Fraction Class 6 ICSE — Maths Chapter 6
This Fraction Class 6 ICSE chapter, Decimal Fractions from your Class 6 Mathematics book, shows you how fractions with denominators of 10, 100, 1000 or higher powers of 10 are written using a decimal point. You will convert fractions to decimals and back, and learn to add, subtract, multiply and divide decimal numbers. The chapter closes with word problems using rupees, metres and kilograms. The current Class 6 syllabus is published on the official CISCE website.
Download Decimal Fractions Class 6 ICSE Mathematics Chapter 6 PDF
Download the Decimal Fractions Class 6 ICSE Mathematics chapter PDF to revise offline or print for practice. It is the full chapter as printed in the book — 12 pages, 10 sections, 51 questions.
What is inside Chapter 6
12 pages · 10 sections · 12 worked examples · 51 exercise questions
| Section | Title |
|---|---|
| 6.1 | BASIC CONCEPT |
| 6.2 | NUMBER OF DECIMAL PLACES |
| 6.3 | LIKE AND UNLIKE DECIMAL NUMBERS |
| 6.4 | CONVERSION OF A GIVEN FRACTION INTO A DECIMAL FRACTION |
| 6.5 | CONVERSION OF A GIVEN DECIMAL FRACTION INTO A NON-DECIMAL FRACTION |
| 6.6 | ADDITION OF DECIMAL NUMBERS |
| 6.7 | SUBTRACTION |
| 6.8 | MULTIPLICATION |
| 6.9 | DIVISION |
| 6.11 | WORD PROBLEMS BASED ON DECIMALS |
- EXERCISE 6(A): 5 questions
- EXERCISE 6(B): 9 questions
- EXERCISE 6(C): 12 questions
- EXERCISE 6(E): 25 questions
6.1 BASIC CONCEPT
A decimal fraction is a fraction whose denominator is 10 or a higher power of 10, such as 100, 1000 or 10000. Examples include \frac{7}{10}, \frac{13}{100} and \frac{357}{1000}. The denominator is removed, and a small dot called the decimal point is inserted in its proper place.
The placement follows a clear rule. One zero in the denominator means the point sits one digit from the right. Two zeroes means two digits from the right, and so on. So \frac{2}{10} = 0.2, \frac{24}{100} = 0.24, and \frac{5278}{1000} = 5.278. The digits before the point form the integral part; the digits after it form the decimal part. For example, 3.1 means 3 plus 0.1.
A fraction whose denominator can be turned into a power of 10 is also a decimal fraction. For instance, \frac{3}{5} = \frac{6}{10} = 0.6. Worked pattern: take \frac{9}{50}. Multiply top and bottom by 2 to get \frac{18}{100} = 0.18. The two zeroes in 100 place the point two digits from the right. This connects to the fraction work in earlier chapters of the Class 6 Mathematics book.
6.2 NUMBER OF DECIMAL PLACES
The number of decimal places in a number is the number of digits in its decimal part. In 3.462, the decimal part is.462, which has three digits. So 3.462 has three decimal places. In the same way, 4.83 has two decimal places, and 0.0478 has four. In 0.0478, the decimal part.0478 contains four digits: 0, 4, 7 and 8. The zero before the point is not part of this count.
When a number has only a decimal part, such as.7,.83 or.403, write a zero before the decimal point. Write 0.7, 0.83 and 0.403 instead. This convention prevents confusion when you align decimals for addition and subtraction later in this ICSE chapter.
Worked pattern: the number 0.0065 has four digits after the point, so it has four decimal places. The leading zero before the point is not part of the count. Decimal places matter because like and unlike decimals are defined by them, as the next section shows.
6.3 LIKE AND UNLIKE DECIMAL NUMBERS
Like decimal numbers have the same number of decimal places. Unlike decimal numbers do not. For example, 5.7, 0.8 and 329.2 are like decimals because each has one decimal place. But 2.6, 40.32 and 0.009 are unlike, because their decimal place counts differ. Recognising like and unlike decimals is a core skill in this Class 6 ICSE chapter.
Unlike decimals can be converted into like decimals. Find the number with the most decimal places, then add trailing zeros to the others until every count matches. Consider 5.8, 239.06 and 0.5497. The largest count is four, so write 5.8000, 239.0600 and 0.5497.
Adding trailing zeros on the right never changes the value. This is why 0.50 and 0.5 are equal, even though they look different. Why does conversion matter? Addition and subtraction later in the chapter require like decimals, so you convert before you calculate. Practice this now to save time later.
Worked pattern: turn 12.5, 0.34 and 7.891 into like decimals. The largest count is three, so write 12.500, 0.340 and 7.891.
