Section 4.1 Part 1: Introduction to Fractions, Improper Fractions, and Mixed Numbers

Convert the improper fraction 94/9 to a mixed number.

10 and 4/9

***Name the improper fraction. Then, write it as a mixed number. There are two circles divided into fourths. The first circle is completely shaded, and the second circle has three-fourths of the circle shaded. Provide your answer below:

ANSWER IMPROPER FRACTION 7/4 ANSWER MIXED NUMBER 1 and 3/4 Each circle is divided into 4 pieces, so each piece is 1/4 of the circle. There are 7 pieces shaded, so there are 7 fourths, or 7/4. The figure shows that we also have 1 whole circle and 3 fourths, which is 1 and 3/4. So 7/4=1 and 3/4.

***Name the improper fraction. Then, write it as a mixed number. There are two circles divided into ninths. The first circle is completely shaded, and the second circle has seven-ninths of the circle shaded. Provide your answer below:

ANSWER IMPROPER FRACTION 16/9 ANSWER MIXED NUMBER 1 and 7/9 Each circle is divided into 9 pieces, so each piece is 19 of the circle. There are 16 pieces shaded, so there are 16 ninths, or 16/9. The figure shows that we also have 1 whole circle and 7 ninths, which is 1 and 7/9. So 16/9= 1 and 7/9.

***Name the improper fraction. Then, write it as a mixed number. Do not reduce the fractions. There are two circles divided into twelfths. The first circle is completely shaded, and the second circle has eight-twelfths of the circle shaded. Provide your answer below: Improper fraction =​, mixed number =

ANSWER IMPROPER FRACTION 20/12 ANSWER MIXED NUMBER 1 and 8/12 Each circle is divided into 12 pieces, so each piece is 1/12 of the circle. There are 20 pieces shaded, so there are 20 twelfths, or 20/12. The figure shows that we also have 1 whole circle and 8 twelfths, which is 1 and 8/12. So 20/12=1 and 8/12.

***Name the improper fraction. Then, write it as a mixed number. Do not simplify. There are two circles divided into fourths. The first circle is completely shaded, and the second circle has two-fourths of the circle shaded. Provide your answer below:

ANSWER IMPROPER FRACTION 6/4 ANSWER MIXED NUMBER 1 and 2/4 Each circle is divided into 4 pieces, so each piece is 1/4 of the circle. There are 6 pieces shaded, so there are 6 fourths, or 6/4. The figure shows that we also have 1 whole circle and 2 fourths, which is 1 and 2/4. So 6/4=1 and 2/4.

Use a model to rewrite the improper fraction as a mixed number: 6/5.

1 and 1/5 We start with 6 fifths (6/5). We know that 5 fifths makes 1 whole. 5/5=1 That leaves us with 1 more fifth, which is 1 and 5 (6 fifths minus 5 fifths is 1 fifth).So 6/5=1 and 1/5.

Use a model to rewrite the improper fraction as a mixed number: 7/6.

1 and 1/6 We start with 7 sixths (7/6). We know that 6 sixths makes 1 whole. 6/6=1 That leaves us with 1 more sixth, which is 1/6 (7 sixths minus 6 sixths is 1 sixth). So 7/6= 1 and 1/6.

Convert the improper fraction 27/19 to a mixed number.

1 and 8/19

Use a model to rewrite the mixed number 1 and 3/10 as an improper fraction.

13/10

Write the mixed number 1 and 4/9 as an improper fraction.

13/9 The denominator of the improper fraction is the same as the denominator in the mixed number, which is 9. To find the numerator of the improper fraction multiply the denominator times the whole number, and then add the numerator. 9×1+4=13 So the improper fraction is 13/9. Modeling this fraction shows that each circle is divided into 9 pieces, so each piece is 1/9 of the circle. In the circle on the left, all 9 pieces are shaded, which is 9/9 or 1. In the circle on the right, four of the pieces are shaded, or 4/9. There are two circles divided into ninths. The first circle is completely shaded, and the second circle has four-ninths of the circle shaded. Therefore, 9/9+4/9=13/9

Convert the improper fraction 91/6 to a mixed number.

15 and 1/6 Start by dividing the denominator into the numerator. Remember that 91/6 means 6/91. Identify the quotient, remainder, and divisor then write the mixed number as quotient and remainder/divisor. The quotient is 15, the remainder is 1, and the divisor is 6, so 91/6=15 and 1/6.

Convert the improper fraction to a mixed number: 23/7.

3 and 2/7

Convert the mixed number to an improper fraction: 4 and 6/11.

50/11

Convert the mixed number 5 and 5/9 to an improper fraction.

50/9 Step 1. Multiply the whole number by the denominator. The whole number is 5 and the denominator is 9. Step 2. Add the numerator to the product found in Step 1.The numerator of the mixed number is 5. Step 3. Write the final sum over the original denominator.The original denominator is 9.

Question What fraction is being modeled in the figure below? Two rectangles are each divided into five equal parts. The first rectangle has all five of its parts shaded. The second rectangle has two of its five parts shaded. Provide your answer below:

7/5 One whole with two fifths left over makes seven fifths.

Convert the mixed number 1 and 17/61 to an improper fraction.

78/61

Convert the improper fraction 53/6 to a mixed number.

8 and 5/6

What fraction is being modeled in the figure below? Two rectangles are each divided into seven equal parts. The first rectangle has all seven of its parts shaded. The second rectangle has one of its seven parts shaded. Provide your answer below:

8/7 One whole with one seventh left over makes eight sevenths.

What fraction is being modeled in the figure below? Do not simplify. A rectangle is divided into nine equal parts. All nine parts are shaded. Provide your answer below:

9/9

What fraction is being modeled in the figure below? Two rectangles are each divided into three equal parts. The first rectangle has all three of its parts shaded. The second rectangle has two of its three parts shaded. Provide your answer below:

Correct answers: 5/3 One whole with two thirds left over makes five thirds.

Name the improper fraction. Then, write it as a mixed number. There are two circles divided into eighths. The first circle is completely shaded, and the second circle has six-eighths of the circle shaded. Provide your answer below:

Each circle is divided into 8 pieces, so each piece is 18 of the circle. There are 14 pieces shaded, so there are 14 eighths, or 14/8. The figure shows that we also have 1 whole circle and 6 eighths, which is 1 and 6/8. So 14/8= 1 and 6/8. ANSWER Improper Fraction 14/8, Mixed number 1 and 6/8