What is the sum of [tex]37 / 8+25 / 16+3 / 16[/tex] reduced to the lowest denominator?
A. [tex]6^{3 / 8}[/tex]
B. [tex]6 \frac{1}{2}[/tex]
C. [tex]6^{3 / 4}[/tex]
D. [tex]6 \frac{6}{16}[/tex]
Answer (2)
Find a common denominator: Convert all fractions to have the same denominator, which is 16 in this case.
Add the fractions: Add the numerators of the fractions with the common denominator.
Simplify the fraction: Reduce the resulting fraction to its simplest form.
Convert to a mixed number: Express the simplified fraction as a mixed number.
The sum of 37/8 + 25/16 + 3/16 reduced to the lowest denominator is 6 8 3 .
Explanation
Understanding the Problem We need to find the sum of the three fractions 37/8 , 25/16 , and 3/16 . Our goal is to express this sum as a mixed number where the fractional part is reduced to its lowest terms.
Finding a Common Denominator To add these fractions, we first need to find a common denominator. The least common multiple of 8 and 16 is 16. So, we will convert each fraction to an equivalent fraction with a denominator of 16. We have 8 37 = 8 × 2 37 × 2 = 16 74 The other two fractions already have a denominator of 16, so we don't need to change them.
Adding the Fractions Now we can add the fractions: 16 74 + 16 25 + 16 3 = 16 74 + 25 + 3 = 16 102 So the sum is 16 102 .
Simplifying the Fraction Next, we simplify the fraction 16 102 . Both the numerator and the denominator are divisible by 2: 16 102 = 16 ÷ 2 102 ÷ 2 = 8 51 So the simplified fraction is 8 51 .
Converting to a Mixed Number Now we convert the improper fraction 8 51 to a mixed number. We divide 51 by 8. The quotient is 6 and the remainder is 3. Therefore, 8 51 = 6 8 3 So the sum is 6 8 3 .
Final Answer Finally, we compare our result 6 8 3 with the given options. The correct answer is 6 8 3 .
Examples
Fractions are used in everyday life, such as when cooking, baking, or measuring ingredients. For example, if a recipe calls for 37/8 cups of flour, 25/16 cups of sugar, and 3/16 cups of baking powder, you need to add these fractions to determine the total amount of dry ingredients. Understanding how to add and simplify fractions is essential for accurate measurements and successful cooking.
The sum of 8 37 + 16 25 + 16 3 is calculated by finding a common denominator, which is 16. After converting the fractions and adding them, we simplify to get 6 8 3 . The correct answer is option A: 6 8 3 .
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