Fractions, Decimals, Percentages & Ratios

Fractions, decimals, percentages, and ratios are different ways to compare parts to wholes. They appear throughout the syllabus, especially in Consumer Arithmetic, Measurement, Statistics, and Probability.

For CSEC, fluency matters because these conversions are often only one step inside a bigger problem. Before calculating, decide what the whole is, what part is being compared, and whether the question wants a fraction, decimal, percentage, or ratio. That interpretation is what turns a procedure into understanding.

These three forms represent the exact same thing—just written differently. You need to convert between them easily.

What Is a Fraction?¶

A fraction only makes sense when the whole is clear. In word problems, identify the total amount before deciding what the numerator and denominator should be.

A fraction shows a part of something whole.

$\frac{3}{4}$

• Top number (numerator): How many parts you have = 3
• Bottom number (denominator): How many equal parts the whole is divided into = 4

So $\frac{3}{4}$ means: "The whole thing is divided into 4 equal parts, and you have 3 of them."

Converting Fraction to Decimal¶

Decimal form is useful when you need to compare values quickly or use a calculator. The division simply asks how large each fractional part is on the base-10 number system.

To convert a fraction to decimal: Divide the top by the bottom.

$\frac{3}{4} = 3 ÷ 4 = 0.75$

$\frac{1}{2} = 1 ÷ 2 = 0.5$

$\frac{5}{8} = 5 ÷ 8 = 0.625$

Converting Decimal to Percentage¶

Percent means "per hundred", so multiplying by 100 rewrites the decimal as a number out of 100.

To convert decimal to percentage: Multiply by 100 and add the % sign.

$0.75 × 100 = 75\%$

$0.5 × 100 = 50\%$

$0.25 × 100 = 25\%$

Converting All Three¶

Seeing all three forms together helps you choose the most convenient one. Fractions are often exact, decimals are calculator-friendly, and percentages are easiest for real-life comparison.

Now let's see how all three forms are the SAME number:

$\frac{3}{4} = 0.75 = 75\%$

They're three different ways of writing the same value.

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Working with Fractions¶

Adding Fractions¶

Adding fractions is adding parts of the same-sized whole. If the denominators differ, you must first rewrite the fractions so the parts are equal in size.

To add fractions, they must have the SAME denominator (bottom number).

If they don't, you have to make them the same first.

But what if the denominators are different?

Multiplying Fractions¶

Multiplication of fractions often means "a fraction of a fraction". For example, half of three quarters is found by multiplying the fractions.

To multiply fractions: Multiply the tops together and the bottoms together.

$\frac{a}{b} × \frac{c}{d} = \frac{a × c}{b × d}$

Dividing Fractions¶

Dividing by a fraction asks how many of that fraction fit into the first amount. Flipping and multiplying is the shortcut that preserves that meaning.

To divide fractions: Flip the second fraction, then multiply.

$\frac{a}{b} ÷ \frac{c}{d} = \frac{a}{b} × \frac{d}{c}$

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Understanding Percentages in Real Life¶

A percentage is just a way of saying "out of 100."

$50\% = \frac{50}{100}$

$25\% = \frac{25}{100}$

$1\% = \frac{1}{100}$

Finding a Percentage of a Number¶

This is the most common percentage skill in consumer arithmetic. Convert the percentage to a decimal or fraction first, then multiply by the whole amount.

To find X% of a number, multiply the number by $\frac{X}{100}$.

Expressing One Amount as a Percentage of Another¶

Here the first amount is the part and the second amount is the whole. Reversing them gives a completely different percentage, so read the wording carefully.

Formula: $\frac{\text{Part}}{\text{Whole}} × 100\%$

Percentage Increase and Decrease¶

Percentage change always compares the change to the original value. This is why the old value goes in the denominator, not the new value.

Formula: $\frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} × 100\%$

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Ratios: Comparing Quantities¶

A ratio compares two quantities of the same type.

The ratio $2:3$ (read as "2 to 3") means:

"For every 2 of one thing, there are 3 of another thing."

Example of Ratios¶

Ratios compare quantities in a fixed order. "Boys to girls" is not the same as "girls to boys", so keep the order from the question.

Dividing an Amount in a Given Ratio¶

Sometimes you need to split something into parts based on a ratio.