A fraction whose numerator is greater than its denominator is called an improper fraction For example; in the fraction 5/4, the denominator tells you the unit should be divided into 4 equal-sized parts, as shown at the right What do you need to draw in order to show 5 of these 1/4 pieces? Make a sketch of shaded fraction strips to show 5/4. Another way to write 5/4 involves thinking of the number as having a whole number part and a fraction part: How would you do this? Use your drawing of fraction strips in part (a) to explain your answer_ Your answer in part (b), read “one and one-fourth” is called mixed number since it has a whole number part and & fraction part: What does the word “and” indicate in the name of this fraction? Sketch fraction strips to represent each of the following improper fractions Then write the mixed number for each one_ 13/5 11/3 =
The Correct Answer and Explanation is:
To represent an improper fraction like 5/4, begin by recognizing that each whole unit is divided into 4 equal parts. To show 5/4, draw two fraction strips:
- In the first strip, divide it into 4 equal parts and shade all 4 parts to represent one whole.
- In the second strip, divide it into 4 equal parts again and shade only 1 part.
This sketch visually represents the 5 shaded fourths. The first strip shows 4/4, which equals 1 whole, and the second strip adds 1/4. Altogether, 5/4 equals 1 whole and 1/4, or 1 1/4 as a mixed number.
The mixed number 1 1/4 consists of a whole number part (1) and a fractional part (1/4). The word “and” in this context indicates the addition of a fractional part to the whole number. It signals a combination: the entire whole unit plus a portion of another unit.
Representation of Improper Fractions as Mixed Numbers
1. 13/5
- Draw 3 strips, each divided into 5 equal parts.
- Shade 5 parts in the first strip, 5 more parts in the second strip, and 3 parts in the third strip.
- Total shaded: 13 parts out of 5 per strip.
This gives 2 full strips shaded (2 wholes = 10/5) and 3/5 in the third strip.
13/5 = 2 3/5
2. 11/3
- Draw 4 strips, each divided into 3 equal parts.
- Shade 3 parts in the first, 3 parts in the second, 3 parts in the third, and 2 parts in the fourth strip.
- Total shaded: 11 parts out of 3 per group.
This represents 3 full strips shaded (3 wholes = 9/3) and 2/3 on the fourth.
11/3 = 3 2/3
These visual models help in clearly understanding how improper fractions relate to mixed numbers.
