Let’s line them up:

• 9,206,499
• 9,215,300
• 9,206,504
• 9,215,298
• 9,206,909

Millions: All have 9.

Hundred Thousands: All have 2.

Ten Thousands: Some have 0, some have 1.

The numbers with 1 in the ten thousands column are bigger than those with 0. So we only look at:

• 9,215,300
• 9,215,298

We divide the total people by the number of seats per table:

\[ 40 \div 8 = 5 \]

We need to reach 430,070.

Currently we have 400,070.

Let’s look at the columns. The ‘3’ is in the ten-thousands column.

Difference: \(430,070 – 400,070 = 30,000\).

Exact: 1,380

• Amir (1,310): \(1,380 – 1,310 = 70\)
• Olivia (1,220): \(1,380 – 1,220 = 160\)
• Emma (1,400): \(1,400 – 1,380 = 20\)
• John (1,290): \(1,380 – 1,290 = 90\)
• Chen (1,460): \(1,460 – 1,380 = 80\)

Closest: The smallest difference is 20 (Emma).

Furthest: The largest difference is 160 (Olivia).

\[ 2.3 \times 1,000 \]

Move the digits 3 places to the left:

2.3 -> 23 -> 230 -> 2,300

\[ 5.00 – 2.75 \]

Tip: Add decimal zeros to the 5 to make it easier.

  4.9 1  (borrowing)
  5.0 0
- 2.7 5
-------
  2.2 5
                        

The whole race is \(\frac{10}{10}\).

Remaining for bike = Whole – (Swim + Run)

\[ \frac{10}{10} – \frac{4}{10} = \frac{6}{10} \]

Note: \(\frac{6}{10}\) can be simplified to \(\frac{3}{5}\), but \(\frac{6}{10}\) is also correct.

\(2 \times 8 = 16\)

\(16 + 3 = 19\)

So the top number (numerator) is 19. The bottom number (denominator) stays as 8.

\[ \frac{19}{8} \]

\[ 24 \div 3 = 8 \]

Each full circle represents 8 DVDs.

Look at Friday:

There are 6 full circles and 1 half circle.

• 6 full circles: \(6 \times 8 = 48\)
• 1 half circle: Half of 8 is \(4\).

Total: \(48 + 4 = 52\)

Half of £1.90:

Half of £1.80 is 90p.

Half of 10p is 5p.

Total = 95p (or £0.95).

First box: £1.90

Second box: £0.95

\[ 1.90 + 0.95 \]

\(1.90 + 1.00 = 2.90\)

Subtract the extra 5p: \(2.90 – 0.05 = 2.85\)

\[ \frac{3}{10} = \frac{?}{20} \]

Look at the denominators: \(10 \times 2 = 20\).

Whatever we do to the bottom, we must do to the top.

\(3 \times 2 = \mathbf{6}\).

\[ \frac{12}{15} = \frac{4}{?} \]

Look at the numerators: \(12 \div 3 = 4\).

We must divide the denominator by 3 as well.

\(15 \div 3 = \mathbf{5}\).

• 1.4kg = \(1.4 \times 1000 = 1400\text{g}\)
• 1500g = 1500g
• 2kg = \(2 \times 1000 = 2000\text{g}\)
• 300g = 300g

Comparing: 1400, 1500, 2000, 300

1. 2000 (2kg)
2. 1500 (1500g)
3. 1400 (1.4kg)
4. 300 (300g)

\[ 850 \div 17 \]

Let’s find multiples of 17.

• \(17 \times 1 = 17\)
• \(17 \times 2 = 34\)
• …
• \(17 \times 5 = 85\)

So, \(17 \times 50 = 850\).

Left: \(1 \times 2 \times 3 = 6\)

Right: \(1 + 2 + 3 = 6\)

Sign: =

Left: \(2 \times 2 \times 2 = 8\)

Right: \(2 + 2 + 2 = 6\)

8 is bigger than 6.

Sign: >

Left: \(1 \times 10 \times 10 = 100\)

Right: \(1 + 10 + 10 = 21\)

100 is bigger than 21.

