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Have you ever shared a pizza with friends? Or seen the price of something with a dot in between, like '₹50.50'? That's where decimals and fractions come into play! They help us talk about parts of a whole thing, whether it's a slice of pizza or half a rupee. Understanding them makes daily calculations super easy and helps you ace your exams!
For common fractions, try to make the bottom number (denominator) 10, 100, or 1000 by multiplying both top and bottom by the same number. It's like finding equivalent fractions. Then, just write the top number with the decimal point in the right place!
When multiplying decimals, ignore the decimal points at first. Multiply them as if they are whole numbers. After getting the answer, count how many total decimal places were in the original numbers. Put the decimal point in your answer from the right side, counting that many places.
Dividing by a fraction is the same as multiplying by its 'upside-down' version (called its reciprocal). This makes division much simpler because multiplication is usually easier!
To quickly compare two fractions like a/b and c/d, just 'cross-multiply'. Multiply 'a' with 'd' and 'b' with 'c'. The fraction whose numerator's cross-product is larger is the larger fraction.
If you have a decimal like 4.25 and need to write it as a mixed fraction, it's super simple. The number before the decimal point is your whole number. The numbers after the decimal point form your fraction part. Convert just the decimal part to a simple fraction and attach it to the whole number.
Imagine you have a delicious cake. If you cut it into 4 equal pieces and eat 1 piece, you've eaten 1/4 of the cake. This '1/4' is a fraction. A fraction simply shows a part of a whole thing. The number on top (1 in '1/4') is called the Numerator (अंश). It tells you how many parts you have. The number at the bottom (4 in '1/4') is called the Denominator (हर). It tells you how many total equal parts the whole thing was divided into.
Now, think about money. If you have fifty rupees and fifty paise, you write it as ₹50.50. The dot (.) here is called the decimal point (दशमलव बिंदु). Numbers after the decimal point show parts of a whole. '50' after the point means 50 out of 100 paise, which is half a rupee. Decimals are another way to show parts of a whole, especially when the whole is divided into 10, 100, 1000, or similar parts.
You can easily change a fraction into a decimal and a decimal into a fraction!
You can add, subtract, multiply, and divide them too!
Fraction to Decimal Conversion
Decimal = Numerator ÷ DenominatorDecimal to Fraction Conversion
Fraction = Decimal / (10^n) where n is decimal placesAdding/Subtracting Fractions (Same Denominator)
a/b ± c/b = (a ± c) / bMultiplying Fractions
(a/b) × (c/d) = (a × c) / (b × d)Dividing Fractions
(a/b) ÷ (c/d) = (a/b) × (d/c)| Fraction | Decimal | Concept |
|---|---|---|
| 1/2 | 0.5 | Half of a whole |
| 1/4 | 0.25 | One quarter |
| 3/4 | 0.75 | Three quarters |
| 1/5 | 0.2 | One fifth |
| 1/10 | 0.1 | One tenth |
Q: Anjali bought 2.5 kg of apples and 1.75 kg of oranges. What is the total weight of fruits she bought?
Q: A painter used 3/8 of a can of paint for one wall and 1/4 for another. How much paint did he use in total?
Q: A rope is 12.6 meters long. If you cut it into 3 equal pieces, how long will each piece be?
Q: Which is greater: 5/6 or 0.8?
Your family ordered a large pizza with 8 slices. You ate 3 slices, and your friend ate 2 slices. What fraction of the pizza is left?
You saw a toy car for ₹450.50. If you have ₹300.75 saved up, how much more money do you need?
A jug has 0.8 liters of juice. If you pour out 0.25 liters for your sibling, how much juice is left in the jug?
In a math test, you answered 17 out of 20 questions correctly. What is your score as a decimal?
If 0.333... is written as a fraction, it is equivalent to which of the following?
What is the result of (1/2 + 1/4) × (1 - 1/3)?
A recipe calls for 0.75 cups of sugar. If you want to make half of the recipe, how much sugar will you need?
Which of the following is equivalent to 0.6?
1Which of the following is an improper fraction?
2What is 0.75 as a fraction in its simplest form?
3Add 2.3 + 4.75.
4Subtract 1/3 from 5/6.
5Multiply 0.4 × 0.02.
6Divide 2.4 by 0.6.
7What is the mixed fraction equivalent of 11/3?
8Which of these decimals is the smallest: 0.2, 0.02, 0.22, 2.0?
9A recipe requires 1/2 cup of flour. If you only have 1/4 cup, how much more flour do you need?
10Which fraction is equivalent to 0.8?
For common fractions, try to make the bottom number (denominator) 10, 100, or 1000 by multiplying both top and bottom by the same number. It's like finding equivalent fractions. Then, just write the top number with the decimal point in the right place!
When multiplying decimals, ignore the decimal points at first. Multiply them as if they are whole numbers. After getting the answer, count how many total decimal places were in the original numbers. Put the decimal point in your answer from the right side, counting that many places.
Dividing by a fraction is the same as multiplying by its 'upside-down' version (called its reciprocal). This makes division much simpler because multiplication is usually easier!
To quickly compare two fractions like a/b and c/d, just 'cross-multiply'. Multiply 'a' with 'd' and 'b' with 'c'. The fraction whose numerator's cross-product is larger is the larger fraction.
If you have a decimal like 4.25 and need to write it as a mixed fraction, it's super simple. The number before the decimal point is your whole number. The numbers after the decimal point form your fraction part. Convert just the decimal part to a simple fraction and attach it to the whole number.
Decimal = Numerator ÷ DenominatorFraction = Decimal / (10^n) where n is decimal placesa/b ± c/b = (a ± c) / b+2 more formulas below