McGraw Hill Math

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 24.2 Stem-and-Leaf Plots to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 24.2 Stem-and-Leaf Plots

Exercises
INTERPRET
Question 1.
Make a list all of the points scored in the basketball games.

Answer:
Points scored in the basketball games = 39, 40, 41, 45, 47, 47, 47, 47, 49, 52, 56, 56, 56.

Explanation:
Stem 3 leaves 9 = 39 points.
Stem 4 leaves 0,1,5,7,7,7,9 = 40,41,45,47,47,47,47,49 points.
Stem 5 leaves 2,6,6,6 = 52,56,56,56 points.

Question 2.
Make a list of the data shown below.

Answer:
Points scored in the basketball games = 120, 125, 128, 128, 130,131, 132, 134, 136, 137, 139, 141, 142, 143, 145, 145, 149, 161, 165.

Explanation:
Stem 12 leaves 0,5,8,8 = 120, 125, 128, 128 points.
Stem 13 leaves 0,1,2,4,6,7,9 = 130,131, 132, 134, 136, 137, 139 points.
Stem 14 leaves 1,2,3,5,5,9 = 141, 142, 143, 145, 145, 149 points.
Stem 15 leaves no points.
Stem 16 leaves 1,5 = 161, 165 points.

Question 3.
Using the stem-and-leaf plot, determine the median age of people at the family reunion, the range, and the mode of the ages.

Median ______________
Range _____________
Mode _____________
Answer:
Median = 35.5.
Range = 80.
Mode = no number repeating.

Explanation:
Stem 0 leaves 1, 8, 9 = 01, 08, 09.
Stem 3 leaves 2, 4, 7 = 32, 34, 37.
Stem 4 leaves 5 = 45.
Stem 5 leaves 1, 5 = 51, 55.
Stem 8 leaves 1 = 81.
Ages of people at Family Reunion = 1, 8, 9, 32, 34, 37, 45, 51, 55, 81.
Median = (34 + 37) ÷ 2
= 71 ÷ 2
= 35.5.
Range = 81 – 1 = 80.
Mode = no number repeating.

Question 4.
In a biology class, eight students collected shrubs for a study. The number of shrubs collected by the students was 4, 8,12,16, 21, 21, and 23. Make a stem-and-leaf plot of these numbers.

Answer:

Explanation:
Number of students = 8.
Number of shrubs collected by the students was 4, 8,12,16, 21, 21, and 23.
Stem     Leaves
0            4  8
1            2  6
2            1  1  3

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 24.1 Measures of Central Tendency to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 24.1 Measures of Central Tendency

Exercises
CALCULATE
Round all answers to the hundredths place.
Question 1.
1, 2, 3, 4, 9, 8, 7, 6, 5.
Mean ________
Median ____________
Range  __________
Mode __________
Answer:
Mean = 0.05.
Median = 0.05.
Range = 0.08.
Mode = All values appeared just once.

Explanation:
1, 2, 3, 4, 9, 8, 7, 6, 5.
Sum of all numbers given = 1 + 2 + 3 + 4 + 9 + 8 + 7 + 6 + 5  = 45.
Numbers of numbers given= 9.
Mean = Sum of all numbers given ÷ Numbers of numbers given
= 45 ÷ 9
= 5.
To find the median, list the values of the data set in numerical order and identify which value appears in the middle of the list.
Arrange the digits from least to great:
1,2,3,4,5,6,7,8,9.
Median = 5.
Range = 9 – 1 = 8.
To find the mode, identify which value in the data set occurs most often.
1,2,3,4,5,6,7,8,9.
Mode: There is no mean as no number is repeating.

Hundredth value:
Mean – 6 = 6 ÷ 100 = 0.06.
Median – 5 = 5 ÷ 100 = 0.05.
Mode – 0 = 0÷ 100 = 0.
Range – 1 = 1 ÷ 100 = 0.01.

Question 2.
10, 15, 20, 60, 110, 10, 10, 45
Mean ___________
Median ___________
Range ___________
Mode ___________
Answer:
Mean = 0.35.
Median = 0.175.
Range = 1.
Mode = 0.10.

Explanation:
10, 15, 20, 60, 110, 10, 10, 45
Arranging numbers in numerical order:
10,10,10,15,20,45,60,110.
Sum of all numbers given= 10 + 10 + 10 + 15 + 20 + 45 + 60 + 110 = 280.
Numbers of numbers given = 8.
Mean = Sum of all numbers given÷ Numbers of numbers given
Mean = 280 ÷ 8 = 35.
10,10,10,15,20,45,60,110.
Median = (15 + 20) ÷ 2
= 35 ÷ 2
= 17.5.
10,10,10,15,20,45,60,110.
Mode = 10.(because its repeating thrice)
Range = 110 – 10 = 100.

Hundredth value :
Mean – 35 = 35 ÷ 100 = 0.35.
Median – 17.5 =  0.175
Mode – 10 = 10 ÷ 100 = 0.10.
Range – 100 = 100 ÷ 100 = 1.

Question 3.
23, 23, 24, 25, 48, 56, 32, 1, 2
Mean ___________
Median ___________
Range ___________
Mode ___________
Answer:
Mean  = 0.26.
Median  = 0.24.
Mode = 0.23.
Range  = 0.55.

Explanation:
23, 23, 24, 25, 48, 56, 32, 1, 2
Arranging the numbers in numerical order:
1,2,23,23,24,25,32,48,56.
Sum of numbers given = 1 + 2 + 23 + 23 + 24 + 25 + 32 + 48 + 56 = 234
Numbers of numbers given = 9.
Mean = Sum of numbers given ÷ Numbers of numbers given
= 234 ÷ 9
= 26.
1,2,23,23,24,25,32,48,56.
Median = 24.
Mode = 23. (because its repeating twice)
Range = 56 – 1 = 55.

Hundredth value:
Mean – 26 = 26 ÷ 100 = 0.26.
Median – 24 = 24 ÷ 100 = 0.24.
Mode – 23 = 23 ÷ 100 = 0.23.
Range – 55 = 55 ÷ 100 = 0.55.

Question 4.
11, 22, 33, 44, 66, 77, 11, 21
Mean ___________
Median ___________
Range ___________
Mode ___________
Answer:
Mean = 0.35625.
Median = 0.275.
Mode = 0.11.
Range = 0.66.

Explanation:
11, 22, 33, 44, 66, 77, 11, 21
Arranging the numbers in numerical order:
11,11,21,22,33,44,66,77.
Sum of numbers given = 11 + 11 + 21 + 22 + 33 + 44 + 66 + 77 = 285
Numbers of numbers given = 8.
Mean = Sum of numbers given ÷ Numbers of numbers given
= 285 ÷ 8
= 35.625.
11,11,21,22,33,44,66,77.
Median = (22 + 33) ÷ 2
= 55 ÷ 2
= 27.5.
Mode = 11. (because its repeating twice)
Range = 77 – 11 = 66.

Hundredth value:
Mean – 35.625 = 35.625 ÷ 100 = 0.35625.
Median – 27.5 = 27.5 ÷ 100 = 0.275.
Mode – 11 = 11 ÷ 100 = 0.11.
Range – 66 = 66 ÷ 100 = 0.66.

Question 5.
3, 3, 3, 3, 3, 4, 6, 7, 8
Mean ___________
Median ___________
Range ___________
Mode ___________
Answer:
Mean = 0.44.
Median = 0.03.
Mode = 0.03.
Range = 0.05.

Explanation:
3, 3, 3, 3, 3, 4, 6, 7, 8
Arranging the numbers in numerical order:
3, 3, 3, 3, 3, 4, 6, 7, 8.
Sum of numbers given = 3 + 3 + 3 + 3 + 3 + 4 + 6 + 7 + 8 = 40.
Numbers of numbers given = 9.
Mean = Sum of numbers given ÷ Numbers of numbers given
= 40 ÷ 9
= 4.44.
Median = 3.
Mode = 3.(because its repeating 5 times)
Range = 8 – 3 = 5.

Hundredth value :
Mean – 4.44 = 4.44 ÷ 100 = 0.44.
Median – 3 = 3 ÷ 100 = 0.03.
Mode – 3 = 3 ÷ 100 = 0.03.
Range – 5 = 5 ÷ 100 = 0.05.

Question 6.
4, 5, 6, 8, 9, 21, 22, 23, 24, 21, 5, 27
Mean ___________
Median ___________
Range ___________
Mode ___________
Answer:
Mean = 0.145833.
Median = 0.15.
Mode = 0.05, 0.21.
Range = 0.23.

Explanation:
4, 5, 6, 8, 9, 21, 22, 23, 24, 21, 5, 27
Arranging the numbers in numerical order:
4, 5, 5, 6, 8, 9, 21, 21, 22, 23, 24, 27
Sum of numbers given = 4 + 5 + 5 + 6 + 8 + 9 + 21 + 21 + 22 + 23 + 24 + 27 = 175.
Numbers of numbers given = 12.
Mean = Sum of numbers given ÷ Numbers of numbers given
= 154 ÷ 12
= 14.5833.
Median = (9 + 21) ÷ 2
= 30 ÷ 2
= 15.
Mode = 5, 21 (both are repeating twice)
Range = 27 – 4 = 23.

