Three different ways to write 6 7/8 as an improper fraction

Three different ways to write 6 7/8 as an improper fraction

The Correct Answer and Explanation is :

To express the mixed number 6 7/8 as an improper fraction, we need to convert the whole number and the fractional part into a single fraction. Here’s a step-by-step explanation of how to do this, followed by three different ways to write it as an improper fraction:

Step 1: Convert the Whole Number to a Fraction

A whole number can be written as a fraction by putting it over 1. For example, 6 as a fraction is 6/1.

Step 2: Convert the Mixed Number to an Improper Fraction

To convert the mixed number 6 7/8 into an improper fraction, follow these steps:

1. Multiply the whole number (6) by the denominator of the fractional part (8).
   [
   6 \times 8 = 48
   ]
2. Add the numerator of the fractional part (7) to the result:
   [
   48 + 7 = 55
   ]
3. Place this sum over the original denominator (8):
   [
   \frac{55}{8}
   ]

Thus, 6 7/8 is equivalent to 55/8 as an improper fraction.

Three Different Ways to Write 6 7/8 as an Improper Fraction

Method 1: Direct Conversion (as shown above)

Starting with the mixed number 6 7/8, we multiply 6 (the whole number) by 8 (the denominator) and then add the numerator (7). The result is 55/8.

Method 2: Using the Fractional Part Alone

We can also write 6 7/8 as:
[
\frac{6}{1} + \frac{7}{8}
]
To add these fractions, we need a common denominator. The least common denominator (LCD) of 1 and 8 is 8:
[
\frac{6}{1} = \frac{48}{8}
]
Now, add the two fractions:
[
\frac{48}{8} + \frac{7}{8} = \frac{55}{8}
]
This also results in the improper fraction 55/8.

Method 3: Visual Fraction Conversion

We can interpret 6 7/8 as 6 whole parts and 7/8 of an additional part. Converting each part:

• Each whole part is equivalent to 8/8.
  Thus, 6 whole parts would be:
  [
  6 \times \frac{8}{8} = \frac{48}{8}
  ]
  Now, add the 7/8 to this:
  [
  \frac{48}{8} + \frac{7}{8} = \frac{55}{8}
  ]
  Once again, this gives 55/8 as the improper fraction.

Conclusion

The improper fraction form of 6 7/8 is 55/8. All three methods lead to the same result. The key to the conversion is understanding how to handle the whole number and the fraction separately and then combine them to create an improper fraction.