# McGraw Hill Math Grade 8 Lesson 3.3 Answer Key Adding and Subtracting Fractions with Like Denominators

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 3.3 Adding and Subtracting Fractions with Like Denominators to secure good marks & knowledge in the exams.

Question 1.
$$\frac{3}{4}$$ + $$\frac{3}{4}$$
$$\frac{6}{4}$$ or $$\frac{3}{2}$$ or 1$$\frac{1}{2}$$,

Explanation:
Given to add $$\frac{3}{4}$$ + $$\frac{3}{4}$$ as
both have common denominators we add numerators as
$$\frac{3 + 3}{4}$$ = $$\frac{6}{4}$$ or $$\frac{3}{2}$$ as numerator is greater than denominator we write in mixed fraction as $$\frac{1 X 2 + 1}{2}$$ = 1$$\frac{1}{2}$$.

Question 2.
$$\frac{1}{5}$$ + $$\frac{4}{5}$$
$$\frac{5}{5}$$ or 1,

Explanation:
Given to add $$\frac{1}{5}$$ + $$\frac{4}{5}$$ as
both have common denominators we add numerators as
$$\frac{1 + 4}{5}$$ = $$\frac{5}{5}$$ or 1.

Question 3.
$$\frac{5}{8}$$ + $$\frac{5}{8}$$
$$\frac{10}{8}$$ or $$\frac{5}{4}$$ or 1$$\frac{1}{4}$$,

Explanation:
Given to add $$\frac{5}{8}$$ + $$\frac{5}{8}$$ as
both have common denominators we add numerators as
$$\frac{5 + 5}{8}$$ = $$\frac{10}{8}$$ or $$\frac{5}{4}$$ as numerator is greater than denominator we write in mixed fraction as $$\frac{1 X 4 + 1}{4}$$ = 1$$\frac{1}{4}$$.

Question 4.
$$\frac{7}{9}$$ + $$\frac{4}{9}$$
$$\frac{11}{9}$$ or 1$$\frac{2}{9}$$,

Explanation:
Given to add $$\frac{7}{9}$$ + $$\frac{4}{9}$$ as
both have common denominators we add numerators as
$$\frac{7 + 4}{9}$$ = $$\frac{11}{9}$$ as numerator
is greater than denominator we write in mixed fraction as
$$\frac{1 X 9 + 2}{9}$$ = 1$$\frac{2}{9}$$.

Question 5.
$$\frac{4}{11}$$ + $$\frac{3}{11}$$
$$\frac{7}{11}$$,

Explanation:
Given to add $$\frac{4}{11}$$ + $$\frac{3}{11}$$ as
both have common denominators we add numerators as
$$\frac{4 + 3}{11}$$ = $$\frac{7}{11}$$.

Question 6.
$$\frac{15}{17}$$ + $$\frac{5}{17}$$
$$\frac{20}{17}$$ or 1$$\frac{3}{17}$$,

Explanation:
Given to add $$\frac{15}{17}$$ + $$\frac{5}{17}$$ as
both have common denominators we add numerators as
$$\frac{15 + 5}{17}$$ = $$\frac{20}{17}$$ as numerator
is greater than denominator we write in mixed fraction as
$$\frac{1 X 17 + 3}{17}$$ = 1$$\frac{3}{17}$$.

Question 7.
$$\frac{7}{9}$$ + $$\frac{14}{9}$$
$$\frac{21}{9}$$ or $$\frac{7}{3}$$ or 2$$\frac{1}{3}$$,

Explanation:
Given to add $$\frac{7}{9}$$ + $$\frac{14}{9}$$ as
both have common denominators we add numerators as
$$\frac{7 + 14}{9}$$ = $$\frac{21}{9}$$ =
$$\frac{7}{3}$$ as numerator is greater than denominator
we write in mixed fraction as $$\frac{2 X 3 + 1}{3}$$ = 2$$\frac{1}{3}$$.

Question 8.
$$\frac{2}{3}$$ + $$\frac{5}{3}$$
$$\frac{7}{3}$$ or 2$$\frac{1}{3}$$,

Explanation:
Given to add $$\frac{2}{3}$$ + $$\frac{5}{3}$$ as
both have common denominators we add numerators as
$$\frac{2 + 5}{9}$$ = $$\frac{7}{9}$$  as numerator is greater than denominator we write in mixed fraction as
$$\frac{2 X 3 + 1}{3}$$ = 2$$\frac{1}{3}$$.