Hundredth value :
Mean – 14.5833 = 14.5833 ÷ 100 = 0.145833.
Median – 15 = 15 ÷ 100 = 0.15.
Mode – 5,21 = 5 ÷ 100 = 0.05, 21 ÷ 100 = 0.21.
Range – 23 = 23 ÷ 100 = 0.23.

Question 7.
9, 13, 56, 12, 13, 9, 9, 18, 45
Mean ___________
Median ___________
Range ___________
Mode ___________
Answer:
Mean = 0.20444.
Median = 0.13.
Mode = 0.09.
Range = 0.47.

Explanation:
9, 13, 56, 12, 13, 9, 9, 18, 45
Arranging the numbers in numerical order:
9,9,9,12,13,13,18,45,56.
Sum of numbers given = 9 + 9 + 9 + 12+ 13+ 13+ 18 + 45 + 56 = 184.
Numbers of numbers given = 9.
Mean = Sum of numbers given ÷ Numbers of numbers given
= 184 ÷ 9
= 20.444.
Median = 13.
Mode = 9 (because its repeating thrice)
Range = 56 – 9 = 47.

Hundredth value :
Mean – 20.444 = 20.444÷ 100 = 0.20444.
Median – 13 = 13 ÷ 100 = 0.13.
Mode – 9 = 9 ÷ 100 = 0.09.
Range – 47= 47÷ 100 = 0.47.

Question 8.
-3, -10, -10, 14, 16, 22, 21, 30
Mean ___________
Median ___________
Range ___________
Mode ___________
Answer:
Mean = 0.10.
Median = 0.15.
Mode  = – 0.10.
Range = 0.40.

Explanation:
-3, -10, -10, 14, 16, 22, 21, 30
Arranging the numbers in numerical order:
-10, -10, -3, 14, 16, 21, 22, 30
Sum of numbers given = -3 – 10 – 10 + 14 + 16 + 21 + 22 + 30 = – 23 + 103 = 80.
Numbers of numbers given = 8.
Mean = Sum of numbers given ÷ Numbers of numbers given
= 80 ÷ 8
= 10.
Median = (14 + 16) ÷ 2
= 30 ÷ 2
= 15.
Mode = – 10. (because its repeating twice)
Range = 30 – (-10) = 30 + 10 = 40.

Hundredth value :
Mean – 10= 10÷ 100 = 0.10.
Median – 15 = 15 ÷ 100 = 0.15.
Mode – (-10) = (-10) ÷ 100 = – 0.10.
Range – 40 = 40÷ 100 = 0.40.

Question 9.
-1, -1, -5, -6, -7, 10, 1, 14, 27
Mean ___________
Median ___________
Range ___________
Mode ___________
Answer:
Mean = 0.03555.
Median = – 0.01.
Mode = – 0.01.
Range = 0.34.

Explanation:
-1, -1, -5, -6, -7, 10, 1, 14, 27
Arranging the numbers in numerical order:
-7, -6, -5, -1, -1, 1, 10, 14, 27
Sum of numbers given = – 1 – 1 – 5 – 6 – 7 + 10 + 1 + 14 + 27 = – 20 + 52 = 32.
Numbers of numbers given = 9.
Mean = Sum of numbers given ÷ Numbers of numbers given
= 32 ÷ 9
= 3.555.
Median = -1.
Mode = – 1. (because its repeating twice)
Range = 27 – (7) = 27 + 7 = 34.

Hundredth value :
Mean – 3.555 = 3.555 ÷ 100 = 0.03555.
Median – (-1) = – 1÷ 100 = – 0.01.
Mode – (-1) = -1 ÷ 100 = – 0.01.
Range – 34= 34 ÷ 100 = 0.34.

Question 10.
-10, -20, -20, 0, 10, 20, 20
Mean ___________
Median ___________
Range ___________
Mode ___________
Answer:
Mean = 0.00.
Median = 0.00.
Mode = – 0.20 and 0.20.
Range = 0.40.

Explanation:
-10, -20, -20, 0, 10, 20, 20
Arranging the numbers in numerical order:
-20, -20, -10, 0, 10, 20, 20.
Sum of numbers given = – 20 – 20 – 10 + 0 + 10 + 20 + 20 = – 50 + 50 = 0.
Numbers of numbers given = 7.
Mean = Sum of numbers given ÷ Numbers of numbers given
= 0 ÷ 7
= 0.
Median = 0.
Mode = – 20, 20. (because both are repeating twice)
Range = 20 – (-20) = 20 + 20 = 40.

Hundredth value :
Mean – 0 = 0 ÷ 100 = 0.00.
Median – 0 = 0 ÷ 100 = 0.00.
Mode – (-20, 20) = -20 ÷ 100 = – 0.20 and 20 ÷ 100 = 0.20.
Range – 40 = 40 ÷ 100 = 0.40.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 7.3 Multiplying Mixed Numbers: Reducing existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 7.3 Multiplying Mixed Numbers: Reducing

Exercises Multiply

Question 1.
5\(\frac{1}{4}\) × \(\frac{1}{2}\)
Answer:
2\(\frac{5}{8}\)
Explanation:
5\(\frac{1}{4}\) × \(\frac{1}{2}\)
Convert mixed fraction into simplest fraction.
= \(\frac{21}{4}\) × \(\frac{1}{2}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{21 X 1}{4 X 2}\)
= \(\frac{21}{8}\)
= 5\(\frac{5}{8}\)

Question 2.
\(\frac{1}{3}\) × 5\(\frac{1}{3}\)
Answer:
1\(\frac{7}{9}\)
Explanation:
\(\frac{1}{3}\) × 5\(\frac{1}{3}\)
Convert mixed fraction into simplest fraction.
= \(\frac{1}{3}\) × \(\frac{16}{3}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{1 X 16}{3 X 3}\)
= \(\frac{16}{9}\)
= 1\(\frac{7}{9}\)

Question 3.
-12\(\frac{1}{4}\) × \(\frac{3}{2}\)
Answer:
-18\(\frac{3}{8}\)
Explanation:
-12\(\frac{1}{4}\) × \(\frac{3}{2}\)
Convert mixed fraction into simplest fraction.
= –\(\frac{49}{4}\) × \(\frac{3}{2}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= –\(\frac{49 X 3}{4 X 2}\)
= –\(\frac{147}{8}\)
= -12\(\frac{3}{8}\)

Question 4.
3\(\frac{1}{7}\) × \(\frac{14}{3}\)
Answer:
14\(\frac{2}{3}\)
Explanation:
3\(\frac{1}{7}\) × \(\frac{14}{3}\)
Convert mixed fraction into simplest fraction.
= \(\frac{22}{7}\) × \(\frac{14}{3}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{22 X 14}{7 X 3}\)
= \(\frac{308}{21}\)
= \(\frac{44}{3}\)
= 14\(\frac{2}{3}\)

Question 5.
–\(\frac{1}{5}\) × 1\(\frac{3}{4}\)
Answer:
–\(\frac{7}{20}\)
Explanation:
–\(\frac{1}{5}\) × 1\(\frac{3}{4}\)
Convert mixed fraction into simplest fraction.
= –\(\frac{1}{5}\) × \(\frac{7}{4}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= –\(\frac{1 X 7}{5 X 4}\)
= –\(\frac{7}{20}\)

Question 6.
6\(\frac{5}{7}\) × \(\frac{2}{3}\)
Answer:
4\(\frac{10}{21}\)
Explanation:
6\(\frac{5}{7}\) × \(\frac{2}{3}\)
Convert mixed fraction into simplest fraction.
= \(\frac{47}{7}\) × \(\frac{2}{3}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{47 X 2}{7 X 3}\)
= \(\frac{94}{21}\)
= 4\(\frac{10}{21}\)

Question 7.
4\(\frac{2}{5}\) × \(\frac{3}{8}\)
Answer:
1\(\frac{13}{20}\)
Explanation:
4\(\frac{2}{5}\) × \(\frac{3}{8}\)
Convert mixed fraction into simplest fraction.
= \(\frac{22}{5}\) × \(\frac{3}{8}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{22 X 3}{5 X 8}\)
= \(\frac{66}{40}\)
= \(\frac{33}{20}\)
= 1\(\frac{13}{20}\)

Question 8.
3\(\frac{1}{4}\) × \(\frac{5}{8}\)
Answer:
2\(\frac{1}{32}\)
Explanation:
3\(\frac{1}{4}\) × \(\frac{5}{8}\)
Convert mixed fraction into simplest fraction.
= \(\frac{13}{4}\) × \(\frac{5}{8}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{13 X 5}{4 X 8}\)
= \(\frac{65}{32}\)
= 2\(\frac{1}{32}\)

Question 9.
3\(\frac{2}{5}\) × \(\frac{5}{9}\)
Answer:
1\(\frac{8}{9}\)
Explanation:
3\(\frac{2}{5}\) × \(\frac{5}{9}\)
Convert mixed fraction into simplest fraction.
= \(\frac{17}{5}\) × \(\frac{5}{9}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{17 X 5}{5 X 9}\)
= \(\frac{85}{45}\)
= \(\frac{17}{9}\)
= 1\(\frac{8}{9}\)

Question 10.
\(\frac{1}{4}\) × 4\(\frac{1}{3}\)
Answer:
1\(\frac{1}{12}\)
Explanation:
\(\frac{1}{4}\) × 4\(\frac{1}{3}\)
Convert mixed fraction into simplest fraction.
= \(\frac{1}{4}\) × \(\frac{13}{3}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{1 X 13}{4 X 3}\)
= \(\frac{13}{12}\)
= 1\(\frac{1}{12}\)

