Understanding Fractions Fractions are a fundamental concept in mathematics, especially for the 11-plus exam. This section will cover various aspects of working...
Fractions are a fundamental concept in mathematics, especially for the 11-plus exam. This section will cover various aspects of working with fractions, including comparing, simplifying, and performing operations.
Equivalent fractions are different fractions that represent the same value. For example, 1/2 is equivalent to 2/4 and 3/6. To find equivalent fractions, you can multiply or divide the numerator and denominator by the same number.
Problem: Find two equivalent fractions for 3/4.
Solution:
Simplifying fractions means reducing them to their lowest terms. This is done by dividing both the numerator and denominator by their greatest common divisor (GCD).
Problem: Simplify the fraction 8/12.
Solution:
To compare fractions, they must have a common denominator. If they do not, convert them to equivalent fractions with a common denominator before comparing.
Problem: Which is greater: 1/3 or 1/4?
Solution:
When adding or subtracting fractions with different denominators, first find a common denominator.
Problem: Add 1/4 and 1/6.
Solution:
To multiply fractions, multiply the numerators and denominators. To divide fractions, multiply by the reciprocal of the second fraction.
Problem: Multiply 2/3 by 4/5.
Solution:
A mixed number consists of a whole number and a fraction. An improper fraction has a numerator larger than its denominator. To convert, multiply the whole number by the denominator and add the numerator.
Problem: Convert 2 1/3 to an improper fraction.
Solution:
To find a fraction of an amount, multiply the amount by the fraction.
Problem: Find 2/5 of 20.
Solution:
Understanding these concepts is crucial for success in the 11-plus mathematics exam. Practice regularly to enhance your skills in working with fractions.