Choose the improper fraction equivalent to the mixed number below.
$2 \frac{1}{3}$
A. $\frac{7}{3}$
B. $\frac{5}{3}$
C. $\frac{5}{3}$
D. $\frac{8}{3}$
Answer (1)
Convert the mixed number 2 3 1 to an improper fraction.
Multiply the whole number (2) by the denominator (3) and add the numerator (1): ( 2 × 3 ) + 1 = 7 .
Place the result (7) over the original denominator (3) to get the improper fraction 3 7 .
The improper fraction equivalent to 2 3 1 is 3 7 .
Explanation
Understanding the Problem We are given the mixed number 2 f r a c 1 3 and asked to convert it into an improper fraction. An improper fraction is a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number).
Conversion Method To convert a mixed number to an improper fraction, we multiply the whole number part by the denominator of the fractional part, and then add the numerator of the fractional part. The result becomes the new numerator, and we keep the same denominator. In general, for a mixed number a f r a c b c , the improper fraction is f r a c aim esc + b c .
Calculation Applying this to our mixed number 2 f r a c 1 3 , we have:
Numerator = ( 2 im es 3 ) + 1 = 6 + 1 = 7 Denominator = 3
So, the improper fraction is f r a c 7 3 .
Identifying the Correct Option Comparing our result with the given options: A. f r a c 7 3 B. f r a c 5 3 C. f r a c 5 3 D. f r a c 8 3
The correct option is A.
Final Answer Therefore, the improper fraction equivalent to the mixed number 2 f r a c 1 3 is 3 7 .
Examples
Mixed numbers and improper fractions are useful in everyday situations, such as cooking and baking. For example, if a recipe calls for 2 3 1 cups of flour, it might be easier to measure this amount by thinking of it as 3 7 cups. This means you could fill a 3 1 cup measure seven times. Understanding how to convert between mixed numbers and improper fractions allows for more flexibility in measuring ingredients and adjusting recipes.
