Fractions & Decimals
<p>Fractions and decimals are two ways of showing parts of a whole. Being comfortable switching between them — and doing calculations with both — is one of the most important skills for the 11+ exam.</p>
<h2>What Is a Fraction?</h2>
<p>A fraction has a <strong>numerator</strong> (top number) that tells you how many parts you have, and a <strong>denominator</strong> (bottom number) that tells you how many equal parts make up the whole. So 3/8 means you have 3 out of 8 equal parts.</p>
<h2>Equivalent Fractions</h2>
<p>You can multiply or divide both the numerator and denominator by the same number without changing the value: 1/2 = 2/4 = 3/6 = 5/10. This is very useful when you need to add fractions with different denominators.</p>
<h2>Simplifying Fractions</h2>
<p>Divide both parts by their highest common factor (HCF). For 12/18, the HCF of 12 and 18 is 6, so 12 ÷ 6 = 2 and 18 ÷ 6 = 3. The simplified fraction is 2/3.</p>
<h2>Adding and Subtracting Fractions</h2>
<p>The denominators must be the same. If they are not, find a common denominator first.</p>
<p><strong>Worked Example:</strong> 2/5 + 1/3</p>
<p>The lowest common denominator of 5 and 3 is 15.<br>
2/5 = 6/15 (multiply top and bottom by 3)<br>
1/3 = 5/15 (multiply top and bottom by 5)<br>
6/15 + 5/15 = 11/15</p>
<h2>Multiplying Fractions</h2>
<p>Multiply the numerators together and the denominators together. Then simplify if possible.</p>
<p><strong>Worked Example:</strong> 3/4 × 2/5 = (3 × 2) / (4 × 5) = 6/20 = 3/10</p>
<h2>Dividing Fractions</h2>
<p>Flip the second fraction upside down (find its reciprocal) and then multiply.</p>
<p><strong>Worked Example:</strong> 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6</p>
<h2>Mixed Numbers and Improper Fractions</h2>
<p>A mixed number like 2 3/4 can be written as an improper fraction: (2 × 4 + 3) / 4 = 11/4. To convert back, divide: 11 ÷ 4 = 2 remainder 3, so 11/4 = 2 3/4.</p>
<h2>Fractions and Decimals</h2>
<p>To convert a fraction to a decimal, divide the numerator by the denominator: 3/8 = 3 ÷ 8 = 0.375.</p>
<p>Key conversions to memorise:</p>
<ul>
<li>1/2 = 0.5</li>
<li>1/4 = 0.25, 3/4 = 0.75</li>
<li>1/5 = 0.2, 2/5 = 0.4, 3/5 = 0.6, 4/5 = 0.8</li>
<li>1/10 = 0.1</li>
<li>1/3 ≈ 0.333, 2/3 ≈ 0.667</li>
</ul>
<h2>Fraction of an Amount</h2>
<p><strong>Worked Example:</strong> Find 3/5 of 40.</p>
<p>Divide 40 by 5 to find one-fifth: 40 ÷ 5 = 8. Then multiply by 3: 8 × 3 = 24.</p>
<h2>Practice Tips</h2>
<ul>
<li>Always simplify your final answer — examiners expect it</li>
<li>Learn the key fraction-decimal conversions by heart</li>
<li>For "fraction of an amount" questions, divide first, then multiply</li>
<li>Check your work by estimating: 3/5 of 40 should be a bit more than half of 40 (which is 20), and 24 fits</li>
</ul>