Question 11.
3\(\frac{2}{3}\) × 1\(\frac{2}{7}\)
Answer:
4\(\frac{5}{7}\)
Explanation:
3\(\frac{2}{3}\) × 1\(\frac{2}{7}\)
Convert mixed fraction into simplest fraction.
= \(\frac{11}{3}\) × \(\frac{9}{7}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{11 X 9}{3 X 7}\)
= \(\frac{99}{21}\)
= \(\frac{33}{7}\)
= 4\(\frac{5}{7}\)

Question 12.
-4\(\frac{1}{5}\) × -2\(\frac{3}{14}\)
Answer:
9\(\frac{3}{10}\)
Explanation:
-4\(\frac{1}{5}\) × -2\(\frac{3}{14}\)
Convert mixed fraction into simplest fraction.
= –\(\frac{21}{5}\) × –\(\frac{31}{14}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{21 X 31}{5 X 14}\)
= \(\frac{651}{70}\)
= \(\frac{93}{10}\)
= 9\(\frac{3}{10}\)

Question 13.
5\(\frac{1}{4}\) × 3\(\frac{1}{3}\)
Answer:
17\(\frac{1}{2}\)
Explanation:
5\(\frac{1}{4}\) × 3\(\frac{1}{3}\)
Convert mixed fraction into simplest fraction.
= \(\frac{21}{4}\) × \(\frac{10}{3}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{21 X 10}{4 X 3}\)
= \(\frac{210}{12}\)
= \(\frac{35}{2}\)
= 17\(\frac{1}{2}\)

Question 14.
-2\(\frac{4}{5}\) × -4\(\frac{2}{7}\)
Answer:
12
Explanation:
-2\(\frac{4}{5}\) × -4\(\frac{2}{7}\)
Convert mixed fraction into simplest fraction.
= –\(\frac{14}{5}\) × –\(\frac{30}{7}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{14 X 30}{5 X 7}\)
= \(\frac{520}{35}\)
= 12

Question 15.
3\(\frac{3}{4}\) × 3\(\frac{3}{10}\)
Answer:
12\(\frac{3}{8}\)
Explanation:
3\(\frac{3}{4}\) × 3\(\frac{3}{10}\)
Convert mixed fraction into simplest fraction.
= \(\frac{15}{4}\) × \(\frac{33}{10}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{15 X 33}{4 X 10}\)
= \(\frac{495}{40}\)
= \(\frac{99}{8}\)
= 12\(\frac{3}{8}\)

Question 16.
3\(\frac{1}{3}\) × 3\(\frac{3}{5}\)
Answer:
12
Explanation:
3\(\frac{1}{3}\) × 3\(\frac{3}{5}\)
Convert mixed fraction into simplest fraction.
= \(\frac{10}{3}\) × \(\frac{18}{5}\)
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
= \(\frac{10 X 18}{3 X 5}\)
= \(\frac{180}{15}\)
= 12

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 7.2 Multiply Fractions: Reciprocals existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 7.2 Multiply Fractions: Reciprocals

Exercises Multiply

Question 1.
\(\frac{1}{2}\) × \(\frac{2}{3}\)
Answer:
\(\frac{1}{3}\)
Explanation:
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
\(\frac{1}{2}\) × \(\frac{2}{3}\)
= \(\frac{1 X 2}{2 X 3}\)
= \(\frac{2}{6}\)
= \(\frac{1}{3}\)

Question 2.
\(\frac{5}{7}\) × \(\frac{3}{8}\)
Answer:
\(\frac{15}{56}\)
Explanation:
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
\(\frac{5}{7}\) × \(\frac{3}{8}\)
= \(\frac{5 X 3}{7 X 8}\)
= \(\frac{15}{56}\)

Question 3.
\(\frac{20}{21}\) × \(\frac{2}{5}\)
Answer:
\(\frac{8}{21}\)
Explanation:
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
\(\frac{20}{21}\) × \(\frac{2}{5}\)
= \(\frac{20 X 2}{21 X 5}\)
= \(\frac{40}{105}\)
= \(\frac{8}{21}\)

Question 4.
–\(\frac{3}{2}\) × \(\frac{3}{2}\)
Answer:
–\(\frac{9}{4}\) or -2\(\frac{1}{4}\)
Explanation:
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
–\(\frac{3}{2}\) × \(\frac{3}{2}\)
= –\(\frac{3 X 3}{2 X 2}\)
= –\(\frac{9}{4}\)
= -2\(\frac{1}{4}\)

Question 5.
\(\frac{2}{3}\) × \(\frac{3}{2}\)
Answer:
1
Explanation:
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
\(\frac{2}{3}\) × \(\frac{3}{2}\)
= \(\frac{2 X 3}{3 X 2}\)
= \(\frac{6}{6}\)
= 1

Question 6.
–\(\frac{7}{4}\) × \(\frac{16}{3}\)
Answer:
–\(\frac{28}{3}\) or -9\(\frac{1}{3}\)
Explanation:
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
–\(\frac{7}{4}\) × \(\frac{16}{3}\)
= –\(\frac{7 X 16}{2 X 3}\)
= –\(\frac{112}{6}\)
= –\(\frac{28}{3}\)
= -9\(\frac{1}{3}\)

Question 7.
\(\frac{5}{9}\) × \(\frac{90}{10}\)
Answer:
5
Explanation:
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
\(\frac{5}{9}\) × \(\frac{90}{10}\)
= \(\frac{5 X 90}{9 X 10}\)
= \(\frac{450}{90}\)
= 5

Question 8.
\(\frac{4}{7}\) × \(\frac{3}{28}\)
Answer:
\(\frac{3}{49}\)
Explanation:
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
\(\frac{4}{7}\) × \(\frac{3}{28}\)
= \(\frac{4 X 3}{7 X 28}\)
= \(\frac{12}{196}\)
= \(\frac{3}{49}\)

Question 9.
\(\frac{3}{11}\) × \(\frac{11}{3}\)
Answer:
1
Explanation:
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
\(\frac{3}{11}\) × \(\frac{11}{3}\)
= \(\frac{3 X 11}{11 X 3}\)
= \(\frac{33}{33}\)
= 1

Question 10.
\(\frac{12}{13}\) × \(\frac{39}{2}\)
Answer:
18
Explanation:
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
\(\frac{12}{13}\) × \(\frac{39}{2}\)
= \(\frac{12 X 39}{13 X 2}\)
= \(\frac{468}{26}\)
=18

Question 11.
–\(\frac{3}{8}\) × –\(\frac{2}{13}\)
Answer:
\(\frac{3}{52}\)
Explanation:
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
–\(\frac{3}{8}\) × –\(\frac{2}{13}\)
= \(\frac{3 X 2}{8 X 13}\)
= \(\frac{6}{104}\)
= \(\frac{3}{52}\)

Question 12.
\(\frac{7}{8}\) × \(\frac{16}{3}\)
Answer:
\(\frac{14}{3}\) or 4\(\frac{2}{3}\)
Explanation:
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
\(\frac{7}{8}\) × \(\frac{16}{3}\)
= \(\frac{7 X 16}{8 X 3}\)
= \(\frac{112}{24}\)
= \(\frac{14}{3}\)
= 4\(\frac{2}{3}\)

Question 13.
–\(\frac{81}{7}\) × –\(\frac{1}{9}\)
Answer:
\(\frac{9}{7}\) or 1\(\frac{2}{7}\)
Explanation:
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
–\(\frac{81}{7}\) × –\(\frac{1}{9}\)
= \(\frac{81 X 1}{7 X 9}\)
= \(\frac{81}{63}\)
= \(\frac{9}{7}\)
= 1\(\frac{2}{7}\)

Question 14.
\(\frac{7}{3}\) × \(\frac{3}{14}\)
Answer:
\(\frac{1}{2}\)
Explanation:
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
\(\frac{7}{3}\) × \(\frac{3}{14}\)
= \(\frac{7 X 3}{3 X 14}\)
= \(\frac{21}{42}\)
= \(\frac{1}{2}\)

Question 15.
\(\frac{15}{16}\) × \(\frac{3}{5}\)
Answer:
\(\frac{9}{16}\)
Explanation:
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
\(\frac{15}{16}\) × \(\frac{3}{5}\)
= \(\frac{15 X 3}{16 X 5}\)
= \(\frac{45}{80}\)
= \(\frac{9}{16}\)

Question 16.
\(\frac{10}{13}\) × \(\frac{52}{7}\)
Answer:
\(\frac{40}{7}\)or 5\(\frac{5}{7}\)
Explanation:
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
\(\frac{10}{13}\) × \(\frac{52}{7}\)
= \(\frac{10 X 52}{7 X 7}\)
= \(\frac{520}{49}\)
= \(\frac{40}{49}\)
= 5\(\frac{5}{7}\)

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 6.7 Subtracting Mixed Numbers with Unlike Denominators existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 6.7 Subtracting Mixed Numbers with Unlike Denominators