Sign: >

Left: \(0 \times 10 \times 10 = 0\) (Anything multiplied by 0 is 0)

Right: \(0 + 10 + 10 = 20\)

0 is smaller than 20.

Sign: <

28.07 -> 7 is high -> 28.1 (No)

28.65 -> 5 is high -> Round up 6 to 7 -> 28.7 (Yes)

28.71 -> 1 is low -> Keep 7 -> 28.7 (Yes)

28.75 -> 5 is high -> Round up 7 to 8 -> 28.8 (No)

28.97 -> 7 is high -> Round up 9 -> 29.0 (No)

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.

BUT: The number must be bigger than the remainder (4).

Possible answers: 9, 12, 18, 36.

Let’s check 9: \(40 \div 9 = 4 \text{ r} 4\). Correct.

Total spaces: 800

Empty spaces: 268

Parked: \(800 – 268\)

\(800 – 200 = 600\)

\(600 – 60 = 540\)

\(540 – 8 = \mathbf{532}\)

Total spaces: 800

Empty spaces: 511

Parked: \(800 – 511\)

\(800 – 500 = 300\)

\(300 – 11 = \mathbf{289}\)

Add Level 1 and Level 2:

\(532 + 289\)

\(532 + 200 = 732\)

\(732 + 80 = 812\)

\(812 + 9 = \mathbf{821}\)

Total circumference = 60 cm.

We need \(\frac{1}{4}\) of 60.

\[ 60 \div 4 = 15 \]

15 classes of 16 pupils.

\(15 \times 16\)

\(10 \times 16 = 160\)

\(5 \times 16 = 80\) (half of 160)

\(160 + 80 = \mathbf{240}\)

10 classes of 18 pupils.

\(10 \times 18 = \mathbf{180}\)

\(240 + 180 = \mathbf{420}\)

Total places allowed: 432

Taken places: 420

\(432 – 420 = \mathbf{12}\)

\[ 48 \div 3 = 16 \]

Triangle = 16

Total of ALL shapes = 200.

Let’s count them:

• Triangles: 5
• Circles: 4

We know Triangle = 16.

Value of 5 Triangles: \(5 \times 16 = 80\).

Remaining value for Circles: \(200 – 80 = 120\).

There are 4 Circles.

\[ 120 \div 4 = 30 \]

Circle = 30

Method A: Calculate total of one batch first

Single batch = \(250 + 1150 = 1400 \text{ ml}\).

Triple batch = \(1400 \times 3 = 4200 \text{ ml}\).

Method B: Calculate Yellow first

Yellow needed: \(1150 \times 3 = 3450\).

Total green = Blue (750) + Yellow (3450).

\(750 + 3450 = 4200 \text{ ml}\).

Start: 1.25 kg

After Banana: 1.1 kg

Banana = \(1.25 – 1.1 = \mathbf{0.15 \text{ kg}}\)

(In grams: \(0.15 \times 1000 = 150 \text{ g}\))

After Banana: 1.1 kg (which is 1100 g)

After Orange: 920 g

Orange = \(1100 – 920\)

\(1100 – 900 = 200\)

\(200 – 20 = \mathbf{180 \text{ g}}\)

Orange: 180 g

Banana: 150 g

\(180 – 150 = \mathbf{30 \text{ g}}\)

\(180 – 30 = 150\)

\(150 \div 2 = \mathbf{75}\)

So, \(x = 75^\circ\).

The corner of a rectangle is a right angle (90°).

The base angle of the triangle (75°) and angle \(y\) make up this corner.

\(75 + y = 90\)

\(90 – 75 = \mathbf{15}\)

Original Coordinates:

• Point A: (-4, 5)
• Point B: (-1, 4)
• Point C: (-4, 1)

Move y-coordinate down by 7 (subtract 7):

• A’: (-4, 5 – 7) = (-4, -2)
• B’: (-1, 4 – 7) = (-1, -3)
• C’: (-4, 1 – 7) = (-4, -6)

Reflecting in the y-axis changes the sign of the x-coordinate.

• A’ (-4, -2) becomes (4, -2)
• B’ (-1, -3) becomes (1, -3)
• C’ (-4, -6) becomes (4, -6)