Question 9.
$$\frac{6}{23}$$ + $$\frac{14}{23}$$
$$\frac{20}{23}$$,

Explanation:
Given to add $$\frac{6}{23}$$ + $$\frac{14}{23}$$ as
both have common denominators we add numerators as
$$\frac{6 + 14}{23}$$ = $$\frac{20}{23}$$.

Question 10.
$$\frac{13}{37}$$ + $$\frac{24}{37}$$
$$\frac{37}{37}$$ or 1,

Explanation:
Given to add $$\frac{13}{37}$$ + $$\frac{24}{37}$$ as
both have common denominators we add numerators as
$$\frac{13 + 24}{37}$$ = $$\frac{37}{37}$$ = 1.

Question 11.
$$\frac{1}{4}$$ + $$\frac{7}{4}$$
$$\frac{8}{4}$$ or 2,

Explanation:
Given to add $$\frac{1}{4}$$ + $$\frac{7}{4}$$ as
both have common denominators we add numerators as
$$\frac{1 + 7}{4}$$ = $$\frac{8}{4}$$ = 2.

Question 12.
$$\frac{3}{11}$$ + $$\frac{7}{11}$$
$$\frac{10}{11}$$,

Explanation:
Given to add $$\frac{3}{11}$$ + $$\frac{7}{11}$$ as
both have common denominators we add numerators as
$$\frac{3 + 7}{11}$$ = $$\frac{10}{11}$$.

Question 13.
$$\frac{13}{27}$$ + $$\frac{11}{27}$$
$$\frac{24}{27}$$ or $$\frac{8}{9}$$,

Explanation:
Given to add $$\frac{13}{27}$$ + $$\frac{11}{27}$$ as
both have common denominators we add numerators as
$$\frac{13 + 11}{27}$$ = $$\frac{24}{27}$$ = $$\frac{8}{9}$$.

Question 14.
$$\frac{11}{14}$$ + $$\frac{13}{14}$$
$$\frac{24}{14}$$ or $$\frac{12}{7}$$ or 1$$\frac{5}{7}$$,

Explanation:
Given to add $$\frac{11}{14}$$ + $$\frac{13}{14}$$ as
both have common denominators we add numerators as
$$\frac{11 + 13}{14}$$ = $$\frac{24}{14}$$ =
$$\frac{12}{7}$$ as numerator is greater than denominator
we write in mixed fraction as $$\frac{1 X 7 + 5}{7}$$ = 1$$\frac{5}{7}$$.

Question 15.
$$\frac{13}{24}$$ + $$\frac{16}{24}$$
$$\frac{29}{24}$$ or 1$$\frac{5}{24}$$,

Explanation:
Given to add $$\frac{13}{24}$$ + $$\frac{16}{24}$$ as
both have common denominators we add numerators as
$$\frac{13 + 16}{24}$$ = $$\frac{29}{24}$$ as numerator is greater than denominator we write in mixed fraction as
$$\frac{1 X 24 + 5}{24}$$ = 1$$\frac{5}{24}$$.

Question 16.
$$\frac{13}{37}$$ + $$\frac{11}{37}$$
$$\frac{24}{37}$$,

Explanation:
Given to add $$\frac{13}{37}$$ + $$\frac{11}{37}$$ as
both have common denominators we add numerators as
$$\frac{13 + 11}{37}$$ = $$\frac{24}{37}$$.

Question 17.
Manny combined $$\frac{1}{7}$$ quarts of orange juice, $$\frac{2}{7}$$ quarts of lemonade, and $$\frac{5}{7}$$ quarts of raspberry tea into one container. How much liquid is now in the container? Express your answer as a mixed number.
1$$\frac{1}{7}$$ quarts is in the container,

Explanation:
As Manny combined $$\frac{1}{7}$$ quarts of orange juice, $$\frac{2}{7}$$ quarts of lemonade, and $$\frac{5}{7}$$ quarts of raspberry tea into one container.
Liquid is now in the container is $$\frac{1}{7}$$ quarts + $$\frac{2}{7}$$ quarts + $$\frac{5}{7}$$ quarts =
$$\frac{1 + 2 + 5}{7}$$ quarts = $$\frac{8}{7}$$ quarts ,
as numerator is greater than denominator we write in mixed fraction as
$$\frac{1 X 7 + 1}{7}$$ = 1$$\frac{1}{7}$$ quarts.