Add Mixed Numbers

Question 1.
5\(\frac{1}{2}\) – 2\(\frac{1}{4}\)
Answer:
First subtract the whole numbers.
5 – 2 = 3
Second find a common denominator for the fractions.
\(\frac{1}{2}\) = \(\frac{2}{4}\) 
Third subtract the fractions.
\(\frac{2}{4}\) – \(\frac{1}{4}\) = \(\frac{1}{4}\) 
Fourth add the difference of the fractions to the difference of the whole numbers.
3 + \(\frac{1}{4}\) = 3\(\frac{1}{4}\) 

Question 2.
10\(\frac{3}{7}\) – 4\(\frac{2}{11}\)
Answer:
First subtract the whole numbers.
10 – 4 = 6
Second find a common denominator for the fractions.
\(\frac{3}{7}\) = \(\frac{33}{77}\)
\(\frac{2}{11}\) = \(\frac{14}{77}\) 
Third subtract the fractions.
\(\frac{33}{77}\) – \(\frac{14}{77}\) = \(\frac{19}{77}\) 
Fourth add the difference of the fractions to the difference of the whole numbers.
6 + \(\frac{19}{77}\) = 6\(\frac{19}{77}\) 

Question 3.
21\(\frac{5}{9}\) – 4\(\frac{2}{5}\)
Answer:
First subtract the whole numbers.
21 – 4 = 17
Second find a common denominator for the fractions.
\(\frac{5}{9}\) = \(\frac{25}{45}\)
\(\frac{2}{5}\) = \(\frac{18}{45}\) 
Third subtract the fractions.
\(\frac{25}{45}\) – \(\frac{18}{45}\) = \(\frac{7}{45}\) 
Fourth add the difference of the fractions to the difference of the whole numbers.
17 + \(\frac{7}{45}\) = 17\(\frac{7}{45}\) 

Question 4.
13\(\frac{5}{6}\) – 10\(\frac{2}{9}\)
Answer:
First subtract the whole numbers.
13 – 10 = 3
Second find a common denominator for the fractions.
\(\frac{5}{6}\) = \(\frac{15}{18}\)
\(\frac{2}{9}\) = \(\frac{4}{18}\) 
Third subtract the fractions.
\(\frac{15}{18}\) – \(\frac{4}{18}\) = \(\frac{11}{18}\) 
Fourth add the difference of the fractions to the difference of the whole numbers.
3 + \(\frac{11}{18}\) = 3\(\frac{11}{18}\) 

Question 5.
14\(\frac{2}{3}\) – 5\(\frac{1}{6}\)
Answer:
First subtract the whole numbers.
14 – 5 = 9
Second find a common denominator for the fractions.
\(\frac{2}{3}\) = \(\frac{4}{6}\) 
Third subtract the fractions.
\(\frac{4}{6}\) – \(\frac{1}{6}\) = \(\frac{3}{6}\) 
Fourth add the difference of the fractions to the difference of the whole numbers.
9 + \(\frac{3}{6}\) = 9\(\frac{3}{6}\) or 9\(\frac{1}{2}\)

Question 6.
21\(\frac{3}{4}\) – 11\(\frac{5}{9}\)
Answer:
First subtract the whole numbers.
21 – 11 = 10
Second find a common denominator for the fractions.
\(\frac{3}{4}\) = \(\frac{27}{36}\)
\(\frac{5}{9}\) = \(\frac{20}{36}\) 
Third subtract the fractions.
\(\frac{27}{36}\) – \(\frac{20}{36}\) = \(\frac{7}{36}\) 
Fourth add the difference of the fractions to the difference of the whole numbers.
10 + \(\frac{7}{36}\) = 10\(\frac{7}{36}\) 

Question 7.
13\(\frac{5}{6}\) – 3\(\frac{1}{7}\)
Answer:
First subtract the whole numbers.
13 – 3 = 10
Second find a common denominator for the fractions.
\(\frac{5}{6}\) = \(\frac{35}{42}\)
\(\frac{1}{7}\) = \(\frac{6}{42}\) 
Third subtract the fractions.
\(\frac{35}{42}\) – \(\frac{6}{42}\) = \(\frac{29}{42}\) 
Fourth add the difference of the fractions to the difference of the whole numbers.
10 + \(\frac{29}{42}\) = 10\(\frac{29}{42}\) 

Question 8.
43\(\frac{4}{5}\) – 29\(\frac{3}{11}\)
Answer:
First subtract the whole numbers.
43 – 29 = 14
Second find a common denominator for the fractions.
\(\frac{4}{5}\) = \(\frac{44}{55}\)
\(\frac{3}{11}\) = \(\frac{15}{55}\) 
Third subtract the fractions.
\(\frac{44}{55}\) – \(\frac{15}{55}\) = \(\frac{29}{55}\) 
Fourth add the difference of the fractions to the difference of the whole numbers.
14 + \(\frac{29}{55}\) = 14\(\frac{29}{55}\) 

Question 9.

Answer:

Explanation:
First subtract the whole numbers.
10 – 4 = 6
Second find a common denominator for the fractions.
\(\frac{6}{11}\) = \(\frac{12}{22}\)
\(\frac{1}{2}\) = \(\frac{11}{22}\) 
Third subtract the fractions.
\(\frac{12}{22}\) – \(\frac{11}{22}\) = \(\frac{1}{22}\) 
Fourth add the difference of the fractions to the difference of the whole numbers.
6 + \(\frac{1}{22}\) = 6\(\frac{1}{22}\) 

Question 10.

Answer:

Explanation:
First subtract the whole numbers.
13 – 11 = 2
Second find a common denominator for the fractions.
\(\frac{2}{3}\) = \(\frac{6}{9}\) 
Third subtract the fractions.
\(\frac{6}{9}\) – \(\frac{5}{9}\) = \(\frac{1}{9}\) 
Fourth add the difference of the fractions to the difference of the whole numbers.
2 + \(\frac{1}{9}\) = 2\(\frac{1}{9}\) 

Question 11.

Answer:

Explanation:
First subtract the whole numbers.
77 – 41 = 36
Second find a common denominator for the fractions.
\(\frac{2}{3}\) = \(\frac{34}{51}\)
\(\frac{2}{17}\) =\(\frac{6}{51}\) 
Third subtract the fractions.
\(\frac{34}{51}\) – \(\frac{6}{51}\) = \(\frac{28}{51}\) 
Fourth add the difference of the fractions to the difference of the whole numbers.
36 + \(\frac{28}{51}\) = 36\(\frac{28}{51}\) 

Question 12.

Answer:

Explanation:
First subtract the whole numbers.
19 – 3 = 16
Second find a common denominator for the fractions.
\(\frac{5}{7}\) = \(\frac{10}{14}\)  
Third subtract the fractions.
\(\frac{10}{14}\) – \(\frac{1}{14}\) = \(\frac{9}{14}\) 
Fourth add the difference of the fractions to the difference of the whole numbers.
16 + \(\frac{9}{14}\) = 16\(\frac{9}{14}\)

Question 13.
Janelle practiced playing the piano 2\(\frac{1}{2}\) hours on Saturday. On Sunday, she practiced for 3\(\frac{1}{4}\) hours. How many more hours did Janelle practice on Sunday than on Saturday?
Answer:

Question 14.
Robby is helping his father make a casserole for dinner. They purchased 1\(\frac{1}{4}\) pounds of potatoes, and used \(\frac{2}{3}\) pounds of potatoes to make one casserole.
Do they have enough potatoes left over to make the casserole a second time?
Answer:

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 6.6 Adding Mixed Numbers with Unlike Denominators existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 6.6 Adding Mixed Numbers with Unlike Denominators

Add Mixed Numbers

Question 1.
2\(\frac{1}{2}\) + 3\(\frac{1}{4}\)
Answer:
First add the whole numbers.
2 + 3 = 5
Second find a common denominator for the fractions.
\(\frac{1}{2}\) = \(\frac{2}{4}\)
Third add the fractions.
\(\frac{2}{4}\) + \(\frac{1}{4}\) = \(\frac{3}{4}\)
Fourth add the sum of the fractions to the sum of the whole numbers.
2\(\frac{1}{2}\) + 3\(\frac{1}{4}\) = 5 + \(\frac{3}{4}\) = 5\(\frac{3}{4}\)

Question 2.
3\(\frac{2}{3}\) + 4\(\frac{3}{7}\)
Answer:
First add the whole numbers.
3 + 4 = 7
Second find a common denominator for the fractions.
\(\frac{2}{3}\) = \(\frac{14}{21}\)
\(\frac{3}{7}\) = \(\frac{9}{21}\)
Third add the fractions.
\(\frac{14}{21}\) + \(\frac{9}{21}\) = \(\frac{23}{21}\) = 1\(\frac{2}{21}\)
Fourth add the sum of the fractions to the sum of the whole numbers.
3\(\frac{2}{3}\) + 4\(\frac{3}{7}\) = 7 + 1\(\frac{2}{21}\) = 8\(\frac{2}{21}\)

Question 3.
4\(\frac{5}{6}\) + 7\(\frac{3}{4}\)
Answer:
First add the whole numbers.
4 + 7 = 11
Second find a common denominator for the fractions.
\(\frac{5}{6}\) = \(\frac{10}{12}\)
\(\frac{3}{4}\) = \(\frac{9}{12}\)
Third add the fractions.
\(\frac{10}{12}\) + \(\frac{9}{12}\) = \(\frac{19}{12}\) = 1\(\frac{7}{12}\)
Fourth add the sum of the fractions to the sum of the whole numbers.
4\(\frac{5}{6}\) + 7\(\frac{3}{4}\) = 11 + 1\(\frac{7}{12}\) = 12\(\frac{7}{12}\)

