Understanding Fractions Fractions are a fundamental concept in mathematics, representing parts of a whole. In the 11-plus exam, it is essential to have a strong...
Fractions are a fundamental concept in mathematics, representing parts of a whole. In the 11-plus exam, it is essential to have a strong grasp of fractions, including how to compare, simplify, and perform operations on them.
Equivalent fractions are different fractions that represent the same value. For example, 1/2 is equivalent to 2/4. To find equivalent fractions, you can multiply or divide both the numerator and the denominator by the same number.
Problem: Find two equivalent fractions for 3/5.
Solution:
Simplifying fractions involves reducing them to their lowest terms. This is done by dividing both the numerator and the 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, find the least common multiple (LCM) of the denominators to convert them.
Problem: Compare 1/3 and 1/4.
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When adding or subtracting fractions with different denominators, find a common denominator first.
Problem: Add 1/4 and 1/6.
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To multiply fractions, multiply the numerators and denominators. To divide, multiply by the reciprocal of the second fraction.
Problem: Multiply 2/3 by 3/4.
Solution:
Mixed numbers can be converted to improper fractions by multiplying the whole number by the denominator and adding the numerator.
Problem: Convert 2 1/3 to an improper fraction.
Solution:
To find a fraction of an amount, multiply the amount by the numerator and divide by the denominator.
Problem: Find 2/5 of 20.
Solution:
Understanding fractions is crucial for success in the 11-plus exam. Practice these concepts regularly to build confidence and proficiency.