How to Solve Fraction Word Problems with Methods and Examples
The concept of Less Than is one of the foundational ideas in mathematics. Understanding how to compare numbers using the less than symbol is essential for school maths, competitive exams, and everyday reasoning. Recognising which value is less or greater quickly helps students solve problems and interpret data with confidence.
What is Less Than?
In mathematics, less than is a comparison between two numbers or quantities. If a number is smaller than another number, it is said to be less than the other. This is shown using the less than symbol: <. For example, if we compare 4 and 7, we write 4 < 7, which reads as “4 is less than 7”. This simple symbol is widely used in arithmetic, algebra, number theory, and data analysis. Recognizing which value is less helps in ordering numbers, solving inequalities, and making decisions.
The Less Than Symbol: <
The less than symbol is <. The open side of the symbol always faces the bigger number, while the pointed side faces the smaller number. For example:
- 3 < 6 (Three is less than six)
- -2 < 0 (Negative two is less than zero)
- x < 8 (x is less than eight)
Whenever you see the < symbol between two values, the one on the left is smaller than the one on the right.
How to Use the Less Than Sign
To use the less than sign correctly, place the numbers or expressions you want to compare on either side, with the smaller value on the left and the larger on the right. Here are clear steps:
- Identify the two values you are comparing.
- Write the smaller value first.
- Insert the < symbol.
- Write the greater value after the symbol.
For instance, to say “14 is less than 32,” write: 14 < 32.
Tip: The “<” sign looks like the letter “L” for “less.” This can help you remember it while comparing numbers.
Worked Examples with Less Than
Example 1
Compare 5 and 9. Which is less? How do you write it?
- 5 is smaller than 9.
- Write: 5 < 9
Example 2
Which statement is true: 12 < 7 or 7 < 12?
- 12 is greater than 7, so 12 < 7 is false.
- 7 is less than 12, so 7 < 12 is true.
Example 3
If Ravi has 3 crayons and Saina has 8 crayons, who has fewer crayons?
- Ravi has fewer crayons.
- We write 3 < 8.
Practice Problems
- Write a less than statement for 15 and 22.
- Is 6 < 3 true or false?
- Which is less, -5 or 4? Use the less than symbol.
- Compare: 27 and 30 using <.
- Fill in the blank: 9 ___ 11 (choose < or >)
Common Mistakes to Avoid
- Writing the < symbol the wrong way around. The open side should always face the bigger number.
- Mistaking the < symbol for greater than (>). Remember: < is “less than,” > is “greater than.”
- Using < for equality. If values are equal, use = not <.
- Comparing negative numbers—remember that -3 < -1, because -3 is further left on the number line.
Real-World Applications of Less Than
The less than symbol is used everywhere. For example, when you see a label “Only children less than 12 years old allowed,” it means ages below 12. In shopping, if you have less than $100, you cannot buy items costing $120. In science, temperature limits (like “Keep below 10°C”) use less than conditions. In computers, coding languages use < as a standard comparison symbol.
At Vedantu, we make these daily maths ideas clear and fun, showing how the less than sign helps in life and learning.
Related Concepts and Internal Links
- To understand the opposite comparison, greater than symbol (>) is helpful.
- To learn about numbers on the number line, visit number lines at Vedantu.
- For comparing fractions and decimals, refer to comparing fractions.
In summary, understanding the less than symbol < and using it to compare numbers is a basic but vital skill in maths. It helps in solving problems, understanding data, and making decisions. Practice comparing numbers, avoid common mistakes, and apply this skill in everyday life for exam and real-world success. At Vedantu, we support you in building these fundamental skills for a strong maths foundation.
FAQs on Problem Solving Using Fractions Step by Step Guide
1. What is a fraction in Maths?
A fraction is a number that represents a part of a whole and is written in the form a/b, where a is the numerator and b ≠ 0 is the denominator. The numerator shows how many parts are taken, and the denominator shows the total equal parts. For example, in 3/4, 3 is the numerator and 4 is the denominator, meaning 3 out of 4 equal parts.
2. How do you solve word problems using fractions?
To solve word problems using fractions, identify the operation needed and apply the correct fraction rule. Follow these steps:
- Read the problem carefully and identify given fractions.
- Decide whether to add, subtract, multiply, or divide.
- Convert mixed numbers to improper fractions if needed.
- Perform the operation and simplify the final answer.
3. How do you add fractions with different denominators?
To add fractions with different denominators, first find a common denominator, then add the numerators. Steps:
- Find the LCM of the denominators.
- Convert each fraction to an equivalent fraction with the LCM.
- Add the numerators and keep the common denominator.
- Simplify the result.
4. How do you multiply fractions?
To multiply fractions, multiply the numerators together and the denominators together. The formula is (a/b) × (c/d) = (ac)/(bd). Example:
- 2/3 × 3/5
- Multiply numerators: 2 × 3 = 6
- Multiply denominators: 3 × 5 = 15
- Result = 6/15 = 2/5 (simplified)
5. How do you divide fractions?
To divide fractions, multiply the first fraction by the reciprocal of the second fraction. The rule is (a/b) ÷ (c/d) = (a/b) × (d/c). Example:
- 3/4 ÷ 2/5
- Reciprocal of 2/5 is 5/2
- Multiply: 3/4 × 5/2 = 15/8
- Final answer = 15/8 or 1 7/8
6. What is the difference between proper, improper, and mixed fractions?
The difference lies in the relationship between the numerator and denominator.
- Proper fraction: numerator < denominator (e.g., 3/5).
- Improper fraction: numerator ≥ denominator (e.g., 7/4).
- Mixed fraction: whole number + proper fraction (e.g., 1 3/4).
7. How do you simplify or reduce a fraction?
To simplify a fraction, divide the numerator and denominator by their greatest common factor (GCF). Steps:
- Find the GCF of numerator and denominator.
- Divide both by the GCF.
8. How do you convert a mixed number to an improper fraction?
To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. Formula: (whole × denominator + numerator) / denominator. Example:
- Convert 2 3/5
- (2 × 5 + 3)/5 = (10 + 3)/5 = 13/5
9. How are fractions used in real life problem solving?
Fractions are used in real life to represent parts of quantities in situations like cooking, shopping, and measurements. Common applications include:
- Recipes (e.g., 1/2 cup of sugar)
- Discounts (e.g., 1/4 off the price)
- Time management (e.g., 3/4 hour)
- Sharing items equally
10. What are common mistakes when solving fraction problems?
Common mistakes in solving fraction problems include using incorrect operations or forgetting key rules. Typical errors are:
- Adding or subtracting numerators without a common denominator.
- Not simplifying the final answer.
- Forgetting to use the reciprocal when dividing.
- Mixing up numerator and denominator.