6.4 CONVERSION OF A GIVEN FRACTION INTO A DECIMAL FRACTION
Case 1: the denominator is already 10, 100, 1000 or another power of 10. Count the zeroes in the denominator. Mark the decimal point that many digits from the right in the numerator, then remove the denominator. For \frac{327}{100}, two zeroes give 3.27. For \frac{7}{10}, one zero gives 0.7.
Placeholder zero: for \frac{14}{1000}, the denominator has three zeroes but the numerator has only two digits. Write one zero to the left of 14 before placing the point, giving 0.014. Writing 0.14 here is a common mistake; the value is ten times too large. Watch for these point-placement errors:
- For \frac{14}{1000}, writing 0.14 instead of 0.014. The numerator needs a placeholder zero before the point.
- For \frac{254}{10}, writing 2.54 instead of 25.4. One zero means exactly one digit from the right.
- For \frac{5}{1000}, writing 0.5 instead of 0.005. Every zero in the denominator must be accounted for.
Case 2: the denominator can be made into a power of 10. Multiply both numerator and denominator by a suitable number. For \frac{1}{4}, multiply by 25 to get \frac{25}{100} = 0.25. For \frac{73}{125}, multiply by 8 to get \frac{584}{1000} = 0.584.
Edge case: some fractions have denominators that cannot be turned into a power of 10. Their conversion into decimals is left for Class 7. In the Class 6 ICSE syllabus, only the two cases above are examined.
Worked pattern: convert \frac{11}{40}. Multiply top and bottom by 25 to get \frac{275}{1000} = 0.275. The three zeroes place the point three digits from the right.
6.5 CONVERSION OF A GIVEN DECIMAL FRACTION INTO A NON-DECIMAL FRACTION
This is the reverse process. Remove the decimal point, then write a denominator of 1 followed by as many zeroes as there are digits in the decimal part. Then simplify. For 0.42, the decimal part has two digits, so write \frac{42}{100}, which simplifies to \frac{21}{50}. For 0.021, three digits give \frac{21}{1000}. The leading zero in 021 disappears because 021 is the same as 21.
The denominator’s zero count always matches the decimal place count. A two-digit decimal part gives a denominator of 100. A three-digit part gives 1000. This keeps the fraction equal in value to the original decimal.
When the number has a whole part, include it in the numerator. For 1.75, write \frac{175}{100} = \frac{7}{4} = 1\frac{3}{4}. Always reduce the fraction to its lowest terms at the end.
Worked pattern: convert 0.35. Two digits give \frac{35}{100} = \frac{7}{20}. Now convert 2.5. One digit gives \frac{25}{10} = \frac{5}{2}. The whole part becomes part of the numerator.
6.6 ADDITION OF DECIMAL NUMBERS
Addition follows three steps. First, convert the numbers to like decimals if needed. Second, write them one below the other with the decimal points in the same vertical line. Third, add, then place the point in the result directly below the other points.
Why convert first? Like decimals have equal place counts, so every column has the same unit. Tenths sit with tenths, hundredths with hundredths. The addition then works exactly like whole-number addition, with the point marking where the units end.
The decimal point is the anchor of each column. If the points are not aligned, tenths get added to hundredths and the answer is wrong. This is the step students most often rush.
Worked pattern: add 4.5, 12.63 and 0.078. The largest decimal place count is three, so write 4.500, 12.630 and 0.078. Align the points and add: 4.500 + 12.630 + 0.078 = 17.208. Always check that every number in the column has the same count of digits after the point before you start.
6.7 SUBTRACTION
Subtraction uses the same alignment as addition. Convert to like decimals if needed, keep the points in one vertical line, and subtract. When a digit is too small, borrow from the column on its left. For example, 50.20 - 12.35 = 37.85, because you borrow twice, once in the hundredths column and once in the tenths.
Why group positives and negatives? Adding all positives first and all negatives first gives two single numbers. Combining those two is simpler than switching signs several times in one long chain. This method also reduces sign errors.
In subtraction, write the larger number on top. The result keeps the same sign as the larger number. For mixed chains, check each sign before grouping so no term is missed. Like addition, subtraction needs equal decimal place counts. Convert first, then subtract column by column from right to left.
Worked pattern: simplify 20.5 - 4.36 + 7.08. Group the positives: 20.5 + 7.08 = 27.58. Then subtract: 27.58 - 4.36 = 23.22.
6.8 MULTIPLICATION
Multiplication has two steps. First, multiply the numbers ignoring the decimal points. Second, place the point in the product so it has as many decimal places as the sum of the decimal places in the two factors.
Why count decimal places? The product of two numbers with one decimal place each must have two. This rule comes from the fact that tenths times tenths gives hundredths. The count is always the sum of the two factor counts.
