Choose the improper fraction equivalent to the mixed number below.
$9 \frac{4}{8}$
A. $\frac{77}{80}$
B. $\frac{76}{8}$
C. $\frac{75}{9}$
D. $\frac{75}{8}$
Answer (1)
Convert the mixed number 9 8 4 to an improper fraction using the formula c a × c + b .
Substitute a = 9 , b = 4 , and c = 8 into the formula: 8 9 × 8 + 4 .
Calculate the numerator: 9 × 8 + 4 = 72 + 4 = 76 .
The improper fraction is 8 76 .
Explanation
Understanding Improper Fractions We need to convert the mixed number 9 R A C 4 8 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).
Formula for Conversion To convert a mixed number to an improper fraction, we use the formula: a R A C b c = R A C a \tIMES c + b c Where:
a is the whole number part of the mixed number,
b is the numerator of the fractional part,
c is the denominator of the fractional part.
Applying the Formula In our case, a = 9 , b = 4 , and c = 8 . Plugging these values into the formula, we get: 9 R A C 4 8 = R A C 9 \tIMES 8 + 4 8 Now, we perform the multiplication and addition in the numerator: 9 \tIMES 8 = 72 72 + 4 = 76 So, the improper fraction is: R A C 76 8
Identifying the Correct Option Now, we compare our result, 8 76 , with the given options: A. 80 77 B. 8 76 C. 9 75 D. 8 75 We see that option B, 8 76 , matches our calculated improper fraction.
Final Answer Therefore, the improper fraction equivalent to the mixed number 9 8 4 is 8 76 .
Examples
Mixed numbers and improper fractions are useful in everyday situations, such as cooking and baking. For example, if a recipe calls for 2 2 1 cups of flour, you might want to convert this to an improper fraction, which is 2 5 cups. This helps in measuring out the correct amount, especially when you need to combine multiple portions of the recipe. Understanding how to convert between mixed numbers and improper fractions makes it easier to work with quantities in various real-life scenarios.