Question 4.
3\(\frac{3}{4}\) + 2\(\frac{1}{3}\)
Answer:
First add the whole numbers.
3 + 2 = 5
Second find a common denominator for the fractions.
\(\frac{3}{4}\) = \(\frac{9}{12}\)
\(\frac{1}{3}\) = \(\frac{4}{12}\)
Third add the fractions.
\(\frac{9}{12}\) + \(\frac{4}{12}\) = \(\frac{13}{12}\) = 1\(\frac{1}{12}\)
Fourth add the sum of the fractions to the sum of the whole numbers.
3\(\frac{3}{4}\) + 2\(\frac{1}{3}\) = 5 + 1\(\frac{1}{12}\) = 6\(\frac{1}{12}\)

Question 5.
9\(\frac{1}{2}\) + 4\(\frac{1}{5}\)
Answer:
First add the whole numbers.
9 + 4 = 13
Second find a common denominator for the fractions.
\(\frac{1}{2}\) = \(\frac{5}{10}\)
\(\frac{1}{5}\) = \(\frac{2}{10}\)
Third add the fractions.
\(\frac{5}{10}\) + \(\frac{2}{10}\) = \(\frac{7}{10}\) 
Fourth add the sum of the fractions to the sum of the whole numbers.
9\(\frac{1}{2}\) + 4\(\frac{1}{5}\) = 13 + \(\frac{7}{10}\) = 13\(\frac{7}{10}\)

Question 6.
54\(\frac{1}{2}\) + 14\(\frac{2}{3}\)
Answer:
First add the whole numbers.
54 + 14 = 68
Second find a common denominator for the fractions.
\(\frac{1}{2}\) = \(\frac{3}{6}\)
\(\frac{2}{3}\) = \(\frac{4}{6}\)
Third add the fractions.
\(\frac{3}{6}\) + \(\frac{4}{6}\) = \(\frac{7}{6}\) = 1 \(\frac{1}{6}\)
Fourth add the sum of the fractions to the sum of the whole numbers.
54\(\frac{1}{2}\) + 14\(\frac{2}{3}\) = 68 + 1\(\frac{1}{6}\) = 69\(\frac{1}{6}\)

Question 7.
10\(\frac{5}{7}\) + 12\(\frac{2}{3}\)
Answer:
First add the whole numbers.
10 + 12 = 22
Second find a common denominator for the fractions.
\(\frac{5}{7}\) = \(\frac{15}{21}\)
\(\frac{2}{3}\) = \(\frac{14}{21}\)
Third add the fractions.
\(\frac{15}{21}\) + \(\frac{14}{21}\) = \(\frac{29}{21}\) = 1\(\frac{8}{21}\)
Fourth add the sum of the fractions to the sum of the whole numbers.
10\(\frac{5}{7}\) + 12\(\frac{2}{3}\) = 22 + 1\(\frac{8}{21}\) = 23\(\frac{8}{21}\)

Question 8.
4\(\frac{2}{9}\) + 3\(\frac{2}{7}\)
Answer:
First add the whole numbers.
4 + 3 = 7
Second find a common denominator for the fractions.
\(\frac{2}{9}\) = \(\frac{14}{63}\)
\(\frac{2}{7}\) = \(\frac{18}{63}\)
Third add the fractions.
\(\frac{14}{63}\) + \(\frac{18}{63}\) = \(\frac{32}{63}\) 
Fourth add the sum of the fractions to the sum of the whole numbers.
4\(\frac{2}{9}\) + 3\(\frac{2}{7}\) = 7 + \(\frac{31}{63}\) = 7\(\frac{32}{63}\)

Question 9.
13\(\frac{4}{5}\) + 4\(\frac{3}{11}\)
Answer:
First add the whole numbers.
13 + 4 = 17
Second find a common denominator for the fractions.
\(\frac{4}{5}\) = \(\frac{44}{55}\)
\(\frac{3}{11}\) = \(\frac{15}{55}\)
Third add the fractions.
\(\frac{44}{55}\) + \(\frac{15}{55}\) = \(\frac{59}{55}\) = 1\(\frac{4}{55}\)
Fourth add the sum of the fractions to the sum of the whole numbers.
13\(\frac{4}{5}\) + 4\(\frac{3}{11}\) = 17 + 1\(\frac{4}{55}\) = 18\(\frac{4}{55}\)

Question 10.
23\(\frac{1}{6}\) + 57\(\frac{3}{13}\)
Answer:
First add the whole numbers.
23 + 57 = 80
Second find a common denominator for the fractions.
\(\frac{1}{6}\) = \(\frac{13}{78}\)
\(\frac{3}{13}\) = \(\frac{18}{78}\)
Third add the fractions.
\(\frac{13}{78}\) + \(\frac{18}{78}\) = \(\frac{31}{78}\) 
Fourth add the sum of the fractions to the sum of the whole numbers.
23\(\frac{1}{6}\) + 57\(\frac{3}{13}\) = 80 + \(\frac{31}{78}\) = 80\(\frac{31}{78}\)

Question 11.
22\(\frac{3}{11}\) + 14\(\frac{2}{5}\)
Answer:
First add the whole numbers.
22 + 14 = 36
Second find a common denominator for the fractions.
\(\frac{3}{11}\) = \(\frac{15}{55}\)
\(\frac{2}{5}\) = \(\frac{22}{55}\)
Third add the fractions.
\(\frac{15}{55}\) + \(\frac{22}{55}\) = \(\frac{37}{55}\) 
Fourth add the sum of the fractions to the sum of the whole numbers.
22\(\frac{3}{11}\) + 14\(\frac{2}{5}\) = 36 + \(\frac{37}{55}\) = 36\(\frac{37}{55}\)

Question 12.
4\(\frac{5}{7}\) + 3\(\frac{1}{3}\)
Answer:
First add the whole numbers.
4 + 3 = 7
Second find a common denominator for the fractions.
\(\frac{5}{7}\) = \(\frac{15}{21}\)
\(\frac{1}{3}\) = \(\frac{7}{21}\)
Third add the fractions.
\(\frac{15}{21}\) + \(\frac{7}{21}\) = \(\frac{22}{21}\) = 1\(\frac{1}{21}\)
Fourth add the sum of the fractions to the sum of the whole numbers.
4\(\frac{5}{7}\) + 3\(\frac{1}{3}\) = 7 + 1\(\frac{1}{21}\) = 8\(\frac{1}{21}\)

Question 13.

Answer:

Explanation:
First add the whole numbers.
5 + 7 = 12
Second find a common denominator for the fractions.
\(\frac{1}{4}\) = \(\frac{15}{60}\)
\(\frac{2}{15}\) = \(\frac{8}{60}\)
Third add the fractions.
\(\frac{15}{60}\) + \(\frac{8}{60}\) = \(\frac{23}{60}\) 
Fourth add the sum of the fractions to the sum of the whole numbers.
5\(\frac{1}{4}\) + 7\(\frac{2}{15}\) = 12 + \(\frac{23}{60}\) = 12\(\frac{23}{60}\)

Question 14.

Answer:

Explanation:
First add the whole numbers.
102 + 355 = 457
Second find a common denominator for the fractions.
\(\frac{5}{6}\) = \(\frac{55}{66}\)
\(\frac{1}{11}\) = \(\frac{6}{66}\)
Third add the fractions.
\(\frac{55}{66}\) + \(\frac{6}{66}\) = \(\frac{61}{66}\) 
Fourth add the sum of the fractions to the sum of the whole numbers.
102\(\frac{5}{6}\) + 355\(\frac{1}{11}\) = 457 + \(\frac{61}{66}\) = 457\(\frac{61}{66}\)

Question 15.

Answer:

Explanation:
First add the whole numbers.
56 + 89 = 145
Second find a common denominator for the fractions.
\(\frac{1}{3}\) = \(\frac{14}{42}\)
\(\frac{5}{14}\) = \(\frac{15}{42}\)
Third add the fractions.
\(\frac{14}{42}\) + \(\frac{15}{42}\) = \(\frac{29}{42}\) 
Fourth add the sum of the fractions to the sum of the whole numbers.
56\(\frac{1}{3}\) + 89\(\frac{5}{14}\) = 145 + \(\frac{29}{42}\) = 145\(\frac{29}{42}\)

Question 16.

