Section 4.6 Part 1: Adding and Subtracting Mixed Numbers with Common Denominators

Subtract: 5 and 1/10− 3 and 7/10. (Enter your answer as a mixed number, whole number, or proper fraction. Any fractions should be in lowest terms.) Provide your answer below:

1 and 2/5 Convert the mixed numbers to improper fractions and then subtract to find 5 and 1/10−3 and 7/10 51/10−37/10 51−37/10 14/10 Since the problem was given in mixed number form, we will write the difference as a mixed number then simplify the fraction to find 1 and 4/10 1 and 2/5

Subtract: 2 and 1/4−1 and 3/4.(Enter your answer as a mixed number, whole number, or proper fraction. Any fractions should be in lowest terms.) Provide your answer below:

1/2 Convert the mixed numbers to improper fractions and then subtract to find 2 and 1/4−1 and 3/4 9/4−7/4 9−7/4 2/4 1/2

Add: 4 and 1/4+8 and 3/4.(Enter your answer as a mixed number, whole number, or proper fraction. Any fractions should be in lowest terms.)

13 Convert the addends to improper fractions and then add to find 4 and 1/4+8 and 3/4 17/4+35/4 17+35/4 52/4. Since the problem was given in mixed number form, we will write the answer as a mixed number. 52/4 =13.

Use a model to subtract: 1 and −1/4.

3/4

Question What sum is being modeled below? One piece of a circle. The piece appears to be one eighth of a circle. Plus four pieces of a circle. Each piece appears to be one eighth of a circle. Provide your answer below:

3/8 + 4/8

What is the sum shown in the following model? Enter a mixed number in simplest form. Note, the circles on the far right are divided into five equal pieces. Four whole circles and 2 pieces of a circle, plus 3 whole circles and 3 pieces of a circle. Each piece appears to be one-fifth of a circle. Provide your answer below:

8 Four wholes and two 1/5 pieces plus three wholes and three 1/5 pieces equals seven wholes and five 1/5 pieces. Since 5/5 is equal to one whole, we add that to the 7 to get 8.

What is the sum shown in the following model? Write your answer as a simplified mixed number. One whole circle and 2 pieces of a circle. Each piece appears to be one fifth of a circle.

One whole and two 1/5s plus three wholes and three 1/5s equals four wholes and five 1/5s. Since 5/5 is equal to one whole, we add that to the 4 to get 5.

Use a model to subtract 2 and 3/10−7/10.

1 and 3/5 Rewrite vertically. Start with two wholes and three tenths. Two whole circles and 3 pieces of a circle. The whole circles are shaded in. The pieces appear to be one-tenth of a circle each and are shaded in. 2 and 3/10−7/10 Since the fractions have denominator 10, cut one of the wholes into 10 pieces. You now have 1 and 10/10 and 3/10, which is 1 and 13/10. Two whole circles and 3 pieces of a circle. The pieces appear to be one-tenth of a circle each and are shaded in. One of the whole circles is divided into 10 equal pieces; each piece is shaded in. The other whole circle is shaded in. 1 and 13/10−7/10 Take away 7/10.There is 1 and 6/10= 1 and 3/5 left. Two whole circles and 3 pieces of a circle. Each piece appears to be one-tenth of a circle, and they are not shaded in. One of the circles is completely shaded in. The other circle is divided into 10 equal-sized pieces, 6 of which are shaded in. 1 and 13/10−7/10 1 and 6/10=13/5

Add: 4 and 8/15+8 and 13/15.(Enter your answer as a mixed number, whole number, or proper fraction. Any fractions should be in lowest terms.) Provide your answer below:

13 and 2/5 Convert the addends to improper fractions and then add to find 4 and 8/15+8 and 13/15 68/15+133/15 68+133/15 201/15. Since the problem was given in mixed number form, we will write the sum as a mixed number then simplify the fraction to find 201/15 13 and 6/15 13 and 2/5.

Add: 6 and 12/13+9 and 4/13.(Enter your answer as a mixed number, whole number, or proper fraction. Any fractions should be in lowest terms.)

16 and 3/13 Convert the addends to improper fractions and then add to find 6 and 12/13+9 and 4/13 90/13+121/13 90+121/13 211/13. Since the problem was given in mixed number form, we will write the answer as a mixed number. 211/13 16 and 3/13.

Subtract: 1 and 1/3−23.

2/3 Answer Explanation Correct answers:$\frac{2}{3}$23​​ Rewrite vertically. Start with one whole and one third. One whole circle and one-third of a circle. 113−23−−−−−−−−− Since the fractions have denominator 3, cut the whole into 3 pieces. You now have 33 and 13, which is 43. One whole circle divided into 3 equal pieces and one-third of a circle. 43−23−−−−−−−−− Take away 23. One whole circle divided into 3 equal pieces with two shaded. One unshaded third of a circle. There is 23 left. 43−23−−−−−−−−−23

Subtract: 8 and 2/13−4 and 4/13.(Enter your answer as a mixed number, whole number, or proper fraction. Any fractions should be in lowest terms.) Provide your answer below:

3 11/13 Convert the mixed numbers to improper fractions and then subtract to find 8 and 2/13−4 and 4/13 106/13−56/13 106−56/13 50/13 Since the problem was given in mixed number form, we will write the difference as a mixed number. 50/13 3 and 11/13

Use a model to subtract 5 −1 and 3/8. Write your answer as a simplified Mixed Fraction.