Question 18.
James, Riley and Nancy surveyed their class about the cafeteria food. James surveyed $$\frac{2}{9}$$ of the class, Riley surveyed another $$\frac{5}{9}$$ of the class, and Nancy surveyed another $$\frac{1}{9}$$ of the class. Were the three of them able to po11 the entire class?
No,

Explanation:
As James, Riley and Nancy surveyed their class about the cafeteria food. James surveyed $$\frac{2}{9}$$ of the class, Riley surveyed another $$\frac{5}{9}$$ of the class, and Nancy surveyed another $$\frac{1}{9}$$ of the class.
Now checking the three of them able to po11 the entire class as
$$\frac{2}{9}$$ + $$\frac{5}{9}$$ + $$\frac{1}{9}$$  = $$\frac{2 + 5 + 1}{9}$$ quarts = $$\frac{8}{9}$$
No, the three of them were not able to po11 the entire class as it is
not 1.

Exercises Subtract

Question 1.
$$\frac{3}{4}$$ – $$\frac{1}{4}$$
$$\frac{2}{4}$$ or $$\frac{1}{2}$$,

Explanation:
Given to subtract $$\frac{3}{4}$$ – $$\frac{1}{4}$$ as
both have common denominators we subtract numerators as
$$\frac{3 – 1}{4}$$ = $$\frac{2}{4}$$ further
can be divided by 2 we get $$\frac{2}{4}$$.

Question 2.
$$\frac{3}{3}$$ – $$\frac{2}{3}$$
$$\frac{1}{3}$$,

Explanation:
Given to subtract $$\frac{3}{3}$$ – $$\frac{2}{3}$$ as
both have common denominators we subtract numerators as
$$\frac{3 – 2}{3}$$ = $$\frac{1}{3}$$.

Question 3.
$$\frac{8}{9}$$ – $$\frac{5}{9}$$
$$\frac{3}{9}$$ or $$\frac{1}{3}$$,

Explanation:
Given to subtract $$\frac{8}{9}$$ – $$\frac{5}{9}$$ as
both have common denominators we subtract numerators as
$$\frac{8 – 5}{9}$$ = $$\frac{3}{9}$$ further
can be divided by 3 we get $$\frac{1}{3}$$.

Question 4.
$$\frac{7}{8}$$ – $$\frac{1}{8}$$
$$\frac{6}{8}$$ or $$\frac{3}{4}$$,

Explanation:
Given to subtract $$\frac{7}{8}$$ – $$\frac{1}{8}$$ as
both have common denominators we subtract numerators as
$$\frac{7 – 1}{8}$$ = $$\frac{6}{8}$$ further
can be divided by 2 we get $$\frac{3}{4}$$.

Question 5.
$$\frac{5}{7}$$ – $$\frac{3}{7}$$
$$\frac{2}{7}$$,

Explanation:
Given to subtract $$\frac{5}{7}$$ – $$\frac{3}{7}$$ as
both have common denominators we subtract numerators as
$$\frac{5 – 3}{7}$$ = $$\frac{2}{7}$$.

Question 6.
$$\frac{1}{2}$$ – $$\frac{1}{2}$$
0,

Explanation:
Given to subtract $$\frac{1}{2}$$ – $$\frac{1}{2}$$ as
both have common denominators we subtract numerators as
$$\frac{1 – 1}{2}$$ = 0.

Question 7.
$$\frac{2}{3}$$ – $$\frac{1}{3}$$
$$\frac{1}{3}$$,

Explanation:
Given to subtract $$\frac{2}{3}$$ – $$\frac{1}{3}$$ as
both have common denominators we subtract numerators as
$$\frac{2 – 1}{3}$$ = $$\frac{1}{3}$$.

Question 8.
$$\frac{5}{3}$$ – $$\frac{2}{3}$$
1,

Explanation:
Given to subtract $$\frac{5}{3}$$ – $$\frac{2}{3}$$ as
both have common denominators we subtract numerators as
$$\frac{5 – 2}{3}$$ = $$\frac{3}{3}$$ further
can be divided by 3 we get 1.

Question 9.
$$\frac{7}{5}$$ – $$\frac{4}{5}$$
$$\frac{3}{5}$$,

Explanation:
Given to subtract $$\frac{7}{5}$$ – $$\frac{4}{5}$$ as
both have common denominators we subtract numerators as
$$\frac{7 – 4}{5}$$ = $$\frac{3}{5}$$.

