Learning objectives
- Recognise equivalent fractions.
- Compare fractions using common denominators.
- Convert simple fractions to decimals.
- Solve money and measurement problems.
Understanding a fraction
A fraction represents part of a whole or part of a group. The numerator tells how many equal parts are being considered, while the denominator tells how many equal parts make the whole.
Fractions are equivalent when they describe the same value. Multiplying or dividing both numerator and denominator by the same non-zero number keeps the fraction's value unchanged.
Comparing and operating
Fractions with the same denominator can be compared by looking at their numerators. For unlike denominators, convert them to equivalent fractions with a common denominator.
To add or subtract unlike fractions, first find a common denominator. Then combine the numerators and simplify the result where possible.
Decimals and place value
Decimals are another way to write fractions based on tenths, hundredths and thousandths. In 3.47, the 4 represents four tenths and the 7 represents seven hundredths.
Money and metric measurements commonly use decimals. Align decimal points before adding or subtracting.
Why equivalent fractions really are equal
A fraction is not just two whole numbers written one above the other; it represents a relationship. Multiplying numerator and denominator by the same non-zero number divides the whole into more equal pieces while selecting proportionally more of them.
Number-line challenge
Draw a number line from 0 to 1. Mark 1/2, 2/4, 4/8 and 0.5. They should land at exactly the same point. Then place 3/4 and 0.75. This is a useful way to detect mistakes: equivalent fractions and decimals must represent the same position, not merely look similar.
Worked example: equivalent fractions and decimal values
Suppose a class shares one chocolate bar evenly. Three of four equal pieces represent 3/4 of the bar. If every piece is divided into two smaller equal pieces, six of eight pieces represent the same quantity: 3/4 = 6/8. The number of pieces changed, but the amount of chocolate did not.
To write 3/4 as a decimal, convert the denominator to 100: multiply the top and bottom by 25 to get 75/100. Therefore, 3/4 = 0.75. In money, this is the same proportion as 75 paise out of one rupee.
Comparing decimals without guessing
To compare 0.7 and 0.65, rewrite 0.7 as 0.70. Now compare hundredths: 70 hundredths is greater than 65 hundredths, so 0.7 is greater than 0.65. Adding a zero at the end of the decimal part does not change its value.
Try these two questions
A ribbon is 2.5 m long. You use 0.75 m. How much is left?
Align decimal places: 2.50 − 0.75 = 1.75 m.
Which is larger: 5/8 or 0.6?
Convert 5/8 to 0.625, or 625 thousandths. Since 0.625 is greater than 0.600, 5/8 is larger.
Common mistake: Adding denominators when adding fractions. First express fractions with a common denominator; for example, 1/2 + 1/4 = 2/4 + 1/4 = 3/4.
Number-line diagnosis
Ask which is larger, 0.4 or 0.35, without using an algorithm. Place both on a 0-to-1 number line, then rewrite 0.4 as 0.40. If a learner chooses 0.35 because 35 is larger than 4, the issue is place value, not arithmetic.
For operations, estimate first. A product of two numbers less than one should not become larger than both factors; that check catches many misplaced decimal points.
Fraction-decimal bridge
Equivalent fractions name the same amount with different partitions. Decimals are place-value notation for tenths, hundredths and so on. Convert by preserving value, and use a diagram or number line when a symbolic step feels unconvincing.
Practice questions with explanations
Try each question before opening the answer. The explanation shows the reasoning, not only the final response.
Q1. In the fraction 5/8, what does the denominator represent?
Answer: The whole is divided into eight equal parts.
Explanation: The denominator gives the total number of equal parts.
Q2. Write an equivalent fraction for 3/4 with denominator 12.
Answer: 9/12.
Explanation: Multiply both numerator and denominator by 3.
Q3. Which is greater: 2/3 or 3/5?
Answer: 2/3.
Explanation: Using denominator 15 gives 10/15 and 9/15.
Q4. Calculate 1/4 + 2/4.
Answer: 3/4.
Explanation: The denominators are equal, so add the numerators.
Q5. Calculate 1/2 + 1/3.
Answer: 5/6.
Explanation: Convert to 3/6 + 2/6.
Q6. Convert 7/10 to a decimal.
Answer: 0.7.
Explanation: Seven tenths is written in the tenths place.
Q7. Convert 0.25 to a fraction in simplest form.
Answer: 1/4.
Explanation: 0.25 is 25/100, which simplifies by dividing by 25.
Q8. What is 3.6 + 1.45?
Answer: 5.05.
Explanation: Align the decimal points and add place by place.
Q9. A ribbon is 2.5 m long. If 0.75 m is cut off, how much remains?
Answer: 1.75 m.
Explanation: Subtract 0.75 from 2.50.
Q10. Why must fractions have a common denominator before addition?
Answer: The parts must be the same size.
Explanation: Only equal-sized parts can be counted together directly.