3 and 5/8 Rewrite vertically. Start with five wholes. Five whole shaded circles. 5 −1 and 3/8 Since the fraction has denominator 8, cut one whole into 8 pieces. You now have 4and 8/8. Five whole circles. Four of the circles are shaded in completely. The other circle is divided into 8 equal-sized pieces, all of which are shaded in. 4 and 8/8−1 and 3/8 Take away one whole and 3/8.There is 3 and 5/8left. Five whole circles. Three of the circles are shaded in completely. Another circle is divided into 8 equal-sized pieces, 5 of which are shaded in. The other circle is not shaded in. 4 and 8/8−1 and 3/8 3 and 5/8

What is the sum shown in the following model? Write your answer as a simplified mixed number. Two whole circles and 5 pieces of a circle. Each piece appears to be one sixth of a circle. Plus one whole circle and 5 pieces of a circle. Each piece appears to be one sixth of a circle. photo described 3 circles in photo.5 slices, 5 slice

4 and 2/3 Two wholes and five 1/6s plus one whole and five 1/6s equals three wholes and ten 1/6s. Since 10/6 is equal to one whole and 4/6, we add that to the 3 to get 4 and 46, which is 4 and 2/3.

Use a model to subtract: 1 and 1/5−2/5.

4/5

What is the sum shown in the following model? Enter a mixed number in simplest form. Three whole circles and 3 pieces of a circle, plus 2 whole circles and 3 pieces of a circle. Each piece appears to be one-fourth of a circle. Provide your answer below:

6 and 1/2 Three wholes and three 1/4 pieces plus two wholes and three 1/4 pieces equals five wholes and six 1/4 pieces.Since 6/4 is equal to one whole and 2/4, we add that to the 5 to get 6 and 2/4, which is 6 ans 2/4. Reducing the fraction, gives us 6 and 1/2

Add: 4 and 7/12+2 and 1/12.(Enter your answer as a mixed number, whole number, or proper fraction. Any fractions should be in lowest terms.) Provide your answer below:

6 and 2/3 Convert the addends to improper fractions and then add to find 4 and 7/12+2 and 1/12 55/12+25/12 55+25/12 80/12. Since the problem was given in mixed number form, we will write the sum as a mixed number then simplify the fraction to find 80/12 6 and 8/12 6 and 2/3.

Question What is the sum shown in the following model? Enter a mixed number in simplest form. Three whole circles and 1 piece of a circle, plus 3 whole circles and 3 pieces of a circle. Each piece appears to be one-fourth of a circle. Provide your answer below:

7 Three wholes and one 1/4 piece plus three wholes and three 1/4 pieces equals six wholes and four 1/4 pieces.Since 44 is equal to one whole, we add that to the 6 to get 7.

What is the sum shown in the following model? Enter a mixed number in simplest form. Three whole circles and 3 pieces of a circle, plus 3 whole circles and 5 pieces of a circle. Each piece appears to be one-eighth of a circle. Provide your answer below:

7 Three wholes and three 1/8 pieces plus three wholes and five 1/8 pieces equals six wholes and eight 18 pieces.Since 8/8 is equal to one whole, we add that to the 6 to get 7.

Subtract: 9 and 1/7−1 and 3/7.(Enter your answer as a mixed number, whole number, or proper fraction. Any fractions should be in lowest terms.) Provide your answer below:

7 and 5/7 Convert the mixed numbers to improper fractions and then subtract to find 9 and 1/7−1 and 3/7 64/7−10/7 64−10/7 54/7 Since the problem was given in mixed number form, we will write the difference as a mixed number. 54/7 7 and 5/7

What is the sum shown in the following model? Enter a mixed number in simplest form. Three whole circles and 2 pieces of a circle, plus 2 whole circles and 2 pieces of a circle. Each piece appears to be one-third of a circle. Provide your answer below:

Answer Explanation Correct answers:6 and 1/3​​ Three wholes and two 1/3 pieces plus two wholes and two 1/3 pieces equals five wholes and four 1/3 pieces.Since 4/3 is equal to one whole and 1/3, we add that to the 5 to get 6 and 1/3, which is 6 and 1/3.

What is the sum shown in the following model? Enter a mixed number in simplest form. Two whole circles and 3 pieces of a circle, plus 1 whole circle and 1 piece of a circle. Each piece appears to be one-eighth of a circle. Provide your answer below: top 3 circles 3 slices below one circle one slice

Correct answers: 3 and 1/2​​ Two wholes and three 1/8 pieces plus one whole and one 1/8 piece equals three wholes and four 1/8pieces, which is 3 and 4/8. Reducing the fraction, gives us 3 and 1/2.