Answer:

First add the whole numbers.
21 + 122 = 143
Second find a common denominator for the fractions.
\(\frac{1}{2}\) = \(\frac{4}{8}\)
Third add the fractions.
\(\frac{4}{8}\) + \(\frac{3}{8}\) = \(\frac{7}{8}\) 
Fourth add the sum of the fractions to the sum of the whole numbers.
21\(\frac{1}{2}\) + 122\(\frac{3}{8}\) = 143 + \(\frac{7}{8}\) = 143\(\frac{7}{8}\)

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 6.5 Adding or Subtracting Fractions with Unlike Denominators existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 6.5 Adding or Subtracting Fractions with Unlike Denominators

Exercises Add or Subtract

Question 1.
\(\frac{1}{4}\) + \(\frac{1}{5}\)
Answer:
First find the common multiple for both the denominators. The common multiple is 20.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{1}{4}\) = (1 x 5)/(4 x 5) = \(\frac{5}{20}\)
\(\frac{1}{5}\) = (1 x 4)/(5 x 4) = \(\frac{4}{20}\)
Third add the fractions.
\(\frac{5}{20}\) +\(\frac{4}{20}\) = \(\frac{9}{20}\)
\(\frac{1}{4}\) + \(\frac{1}{5}\) = \(\frac{9}{20}\)

Question 2.
\(\frac{2}{7}\) + \(\frac{2}{3}\)
Answer:
First find the common multiple for both the denominators. The common multiple is 21.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{2}{7}\) = (2 x 3)/(7 x 3) = \(\frac{6}{21}\)
\(\frac{2}{3}\) = (2 x 7)/(3 x 7) = \(\frac{14}{21}\)
Third add the fractions.
\(\frac{6}{21}\) +\(\frac{14}{21}\) = \(\frac{20}{21}\)
\(\frac{2}{7}\) + \(\frac{2}{3}\) = \(\frac{20}{21}\)

Question 3.
\(\frac{21}{20}\) + \(\frac{1}{3}\)
Answer:
First find the common multiple for both the denominators. The common multiple is 60.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{21}{20}\) = (21 x 3)/(20 x 3) = \(\frac{63}{60}\)
\(\frac{1}{3}\) = (1 x 20)/(3 x 20) = \(\frac{20}{60}\)
Third add the fractions.
\(\frac{63}{60}\) +\(\frac{20}{60}\) = \(\frac{83}{60}\)
\(\frac{21}{20}\) + \(\frac{1}{3}\) = \(\frac{83}{60}\)

Question 4.
\(\frac{12}{13}\) – \(\frac{1}{2}\)
Answer:
First find the common multiple for both the denominators. The common multiple is 26.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{12}{13}\) = (12 x 2)/(13 x 2) = \(\frac{24}{26}\)
\(\frac{1}{2}\) = (1 x 13)/(2 x 13) = \(\frac{13}{26}\)
Third subtract the fractions.
\(\frac{24}{26}\) – \(\frac{13}{26}\) = \(\frac{11}{26}\)
\(\frac{12}{13}\) – \(\frac{1}{2}\) = \(\frac{11}{26}\)

Question 5.
\(\frac{3}{4}\) – \(\frac{1}{7}\)
Answer:
First find the common multiple for both the denominators. The common multiple is 28.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{3}{4}\) = (3 x 7)/(4 x 7) = \(\frac{21}{28}\)
\(\frac{1}{7}\) = (1 x 4)/(7 x 4) = \(\frac{4}{28}\)
Third subtract the fractions.
\(\frac{21}{28}\) – \(\frac{4}{28}\) = \(\frac{17}{28}\)
\(\frac{3}{4}\) – \(\frac{1}{7}\) = \(\frac{17}{28}\)

Question 6.
\(\frac{23}{21}\) + \(\frac{1}{5}\)
Answer:
First find the common multiple for both the denominators. The common multiple is 105.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{23}{21}\) = (23 x 5)/(21 x 5) = \(\frac{115}{105}\)
\(\frac{1}{5}\) = (1 x 21)/(5 x 21) = \(\frac{21}{105}\)
Third add the fractions.
\(\frac{115}{105}\) +\(\frac{21}{105}\) = \(\frac{136}{105}\)
\(\frac{23}{21}\) + \(\frac{1}{5}\) = \(\frac{136}{105}\)

Question 7.
\(\frac{32}{11}\) – \(\frac{2}{3}\)
Answer:
First find the common multiple for both the denominators. The common multiple is 33.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{32}{11}\) = (32 x 3)/(11 x 3) = \(\frac{96}{33}\)
\(\frac{2}{3}\) = (2 x 11)/(3 x 11) = \(\frac{22}{33}\)
Third subtract the fractions.
\(\frac{96}{33}\) – \(\frac{22}{33}\) = \(\frac{74}{33}\)
\(\frac{32}{11}\) – \(\frac{2}{3}\) = \(\frac{74}{33}\)

Question 8.
\(\frac{12}{7}\) + \(\frac{2}{3}\)
Answer:
First find the common multiple for both the denominators. The common multiple is 21.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{12}{7}\) = (12 x 3)/(7 x 3) = \(\frac{36}{21}\)
\(\frac{2}{3}\) = (2 x 7)/(3 x 7) = \(\frac{14}{21}\)
Third add the fractions.
\(\frac{36}{21}\) +\(\frac{14}{21}\) = \(\frac{50}{21}\)
\(\frac{12}{7}\) + \(\frac{2}{3}\) = \(\frac{50}{21}\)

Question 9.
\(\frac{8}{15}\) – \(\frac{1}{3}\)
Answer:
First find the common multiple for both the denominators. The common multiple is 15.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{8}{15}\) = (8 x 1)/(15 x 1) = \(\frac{8}{15}\)
\(\frac{1}{3}\) = (1 x 5)/(3 x 5) = \(\frac{5}{15}\)
Third subtract the fractions.
\(\frac{8}{15}\) – \(\frac{5}{15}\) = \(\frac{3}{15}\)
\(\frac{8}{15}\) – \(\frac{1}{3}\) = \(\frac{3}{15}\) or \(\frac{1}{5}\)

Question 10.
\(\frac{7}{8}\) – \(\frac{2}{5}\)
Answer:
First find the common multiple for both the denominators. The common multiple is 40.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{7}{8}\) = (7 x 5)/(8 x 5) = \(\frac{35}{40}\)
\(\frac{2}{5}\) = (2 x 8)/(5 x 8) = \(\frac{16}{40}\)
Third subtract the fractions.
\(\frac{35}{40}\) – \(\frac{16}{40}\) = \(\frac{19}{40}\)
\(\frac{7}{8}\) – \(\frac{2}{5}\) = \(\frac{19}{40}\)

Question 11.

Answer:

Explanation:
First find the common multiple for both the denominators. The common multiple is 77.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{54}{11}\) = (54 x 7)/(11 x 7) = \(\frac{378}{77}\)
\(\frac{2}{7}\) = (2 x 11)/(7 x 11) = \(\frac{22}{77}\)
Third add the fractions.
\(\frac{378}{77}\) + \(\frac{22}{77}\) = \(\frac{400}{77}\)

Question 12.

Answer:

Explanation:
First find the common multiple for both the denominators. The common multiple is 60.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{13}{12}\) = (13 x 5)/(12 x 5) = \(\frac{65}{60}\)
\(\frac{4}{5}\) = (4 x 12)/(5 x 12) = \(\frac{48}{60}\)
Third subtract the fractions.
\(\frac{65}{60}\) – \(\frac{48}{60}\) = \(\frac{17}{60}\)
Question 13.

Answer:

Explanation:
First find the common multiple for both the denominators. The common multiple is 39.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{56}{13}\) = (56 x 3)/(13 x 3) = \(\frac{168}{39}\)
\(\frac{2}{3}\) = (2 x 13)/(3 x 13) = \(\frac{26}{39}\)
Third subtract the fractions.
\(\frac{168}{39}\) – \(\frac{26}{39}\) = \(\frac{142}{39}\)

Question 14.

Answer:

Explanation:
First find the common multiple for both the denominators. The common multiple is 20.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{3}{4}\) = (3 x 5)/(4 x 5) = \(\frac{15}{20}\)
\(\frac{2}{5}\) = (2 x 4)/(5 x 4) = \(\frac{8}{20}\)
Third subtract the fractions.
\(\frac{15}{20}\) – \(\frac{8}{20}\) = \(\frac{7}{20}\)

Question 15.

Answer:

Explanation:
First find the common multiple for both the denominators. The common multiple is 4.
Second multiply both the numerator and denominator by the number that will make the denominator equal the common multiple. Do this for both the fractions.
\(\frac{21}{4}\) = (21 x 1)/(4 x 1) = \(\frac{21}{4}\)
\(\frac{5}{2}\) = (5 x 2)/(2 x 2) = \(\frac{10}{4}\)
Third subtract the fractions.
\(\frac{21}{4}\) – \(\frac{10}{4}\) = \(\frac{11}{4}\)

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 6.4 Subtracting Fractions with Like Denominators existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 6.4 Subtracting Fractions with Like Denominators

Exercises Subtract

Question 1.
\(\frac{3}{4}\) – \(\frac{1}{4}\)
Answer:
\(\frac{3}{4}\) – \(\frac{1}{4}\) = (3-1)/4 = \(\frac{2}{4}\) = \(\frac{1}{2}\) 
Explanation:
Perform subtraction operation on above two given fractions. Subtract \(\frac{1}{4}\) from \(\frac{3}{4}\) the difference is equal to \(\frac{2}{4}\) or \(\frac{1}{2}\).

Question 2.
\(\frac{7}{8}\) – \(\frac{5}{8}\)
Answer:
\(\frac{7}{8}\) – \(\frac{5}{8}\) = (7 – 5)/8 = \(\frac{2}{8}\) = \(\frac{1}{4}\) 
Explanation:
Perform subtraction operation on above two given fractions. Subtract \(\frac{5}{8}\) from \(\frac{7}{8}\) the difference is equal to \(\frac{2}{8}\) or \(\frac{1}{4}\).