Worked pattern: multiply 3.2 by 4.5. Ignore the points and multiply 32 \times 45 = 1440. The factors have 1 + 1 = 2 decimal places, so the product is 14.40, which equals 14.4. A trailing zero does not change the value; 0.0480 and 0.048 are the same number.
Multiplying by powers of 10 shifts the point right. 3.29 \times 10 = 32.9, 3.29 \times 100 = 329, and 3.29 \times 1000 = 3290. Count the zeroes in the multiplier to know how many places to shift. This rule works for any decimal, large or small. For 0.008 × 1000, shift three places right to get 8.
6.9 DIVISION
Division has three cases. Case (a): divide by a natural number. Divide normally, and place the point in the quotient just after the integral part is divided. For example, 96.4 \div 4 = 24.1. The 96 divides to give 24, then the point is placed, then 4 ÷ 4 gives 1.
Case (b): divide by a decimal. Write the division as a fraction with the dividend on top and the divisor below. Multiply both terms by 10, 100 or 1000 to clear the decimal point from the divisor, then divide. Worked pattern: 6.3 \div 0.15. Write \frac{6.3}{0.15}, multiply both by 100 to get \frac{630}{15} = 42.
Case (c): divide by 10, 100 or 1000. Shift the point left by one, two or three places. For example, 27.5 \div 10 = 2.75 and 27.5 \div 100 = 0.275.
This ICSE chapter also connects decimals to real-life units. In currency, 100 paise make ₹1, so rupees go before the point and paise after. In length, 100 cm make 1 m. In weight, 1000 gm make 1 kg. The table shows the pattern.
| Quantity | Unit relation | Decimal form |
|---|---|---|
| ₹25 and 8 paise | 100 paise = ₹1 | ₹25.08 |
| 4 m and 6 cm | 100 cm = 1 m | 4.06 m |
| 2 kg and 350 gm | 1000 gm = 1 kg | 2.350 kg |
More practice material sits in the Class 6 ICSE books collection.
6.11 WORD PROBLEMS BASED ON DECIMALS
Word problems combine the operations from the earlier sections. Three shapes recur. One: cost per unit times quantity. Two: total length divided into equal pieces. Three: total weight divided by the number of items. Decide which operation the question asks for before calculating.
Worked pattern 1: cloth costs ₹22.40 per metre. For 3.5 m, multiply: 22.40 \times 3.5 = 78.40. The cost is ₹78.40. The operation is multiplication because the quantity is a multiple of the unit price.
Worked pattern 2: a 15.6 m rod is cut into 4 equal pieces. Divide: 15.6 \div 4 = 3.9. Each piece is 3.9 m. Here the operation is division because the total is shared equally.
Worked pattern 3: 12 identical books weigh 30 kg. Each book weighs 30 \div 12 = 2.5 kg. This is the same shape as the rod problem, but with weight instead of length.
Word problems in this Class 6 ICSE chapter give you the numbers in sentences. Read each question carefully to spot which operation fits.
What to practise from Fraction Class 6 ICSE Chapter 6
The exercises in this Fraction Class 6 ICSE chapter build from basic definitions to word problems. Practise each block in order. The chapter has no separate Exercise 6(D).
- EXERCISE 6(A) — 5 questions: decimal places, like and unlike decimals, fractions to decimals.
- EXERCISE 6(B) — 9 questions: addition, subtraction, simplification of mixed chains.
- EXERCISE 6(C) — 12 questions: multiplication, division, powers of 10.
- EXERCISE 6(E) — 25 questions: word problems on money, length and weight.
Fraction Class 6 ICSE Chapter 6 frequently asked questions
What is a decimal fraction in class 6 ICSE?
A decimal fraction is a fraction whose denominator is 10 or a higher power of 10, such as 100 or 1000. The denominator is removed and replaced by a decimal point placed in the proper position. For example, \frac{7}{10} = 0.7.
How do you convert a fraction into a decimal?
If the denominator is a power of 10, count its zeroes and place the point that many digits from the right. If not, multiply both numerator and denominator by a suitable number to make the denominator a power of 10, then proceed as before.
When do I write a zero before the decimal point?
When a number has only a decimal part, such as.7 or.83, write 0.7 and 0.83. The zero makes the number clearer and prevents alignment mistakes in addition and subtraction.
How do I divide one decimal by another decimal?
Write the division as a fraction with the dividend on top and the divisor below. Multiply both by a power of 10 to clear the decimal point from the divisor, then divide normally. For example, 6.3 \div 0.15 = 630 \div 15 = 42.
Reference: ICSE Class 6 Mathematics textbook material, chapter 6: Decimal Fractions — CISCE-aligned.