QQuestionMathematics
QuestionMathematics
# 20. Write $6 \frac{7}{8}$ as an improper fraction three different ways.
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Answer
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Step 1:: Understand the problem
We need to write the mixed number $6 extrac{7}{8}$ as an improper fraction.
This means we need to convert the whole number part (6) and the fraction part ($ extrac{7}{8}$) into a single fraction.
Step 2:: Convert the whole number part to a fraction
To convert the whole number part to a fraction, multiply it by the denominator of the fraction part and add the numerator: Whole number part as a fraction = (Whole number * Denominator) + Numerator = (6 * 8) + 7 \ = 48 + 7 \ = 55
Step 3:: Write the improper fraction with the original denominator
Now, write the improper fraction using the original denominator (8): Improper fraction (1) = Improper fraction numeral (from Step 2) / Denominator = 55 / 8
Step 4:: Alternative method: convert the mixed number to a sum of fractions
Another way to write the mixed number as an improper fraction is to convert the whole number part to a fraction with the same denominator as the fraction part, then add the two fractions: Alternative improper fraction (1) = Fraction from whole number part + Original fraction Fraction from whole number part = Whole number as a fraction (from Step 2) = 55 / 8 Alternative improper fraction (1) = Fraction from whole number part + Original fraction = 55 / 8 + 7 / 8
Step 5:: Alternative method: convert the mixed number to a product of the whole number and the sum of 1 and the fraction part
The third way to write the mixed number as an improper fraction is to multiply the whole number by the sum of 1 and the fraction part: Alternative improper fraction (2) = Whole number * (1 + Fraction part) = 1 + extrac{7}{8} \ = extrac{15}{8} Alternative improper fraction (2) = Whole number * (1 + Fraction part) = 6 * extrac{15}{8} \ = 90 / 8 \ = 11 extrac{1}{8}
Final Answer
The mixed number $6 extrac{7}{8}$ can be written as an improper fraction in three different ways: Improper fraction (1): 55 / 8 Alternative improper fraction (1): 55 / 8 + 7 / 8 = 62 / 8 Alternative improper fraction (2): 11 extrac{1}{8}
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