ is $7 \times 6 = 42$ marks.

Shah scored 45, and $45 \ge 42$, so he passes.

Or: $\frac{45}{60} = \frac{3}{4} = 75\%$, which is more than $70\%$.

Martha's share: $0.72 \times 120 = 86.40$

She keeps $100\% - 30\% = 70\%$ of it.

$0.7 \times 86.40 = £60.48$

Interest each year: $450 \div 6 = £75$

As a percentage of £3000: $75 \div 3000 \times 100 = 2.5$

$y = 2.5$

Red: $\frac{3}{8} \times 400 = 150$

Green: $400 - 150 - 82 = 168$

Percentage: $\frac{168}{400} \times 100 = 42\%$

Selling price: $24 \times 50$p $= 1200$p $= £12$.

Profit: $12 - 10 = £2$.

Percentage profit: $\frac{2}{10} \times 100 = 20\%$.

Total marks: $60 + 90 = 150$

Pass mark: $\frac{2}{3} \times 150 = 100$

Paper 1: $70\% \times 60 = 42$

Needed on Paper 2: $100 - 42 = 58$

Boys: $0.55 \times 800 = 440$

Boys with packed lunch: $0.4 \times 440 = 176$

All packed lunches: $0.31 \times 800 = 248$

Girls with packed lunch: $248 - 176 = 72$

Gavin saves 28%.

Harry spends $\frac{3}{4}$, so saves $\frac{1}{4} = 25\%$.

Isabel saves $\frac{3}{3+7} = \frac{3}{10} = 30\%$.

30% is the biggest, so Isabel saves the most.

Interest each year: $75 \div 5 = £15$

Rate: $\frac{15}{600} \times 100 = 2.5\%$

$80\%$ of $70\% = 0.8 \times 0.7 = 0.56$

So $56\%$ of the people asked.

Let B have side 2, so A has side 1.

Area of B $= 4$, area of A $= 1$

The diagonal halves A, so the shaded part $= \frac{1}{2}$

$\frac{0.5}{4} \times 100 = 12.5\%$

Tax is 20% of the interest, so interest $= 28.80 \div 0.2 = £144$

Rate $= \frac{144}{8000} \times 100 = 1.8\%$

Food Mart: $£5 \times 0.8 = £4$ for 400 g, so $400 \div 4 = 100$ g per £1.

Jan's Store: $400 \times 1.3 = 520$ g for £5, so $520 \div 5 = 104$ g per £1.

104 > 100, so Jan's Store is better value.