Question 3.
\(\frac{7}{4}\) – \(\frac{1}{4}\)
Answer:
\(\frac{7}{4}\) – \(\frac{1}{4}\) = (7 – 1)/4 = \(\frac{6}{4}\) = \(\frac{3}{2}\) 
Explanation:
Perform subtraction operation on above two given fractions. Subtract \(\frac{1}{4}\) from \(\frac{7}{4}\) the difference is equal to \(\frac{6}{4}\) or \(\frac{3}{2}\).

Question 4.
\(\frac{14}{5}\) – \(\frac{8}{5}\)
Answer:
\(\frac{14}{5}\) – \(\frac{8}{5}\) = (14 – 8)/5 = \(\frac{6}{5}\) 
Explanation:
Perform subtraction operation on above two given fractions. Subtract \(\frac{8}{5}\) from \(\frac{14}{5}\) the difference is equal to \(\frac{6}{5}\).

Question 5.
\(\frac{33}{7}\) – \(\frac{29}{7}\)
Answer:
\(\frac{33}{7}\) – \(\frac{29}{7}\) = (33-29)/7 = \(\frac{4}{7}\) 
Explanation:
Perform subtraction operation on above two given fractions. Subtract \(\frac{29}{7}\) from \(\frac{33}{7}\) the difference is equal to \(\frac{4}{7}\).

Question 6.
\(\frac{9}{11}\) – \(\frac{7}{11}\)
Answer:
\(\frac{9}{11}\) – \(\frac{7}{11}\) = (9 – 7)/11 = \(\frac{2}{11}\) 
Explanation:
Perform subtraction operation on above two given fractions. Subtract \(\frac{7}{11}\) form \(\frac{9}{11}\) the difference is equal to \(\frac{2}{11}\).

Question 7.
\(\frac{14}{3}\) – \(\frac{7}{3}\)
Answer:
\(\frac{14}{3}\) – \(\frac{7}{3}\) = (14 – 7)/3 = \(\frac{7}{3}\) 
Explanation:
Perform subtraction operation on above two given fractions. Subtract \(\frac{7}{3}\) form \(\frac{14}{3}\) the difference is equal to \(\frac{7}{3}\).

Question 8.
\(\frac{21}{19}\) – \(\frac{13}{19}\)
Answer:
\(\frac{21}{19}\) – \(\frac{13}{19}\) = (21 – 13)/19 = \(\frac{8}{19}\) 
Explanation:
Perform subtraction operation on above two given fractions. Subtract \(\frac{13}{19}\) form \(\frac{21}{19}\) the difference is equal to \(\frac{8}{19}\).

Question 9.

Answer:

Explanation:
Perform subtraction operation on above two given fractions. Subtract \(\frac{2}{5}\) form \(\frac{12}{5}\) the difference is equal to \(\frac{10}{5}\) or 2.

Question 10.

Answer:

Explanation:
Perform subtraction operation on above two given fractions. Subtract \(\frac{17}{7}\) form \(\frac{23}{7}\) the difference is equal to \(\frac{6}{7}\).

Question 11.

Answer:

Explanation:
Perform subtraction operation on above two given fractions. Subtract \(\frac{37}{8}\) form \(\frac{45}{8}\) the difference is equal to \(\frac{8}{8}\) or 1.

Question 12.

Answer:

Explanation:
Perform subtraction operation on above two given fractions. Subtract \(\frac{4}{51}\) form \(\frac{12}{51}\) the difference is equal to \(\frac{8}{51}\).

Question 13.

Answer:

Explanation:
Perform subtraction operation on above two given fractions. Subtract \(\frac{14}{13}\) form \(\frac{43}{13}\) the difference is equal to \(\frac{29}{13}\).

Question 14.

Answer:

Explanation:
Perform subtraction operation on above two given fractions. Subtract \(\frac{35}{17}\) form \(\frac{56}{17}\) the difference is equal to \(\frac{21}{17}\).

Question 15.

Answer:

Explanation:
Perform subtraction operation on above two given fractions. Subtract \(\frac{3}{4}\) form \(\frac{7}{4}\) the difference is equal to \(\frac{4}{4}\) or 1.

Question 16.

Answer:

Explanation:
Perform subtraction operation on above two given fractions. Subtract \(\frac{14}{37}\) form \(\frac{32}{37}\) the difference is equal to \(\frac{18}{37}\).

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 6.3 Adding Fractions with Like Denominators existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 6.3 Adding Fractions with Like Denominators

Exercises Add

Question 1.
\(\frac{1}{2}\) + \(\frac{1}{2}\)
Answer:
\(\frac{1}{2}\) + \(\frac{1}{2}\) = (1+1)/2 = \(\frac{2}{2}\) = 1
Explanation:
Perform addition operation on above two given improper fractions. Add \(\frac{1}{2}\) with \(\frac{1}{2}\) the sum is equal to 1.

Question 2.
\(\frac{4}{5}\) + \(\frac{3}{5}\)
Answer:
\(\frac{4}{5}\) + \(\frac{3}{5}\) = (4+3)/5 = \(\frac{7}{5}\) 
Explanation:
Perform addition operation on above two given improper fractions. Add \(\frac{4}{5}\) with \(\frac{3}{5}\) the sum is equal to \(\frac{7}{5}\).

Question 3.
\(\frac{7}{8}\) + \(\frac{3}{8}\)
Answer:
\(\frac{7}{8}\) + \(\frac{3}{8}\) = (7+3)/8 = \(\frac{10}{8}\) = \(\frac{5}{4}\)
Explanation:
Perform addition operation on above two given improper fractions. Add \(\frac{7}{8}\) with \(\frac{3}{8}\) the sum is equal to \(\frac{5}{4}\).

Question 4.
\(\frac{6}{7}\) + \(\frac{2}{7}\)
Answer:
\(\frac{6}{7}\) + \(\frac{2}{7}\) = (6+2)/7 = \(\frac{8}{7}\) 
Explanation:
Perform addition operation on above two given improper fractions. Add \(\frac{6}{7}\) with \(\frac{2}{7}\) the sum is equal to \(\frac{8}{7}\).

Question 5.
\(\frac{10}{11}\) + \(\frac{14}{11}\)
Answer:
\(\frac{10}{11}\) + \(\frac{14}{11}\) = (10 + 14)/11 = \(\frac{24}{11}\) 
Explanation:
Perform addition operation on above two given improper fractions. Add \(\frac{10}{11}\) with \(\frac{14}{11}\) the sum is equal to \(\frac{24}{11}\).

Question 6.
\(\frac{71}{17}\) + \(\frac{3}{17}\)
Answer:
\(\frac{71}{17}\) + \(\frac{3}{17}\) = (71 + 3)/17 = \(\frac{74}{17}\) 
Explanation:
Perform addition operation on above two given improper fractions. Add \(\frac{71}{17}\) with \(\frac{3}{17}\) the sum is equal to \(\frac{74}{17}\).

Question 7.
\(\frac{4}{9}\) + \(\frac{34}{9}\)
Answer:
\(\frac{4}{9}\) + \(\frac{34}{9}\) = (4+34)/9 = \(\frac{38}{9}\) 
Explanation:
Perform addition operation on above two given improper fractions. Add \(\frac{4}{9}\) with \(\frac{34}{9}\) the sum is equal to \(\frac{38}{9}\).

Question 8.
\(\frac{2}{3}\) + \(\frac{7}{3}\)
Answer:
\(\frac{2}{3}\) + \(\frac{7}{3}\) = (2+7)/3 = \(\frac{9}{3}\) = 3
Explanation:
Perform addition operation on above two given improper fractions. Add \(\frac{2}{3}\) with \(\frac{7}{3}\) the sum is equal to 3.

Question 9.

Answer:

Explanation:
Perform addition operation on above two given improper fractions. Add \(\frac{4}{23}\) with \(\frac{54}{23}\) the sum is equal to \(\frac{58}{23}\).

Question 10.

Answer:

Explanation:
Perform addition operation on above two given improper fractions. Add \(\frac{3}{37}\) with \(\frac{54}{37}\) the sum is equal to \(\frac{57}{37}\).

Question 11.

Answer:

Explanation:
Perform addition operation on above two given improper fractions. Add \(\frac{3}{4}\) with \(\frac{5}{4}\) the sum is equal to \(\frac{8}{4}\) or 2.

Question 12.

Answer:

Explanation:
Perform addition operation on above two given improper fractions. Add \(\frac{7}{11}\) with \(\frac{5}{11}\) the sum is equal to \(\frac{12}{11}\).

Question 13.

Answer:

Explanation:
Perform addition operation on above two given improper fractions. Add \(\frac{5}{27}\) with \(\frac{10}{27}\) the sum is equal to \(\frac{15}{27}\) or \(\frac{5}{9}\).

Question 14.

Answer:

Explanation:
Perform addition operation on above two given improper fractions. Add \(\frac{3}{4}\) with \(\frac{13}{4}\) the sum is equal to \(\frac{16}{4}\) or 4.

Question 15.

Answer:

Explanation:
Perform addition operation on above two given improper fractions. Add \(\frac{23}{24}\) with \(\frac{19}{24}\) the sum is equal to \(\frac{42}{24}\) or \(\frac{7}{4}\).

Question 16.

Answer:

Explanation:
Perform addition operation on above two given improper fractions. Add \(\frac{3}{37}\) with \(\frac{10}{37}\) the sum is equal to \(\frac{13}{37}\).