Question 10.
$$\frac{4}{7}$$ – $$\frac{1}{7}$$
$$\frac{3}{7}$$,

Explanation:
Given to subtract $$\frac{4}{7}$$ – $$\frac{1}{7}$$ as
both have common denominators we subtract numerators as
$$\frac{4 – 1}{7}$$ = $$\frac{3}{7}$$.

Question 11.
$$\frac{9}{7}$$ – $$\frac{6}{7}$$
$$\frac{3}{7}$$,

Explanation:
Given to subtract $$\frac{9}{7}$$ – $$\frac{6}{7}$$ as
both have common denominators we subtract numerators as
$$\frac{9 – 6}{7}$$ = $$\frac{3}{7}$$.

Question 12.
$$\frac{11}{9}$$ – $$\frac{2}{9}$$
1,

Explanation:
Given to subtract $$\frac{11}{9}$$ – $$\frac{2}{9}$$ as
both have common denominators we subtract numerators as
$$\frac{11 – 2}{9}$$ = $$\frac{9}{9}$$ further
can be divided by 9 we get 1.

Question 13.
$$\frac{6}{5}$$ – $$\frac{3}{5}$$
$$\frac{3}{5}$$,

Explanation:
Given to subtract $$\frac{6}{5}$$ – $$\frac{3}{5}$$ as
both have common denominators we subtract numerators as
$$\frac{6 – 3}{5}$$ = $$\frac{3}{5}$$.

Question 14.
$$\frac{12}{11}$$ – $$\frac{9}{11}$$
$$\frac{3}{11}$$,

Explanation:
Given to subtract $$\frac{12}{11}$$ – $$\frac{9}{11}$$ as
both have common denominators we subtract numerators as
$$\frac{12 – 9}{11}$$ = $$\frac{3}{11}$$.

Question 15.
$$\frac{31}{35}$$ – $$\frac{1}{35}$$
$$\frac{30}{35}$$ or $$\frac{6}{7}$$,

Explanation:
Given to subtract $$\frac{31}{35}$$ – $$\frac{1}{35}$$ as
both have common denominators we subtract numerators as
$$\frac{31 – 1}{35}$$ = $$\frac{30}{35}$$ further
can be divided by 5 we get $$\frac{6}{7}$$.

Question 16.
$$\frac{21}{22}$$ – $$\frac{17}{22}$$
$$\frac{4}{22}$$ or $$\frac{2}{11}$$,

Explanation:
Given to subtract $$\frac{21}{22}$$ – $$\frac{17}{22}$$ as
both have common denominators we subtract numerators as
$$\frac{21 – 17}{22}$$ = $$\frac{4}{22}$$ further
can be divided by 2 we get $$\frac{2}{11}$$.

Question 17.
Kira made $$\frac{19}{16}$$ quarts of grape juice and served $$\frac{3}{8}$$ quarts for dinner. How much juice does she have left?
Kira is left with $$\frac{13}{16}$$ quarts of juice,

Explanation:
Given Kira made $$\frac{19}{16}$$ quarts of grape juice and
served $$\frac{3}{8}$$ quarts for dinner.
So juice does she have left is $$\frac{19}{16}$$ quarts – $$\frac{3}{8}$$ quarts as we have to make both common denominators we multiply $$\frac{3}{8}$$ quarts by 2 we get $$\frac{3 X 2}{8 X 2}$$ quarts = $$\frac{6}{16}$$ quarts,
now we subtract numerators as $$\frac{19 – 6}{16}$$ quarts = $$\frac{13}{16}$$ quarts.

Question 18.
Ellen bought $$\frac{19}{16}$$ pounds of flour from the store. On her way home, she spilled $$\frac{11}{16}$$ pounds of flour, If she needs $$\frac{7}{16}$$ pounds of flour to make bread, will she have enough flour?
Given Ellen bought $$\frac{19}{16}$$ pounds of flour from the store. On her way home, she spilled $$\frac{11}{16}$$ pounds of flour now she is left with $$\frac{19}{16}$$ – $$\frac{11}{16}$$ as both have common denominators we subtract numerators as
$$\frac{19 – 11}{16}$$ = $$\frac{8}{16}$$, As
she needs $$\frac{7}{16}$$ pounds of flour to make bread,
$$\frac{8}{16}$$ ≠ $$\frac{7}{16}$$ Ellen will not have enough flour.