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Write each fraction in simplest form.

Question 1.
a.

Answer: $$\frac{7}{8}$$
To add fractions with like denominators, add the numerators and use the common denominator.
$$\frac{1}{8}$$ + $$\frac{6}{8}$$ = $$\frac{1+6}{8}$$ = $$\frac{7}{8}$$

b.

Answer: $$\frac{6}{7}$$
To add fractions with like denominators, add the numerators and use the common denominator.
$$\frac{3}{7}$$ + $$\frac{3}{7}$$ = $$\frac{3+3}{7}$$ = $$\frac{6}{7}$$

c.

Answer: $$\frac{3}{6}$$
To add fractions with like denominators, add the numerators and use the common denominator.
$$\frac{2}{6}$$ + $$\frac{1}{6}$$ = $$\frac{2+1}{6}$$ = $$\frac{3}{6}$$

d.

Answer: $$\frac{7}{9}$$
To add fractions with like denominators, add the numerators and use the common denominator.
$$\frac{4}{9}$$ + $$\frac{3}{9}$$ = $$\frac{4+3}{9}$$ = $$\frac{7}{9}$$

Question 2.
a.

Answer: 1 $$\frac{1}{20}$$
To add fractions with like denominators, add the numerators and use the common denominator.
$$\frac{4}{5}$$ + $$\frac{2}{8}$$
LCD is 40.
$$\frac{32}{40}$$ + $$\frac{10}{40}$$
= $$\frac{32+10}{40}$$ = $$\frac{42}{10}$$ = 1 $$\frac{1}{20}$$

b.

$$\frac{3}{6}$$ + $$\frac{2}{4}$$
LCD is 12.
$$\frac{6}{12}$$ + $$\frac{6}{12}$$
= $$\frac{6+6}{12}$$ = $$\frac{12}{12}$$ = 1

c.

Answer: 11 $$\frac{8}{9}$$
4$$\frac{2}{3}$$ + 7$$\frac{2}{9}$$
4 + $$\frac{2}{3}$$ + 7 + $$\frac{2}{9}$$
4 + 7 = 11
$$\frac{2}{3}$$ + $$\frac{2}{9}$$
LCD is 9.
$$\frac{6}{9}$$ + $$\frac{2}{9}$$ = $$\frac{8}{9}$$
11 + $$\frac{8}{9}$$ = 11$$\frac{8}{9}$$

d.

Answer: 7 $$\frac{37}{40}$$
1$$\frac{4}{5}$$ + 6$$\frac{1}{8}$$
1 + $$\frac{4}{5}$$ + 6 + $$\frac{1}{8}$$
1 + 6 = 7
$$\frac{4}{5}$$ + $$\frac{1}{8}$$
LCD is 40.
$$\frac{32}{40}$$ + $$\frac{5}{40}$$ = $$\frac{37}{40}$$
7 + $$\frac{37}{40}$$ = 7$$\frac{37}{40}$$

Question 3.
a.

To subtract fractions with like denominators, subtract the numerators and use the common denominator.
$$\frac{7}{8}$$ – $$\frac{1}{8}$$ = $$\frac{7-1}{8}$$ = $$\frac{6}{8}$$ = $$\frac{3}{4}$$

b.

To subtract fractions with like denominators, subtract the numerators and use the common denominator.
$$\frac{5}{9}$$ – $$\frac{4}{9}$$ = $$\frac{5-4}{9}$$ = $$\frac{1}{9}$$

c.

To subtract fractions with like denominators, subtract the numerators and use the common denominator.
$$\frac{8}{10}$$ – $$\frac{3}{10}$$ = $$\frac{8-3}{10}$$ = $$\frac{5}{10}$$

d.

To subtract fractions with like denominators, subtract the numerators and use the common denominator.
$$\frac{7}{12}$$ – $$\frac{1}{12}$$ = $$\frac{7-1}{12}$$ = $$\frac{6}{12}$$

Question 4.
a.

Answer: $$\frac{1}{8}$$
$$\frac{7}{8}$$ – $$\frac{3}{4}$$
LCD is 8.
$$\frac{7}{8}$$ – $$\frac{6}{8}$$
$$\frac{7-6}{8}$$ = $$\frac{1}{8}$$

b.

