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How to Convert Mixed Number 2 3/4 to Simplest Form Improper Fraction
Mathematics
Grade 5 (Primary School)
Question Content
Write 2 3/4 as an improper fraction in its simplest form.
Correct Answer
11/4
Detailed Solution Steps
1
Step 1: Recall the method to convert a mixed number to an improper fraction: Multiply the whole number by the denominator of the fractional part, then add the numerator of the fractional part. This result becomes the new numerator, and the denominator stays the same.
2
Step 2: Apply the formula: Whole number = 2, denominator = 4, numerator = 3. Calculate (2 × 4) + 3 = 8 + 3 = 11.
3
Step 3: Use the original denominator 4 as the denominator of the improper fraction. So the improper fraction is 11/4.
4
Step 4: Check if the fraction can be simplified: 11 is a prime number and does not share any common factors with 4 other than 1, so 11/4 is already in simplest form.
Knowledge Points Involved
1
Mixed Numbers
A mixed number is a combination of a whole number and a proper fraction, used to represent values that are greater than 1 but not a whole integer (e.g., 2 3/4 represents 2 whole units plus 3/4 of a unit). It is commonly used in real-life scenarios like measuring quantities of food or materials.
2
Improper Fractions
An improper fraction is a fraction where the numerator is greater than or equal to the denominator, representing a value that is greater than or equal to 1 (e.g., 11/4). It is useful for mathematical operations like addition, subtraction, multiplication, and division of fractions, as these operations are often easier to perform with improper fractions than mixed numbers.
3
Converting Mixed Numbers to Improper Fractions
The conversion formula is: (Whole Number × Denominator) + Numerator / Denominator. This method converts the whole number part into fractions with the same denominator as the fractional part, then combines them into a single improper fraction. It is a foundational skill for fraction arithmetic.
4
Simplest Form of a Fraction
A fraction is in its simplest form (or lowest terms) when the numerator and denominator have no common positive integer factors other than 1. To simplify, divide both the numerator and denominator by their greatest common factor (GCF). If the GCF of the numerator and denominator is 1, the fraction is already in simplest form.
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