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 6.2 Changing Mixed Numbers to Improper Fractions existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 6.2 Changing Mixed Numbers to Improper Fractions

Exercises Change To Improper Fractions

Question 1.
3\(\frac{1}{4}\)
Answer:
To convert the given mixed number 3\(\frac{1}{4}\) to improper fraction.
First multiply the whole number 3 by the denominator 4.
3 × 4 = 12
The product 12 is added to the numerator 1.
12 + 1 = 13
Now, we have to write the answer 13 which is obtained from the above step over the denominator.
The mixed number 3\(\frac{1}{4}\) in improper fraction is \(\frac{13}{4}\).

Question 2.
-5\(\frac{3}{7}\)
Answer:
To convert the given mixed number -5\(\frac{3}{7}\) to improper fraction.
First multiply the whole number 5 by the denominator 7.
5 × 7 = 35
The product 35 is added to the numerator 3.
35 + 3 = 38
Now, we have to write the answer 38 which is obtained from the above step over the denominator.
The mixed number -5\(\frac{3}{7}\) in improper fraction as –\(\frac{38}{7}\).

Question 3.
12\(\frac{3}{11}\)
Answer:
To convert the given mixed number 12\(\frac{3}{11}\) to improper fraction.
First multiply the whole number 12 by the denominator 11.
12 × 11 = 132
The product 132 is added to the numerator 3.
132 + 3 = 135
Now, we have to write the answer 135 which is obtained from the above step over the denominator.
The mixed number 12\(\frac{3}{11}\) in improper fraction as \(\frac{135}{11}\).

Question 4.
14\(\frac{3}{5}\)
Answer:
To convert the given mixed number 14\(\frac{3}{5}\) to improper fraction.
First multiply the whole number 14 by the denominator 5.
14 × 5 = 70
The product 70 is added to the numerator 3.
70 + 3 = 73
Now, we have to write the answer 73 which is obtained from the above step over the denominator.
The mixed number 14\(\frac{3}{5}\) in improper fraction as \(\frac{73}{5}\).

Question 5.
1\(\frac{2}{13}\)
Answer:
To convert the given mixed number 1\(\frac{2}{13}\) to improper fraction.
First multiply the whole number 1 by the denominator 13.
1 × 13 = 13
The product 13 is added to the numerator 2.
13 + 2 = 15
Now, we have to write the answer 15 which is obtained from the above step over the denominator.
The mixed number 1\(\frac{2}{13}\) in improper fraction as \(\frac{15}{13}\).

Question 6.
21\(\frac{3}{14}\)
Answer:
To convert the given mixed number 21\(\frac{3}{14}\) to improper fraction.
First multiply the whole number 21 by the denominator 14.
14 × 21 = 294
The product 28 is added to the numerator 3.
294 + 3 = 297
Now, we have to write the answer 297 which is obtained from the above step over the denominator.
The mixed number 21\(\frac{3}{14}\) in improper fraction as \(\frac{297}{14}\).

Question 7.
33\(\frac{1}{9}\)
Answer:
To convert the given mixed number 33\(\frac{1}{9}\) to improper fraction.
First multiply the whole number 33 by the denominator 9.
33 × 9 = 297
The product 297 is added to the numerator 1.
297 + 1 = 298
Now, we have to write the answer 298 which is obtained from the above step over the denominator.
The mixed number 33\(\frac{1}{9}\) in improper fraction as \(\frac{298}{9}\).

Question 8.
-4\(\frac{1}{17}\)
Answer:
To convert the given mixed number -4\(\frac{1}{17}\) to improper fraction.
First multiply the whole number 4 by the denominator 17.
17 × 4 = 68
The product 68 is added to the numerator 1.
68 + 1 = 69
Now, we have to write the answer 69 which is obtained from the above step over the denominator.
The mixed number -4\(\frac{1}{17}\) in improper fraction as –\(\frac{69}{17}\).

Question 9.
102\(\frac{1}{7}\)
Answer:
To convert the given mixed number 102\(\frac{1}{7}\) to improper fraction.
First multiply the whole number 102 by the denominator 7.
102 × 7 = 714
The product 714 is added to the numerator 1.
714 + 1 = 715
Now, we have to write the answer 715 which is obtained from the above step over the denominator.
The mixed number 102\(\frac{1}{7}\) in improper fraction as \(\frac{715}{7}\).

Question 10.
-32\(\frac{1}{2}\)
Answer:
To convert the given mixed number -32\(\frac{1}{2}\) to improper fraction.
First multiply the whole number 32 by the denominator 2.
32 × 2 = 64
The product 64 is added to the numerator 1.
64 + 1 = 65
Now, we have to write the answer 65 which is obtained from the above step over the denominator.
The mixed number -32\(\frac{1}{2}\) in improper fraction as –\(\frac{65}{2}\).

Question 11.
29\(\frac{1}{29}\)
Answer:
To convert the given mixed number 29\(\frac{1}{29}\) to improper fraction.
First multiply the whole number 29 by the denominator 29.
29 × 29 = 841
The product 841 is added to the numerator 1.
841 + 1 = 842
Now, we have to write the answer 842 which is obtained from the above step over the denominator.
The mixed number 29\(\frac{1}{29}\) in improper fraction as \(\frac{842}{29}\).

Question 12.
37\(\frac{3}{8}\)
Answer:
To convert the given mixed number 37\(\frac{3}{8}\) to improper fraction.
First multiply the whole number 37 by the denominator 8.
37 × 8 = 296
The product 296 is added to the numerator 3.
296 + 3 = 299
Now, we have to write the answer 299 which is obtained from the above step over the denominator.
The mixed number 37\(\frac{3}{8}\) in improper fraction as \(\frac{299}{8}\).

Question 13.
15\(\frac{2}{3}\)
Answer:
To convert the given mixed number 15\(\frac{2}{3}\) to improper fraction.
First multiply the whole number 15 by the denominator 3.
15 × 3 = 45
The product 45 is added to the numerator 2.
45 + 2 = 47
Now, we have to write the answer 47 which is obtained from the above step over the denominator.
The mixed number 15\(\frac{2}{3}\) in improper fraction as \(\frac{47}{3}\).

Question 14.
61\(\frac{5}{14}\)
Answer:
To convert the given mixed number 61\(\frac{5}{14}\) to improper fraction.
First multiply the whole number 61 by the denominator 14.
61 × 14 = 854
The product 854 is added to the numerator 5.
854 + 5 = 859
Now, we have to write the answer 859 which is obtained from the above step over the denominator.
The mixed number 61\(\frac{5}{14}\) in improper fraction as \(\frac{859}{14}\).

Question 15.
7\(\frac{2}{17}\)
Answer:
To convert the given mixed number 7\(\frac{2}{17}\) to improper fraction.
First multiply the whole number 7 by the denominator 17.
7 × 17 = 119
The product 119 is added to the numerator 2.
119 + 2 = 121
Now, we have to write the answer 121 which is obtained from the above step over the denominator.
The mixed number 7\(\frac{2}{17}\) in improper fraction as \(\frac{121}{17}\).

Question 16.
-6\(\frac{3}{22}\)
Answer:
To convert the given mixed number -6\(\frac{3}{22}\) to improper fraction.
First multiply the whole number 6 by the denominator 22.
6 × 22 = 132
The product 132 is added to the numerator 3.
132 + 3 = 135
Now, we have to write the answer 135 which is obtained from the above step over the denominator.
The mixed number -6\(\frac{3}{22}\) in improper fraction as –\(\frac{135}{22}\).

Question 17.
23\(\frac{2}{3}\)
Answer:
To convert the given mixed number 23\(\frac{2}{3}\) to improper fraction.
First multiply the whole number 23 by the denominator 3.
23 × 3 = 69
The product 69 is added to the numerator 2.
69 + 2 = 71
Now, we have to write the answer 71 which is obtained from the above step over the denominator.
The mixed number 23\(\frac{2}{3}\) in improper fraction as \(\frac{71}{3}\).

Question 18.
15\(\frac{4}{7}\)
Answer:
To convert the given mixed number 15\(\frac{4}{7}\) to improper fraction.
First multiply the whole number 15 by the denominator 7.
15 × 7 = 105
The product 105 is added to the numerator 4.
105 + 4= 109
Now, we have to write the answer 109 which is obtained from the above step over the denominator.
The mixed number 15\(\frac{4}{7}\) in improper fraction as \(\frac{109}{7}\).

Question 19.
-13\(\frac{1}{13}\)
Answer:
To convert the given mixed number -13\(\frac{1}{13}\) to improper fraction.
First multiply the whole number 13 by the denominator 13.
13 × 13 = 169
The product 169 is added to the numerator 1.
169 + 1 = 170
Now, we have to write the answer 170 which is obtained from the above step over the denominator.
The mixed number -13\(\frac{1}{13}\) in improper fraction as –\(\frac{170}{13}\).

Question 20.
4\(\frac{4}{44}\)
Answer:
To convert the given mixed number 4\(\frac{4}{44}\) to improper fraction.
First multiply the whole number 4 by the denominator 44.
4 × 44 = 176
The product 176 is added to the numerator 4.
176 + 4 = 180
Now, we have to write the answer 180 which is obtained from the above step over the denominator.
The mixed number 4\(\frac{4}{44}\) in improper fraction as \(\frac{180}{44}\).