💡 Mental Method:

We are taking away 10. Look at the tens column.

\(707\) has 0 in the tens column, so we need to count back from 707.

Counting back 10 from 707 gives 697.

Multiply each digit by 4:

• \(2 \times 4 = 8\)
• \(0 \times 4 = 0\)
• \(7 \times 4 = 28\)

💡 Strategy:

Multiply the first two numbers together, then multiply by the third.

Step 1: \(2 \times 4 = 8\)

Step 2: \(8 \times 30\)

To do \(8 \times 30\), we do \(8 \times 3 = 24\), then multiply by 10 (add a zero).

💡 Mental Method:

When we multiply a whole number by 10, the digits move one place to the left. This is the same as adding a zero to the end.

\(96\) becomes \(960\).

⚠️ Important: Line up the decimal points correctly. You can add placeholder zeros to help align the columns.

Note: We had to exchange from the thousands to the hundreds, and from the hundreds to the tens.

💡 Mental Method:

Use known times tables facts.

We know that \(45 \div 9 = 5\).

Therefore, \(450 \div 9 = 50\).

💡 Mental Method:

We know that \(28 \div 7 = 4\).

Therefore, \(2,800 \div 7 = 400\).

💡 Strategy:

We are looking for the difference between 801 and 795.

We can count up from 795 to 801: 796, 797, 798, 799, 800, 801.

That is 6.

Alternatively: \(801 – 795 = 6\).

💡 Mental Method:

\(27 \div 3 = 9\).

Therefore, \(2,700 \div 3 = 900\).

To multiply fractions, we multiply the numerators (top numbers) together and the denominators (bottom numbers) together.

💡 Strategy:

We need a common denominator. We can change \(\frac{5}{8}\) into sixteenths.

\(8 \times 2 = 16\), so we multiply the numerator by 2 as well:

When dividing by 10, move the digits one place to the right (or move the decimal point one place to the left).

0.3 becomes 0.03

We need all fractions to have the same denominator. The lowest common multiple is 18.

• Convert \(\frac{1}{3}\): Multiply top and bottom by 6 \(\rightarrow \frac{6}{18}\)
• Convert \(\frac{2}{6}\): Multiply top and bottom by 3 \(\rightarrow \frac{6}{18}\)
• \(\frac{5}{18}\) stays the same.

💡 Tip: Add placeholder zeros to 29.5 so it has the same number of decimal places as 16.125. Write it as 29.500.

Use long multiplication (column method). Multiply by 4, then multiply by 70.

💡 Tip: Dividing a fraction by a whole number is the same as multiplying the denominator.

If you split \(\frac{1}{8}\) into 3 equal pieces, the pieces get smaller. The denominator gets 3 times bigger.

First, add the fractions: \(\frac{2}{7} + \frac{5}{7} = \frac{7}{7}\).

We know that \(\frac{7}{7}\) is equal to 1 whole.

So, \(1 + 1 = 2\).

Use Long Division. It helps to list multiples of 47 first:

47, 94, 141, 188…

Break it down:

• 50% is half. Half of 700 is 350.
• 1% is dividing by 100. \(700 \div 100 = 7\).
• 2% is \(7 \times 2 = 14\).

Multiply the denominator by the whole number.

If you have a third of a cake and share it into 6 pieces, the pieces become 18ths.

💡 Strategy: Find 5% and subtract it from 100% (the whole number).

• 100% = 180
• 10% = 18
• 5% = 9 (Half of 10%)

Calculate \(4 \times 37\) first.

\(4 \times 30 = 120\)

\(4 \times 7 = 28\)

\(120 + 28 = 148\)

The question was 0.4 (1 decimal place), so the answer must be 14.8.

Think of 1 whole as \(\frac{10}{10}\).

\(\frac{10}{10} – \text{what} = \frac{7}{10}\)?

We take away 3.

Use Long Division. List multiples of 26: 26, 52, 78, 104…

Common denominator is 12.

• Convert \(\frac{5}{6}\) to \(\frac{10}{12}\)
• Convert \(\frac{3}{4}\) to \(\frac{9}{12}\)

So: \(2\frac{10}{12} – \frac{9}{12} = 2\frac{1}{12}\)

💡 Method 1: Partitioning

10% = 75. So 30% = \(75 \times 3 = 225\).

1% = 7.5. So 8% = \(7.5 \times 8 = 60\).

\(225 + 60 = 285\).

💡 Method 2: Multiplication

\(0.38 \times 750\).

First find \(\frac{1}{3}\) of 900 by dividing by 3.

\(900 \div 3 = 300\).

Now find \(\frac{2}{3}\) by multiplying by 2.

\(300 \times 2 = 600\).