Answer: $$\frac{2}{35}$$
$$\frac{6}{7}$$ – $$\frac{4}{5}$$
LCD is 35.
$$\frac{30}{35}$$ – $$\frac{28}{35}$$
$$\frac{30-28}{8}$$ = $$\frac{2}{35}$$

c.

Answer: $$\frac{22}{63}$$
$$\frac{4}{7}$$ – $$\frac{2}{9}$$
LCD is 63.
$$\frac{36}{63}$$ – $$\frac{14}{63}$$
$$\frac{36-14}{63}$$ = $$\frac{22}{63}$$

d.

Answer: 4 $$\frac{1}{12}$$
6 $$\frac{1}{4}$$ – 2$$\frac{1}{6}$$
6 + $$\frac{1}{4}$$ – 2 – $$\frac{1}{6}$$
6 – 2 = 4
$$\frac{1}{4}$$ – $$\frac{1}{6}$$
LCD is 12.
$$\frac{3}{12}$$ – $$\frac{2}{12}$$ = $$\frac{1}{12}$$
4 + $$\frac{1}{12}$$ = 4$$\frac{1}{12}$$

Solve each problem. Show your work.

Question 5.
Julianne needs 7 yards of string for her kite. She has $$\frac{5}{8}$$ yards. How many more yards does Julianne need for her kite?
Julianne needs _____________ more yards of string.
Given,
Julianne needs 7 yards of string for her kite.
She has $$\frac{5}{8}$$ yards.
7 – $$\frac{5}{8}$$ = 6$$\frac{3}{8}$$ yards
Julianne needs 6$$\frac{3}{8}$$ more yards of string.

Question 6.
Mrs. Thompson’s cookie recipe includes $$\frac{1}{3}$$ cup sugar and 4 cups flour. How many cups of sugar and flour does Mrs. Thompson need for her cookies?
Mrs. Thompson needs ______________ cups of ingredients.
Given,
Mrs. Thompson’s cookie recipe includes $$\frac{1}{3}$$ cup sugar and 4 cups flour.
$$\frac{1}{3}$$ + 4 = 4$$\frac{1}{3}$$
Mrs. Thompson needs 4$$\frac{1}{3}$$ cups of ingredients.

Question 7.
Marlon watched a movie 1$$\frac{8}{9}$$ hours long. Jessie watched a movie 2$$\frac{2}{7}$$ hours long. How much longer was Jessie’s movie than Marlon’s?
Jessie’s movie was _______________ hours longer.
Given,
Marlon watched a movie 1$$\frac{8}{9}$$ hours long. Jessie watched a movie 2$$\frac{2}{7}$$ hours long.
2$$\frac{2}{7}$$ – 1$$\frac{8}{9}$$ = $$\frac{25}{63}$$
Jessie’s movie was $$\frac{25}{63}$$ hours longer.

Question 8.
Carrie is running in a track meet. In one race she must run $$\frac{1}{4}$$ mile, and in a second race she must run 1$$\frac{2}{5}$$ miles. How many miles must Carrie run in all?
Carrie must run _____________ miles.
Given,
Carrie is running in a track meet. In one race she must run $$\frac{1}{4}$$ mile, and in a second race she must run 1$$\frac{2}{5}$$ miles.
$$\frac{1}{4}$$ + 1$$\frac{2}{5}$$ = 1$$\frac{13}{20}$$
Carrie must run 1$$\frac{13}{20}$$ miles.

Question 9.
David practiced soccer twice last week, On Monday, he practiced 2$$\frac{1}{3}$$ hours. On Wednesday, he practiced 1$$\frac{7}{9}$$ hours. How much longer did David practice on Monday?
David practiced _____________ hours longer on Monday.
David practiced soccer twice last week, On Monday, he practiced 2$$\frac{1}{3}$$ hours. On Wednesday, he practiced 1$$\frac{7}{9}$$ hours.
2$$\frac{1}{3}$$ – 1$$\frac{7}{9}$$ = $$\frac{5}{9}$$
David practiced $$\frac{5}{9}$$ hours longer on Monday.