Go Math Answer Key

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 23.4 Circles will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 23.4 Circles

Exercises

IDENTIFY

Question 1.
What is the radius of the circle, if the diameter is 11 cm?

Answer:
The diameter is a straight line that passes through the center of the circle. The radius is half of the diameter.
PG = 11 cm = d
d = 2r
r = d/2
d = 11/2 = 5.5 cm
So, the radius of the circle is 5.5 cm

Question 2.
Identify the chord in the figure below.

Answer:
A chord of a circle is a straight line segment whose endpoints both lie on a circular arc.
In the above figure, AB is the chord of the circle whereas OC is the radius.

Question 3.
Identify the 2 radii below.

Answer:
The radius is half of the diameter.
The radius is the distance from the origin.
OA and OB is the radii of the given circle.

Question 4.
What are the 5 chords formed by inscribing the pentagon inside of the circle?

Answer:
A chord of a circle is a straight line segment whose endpoints both lie on a circular arc.
AB, BC, CD, DE, and AE are the 5 chords formed by inscribing the pentagon inside of the circle

Question 5.
Describe the two line segments from the connected points on the circle.

Answer:
AB and CD are the two line segments from the connection points on the circle.

Question 6.
Identify the diameter.

Answer:
The diameter is a straight line that passes through the center of the circle.
CB is the diameter of the circle.

CALCULATE

Question 1.
Calculate the circumference of the circle below. Use 3.14 for π.

Answer:
The circumference of a circle is the perimeter of the circle.
r = 15 in.
We know that the formula for the circumference of the circle is 2πr
C = 2πr
C = 2 × 3.14 × 15
C  = 94.24 in.

Question 2.
Calculate the area of the circle below. Use 3.14 for π.

Answer:
The area of a circle is π multiplied by the square of the radius.
A = πr²
A = 3.14 × 5 × 5 = 78.5 sq. cm
So, the area of the circle is 78.5 sq. cm

Question 3.
Calculate the area and circumference of the circle below. Use 3.14 for π.

Answer:
The area of a circle is π multiplied by the square of the radius.
A = πr²
r = 3 ft
A = 3.14 × 3 × 3 = 28.27 sq. ft
We know that the formula for the circumference of the circle is 2πr
C = 2πr
C = 2 × 3.14 × 3 = 18.85 ft

Question 4.
Calculate the area and circumference of the circle below. Use 3.14 for π.

Answer:
The area of a circle is π multiplied by the square of the radius.
A = πr²
d = 3 yd
r = 1.5
A = 3.14 × 1.5 × 1.5 = 7.07 sq. yd
We know that the formula for the circumference of the circle is 2πr
C = 2πr
C = 2 × 3.14 × 1.5 = 9.42 yards

Question 5.
Calculate the area and circumference of the circle below. Use 3.14 for π.

Answer:
The area of a circle is π multiplied by the square of the radius.
A = πr²
r = 9 in
A = 3.14 × 9 × 9 = 254.47 sq. in
We know that the formula for the circumference of the circle is 2πr
C = 2πr
C = 2 × 3.14 × 9 = 56.55 in.

Question 6.
Name the two chords that have been drawn in the figure below.

Answer:
AB and PQ are the two chords that have been drawn in the figure above.

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 23.3 Polygons will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 23.3 Polygons

Exercises

IDENTIFY

Determine if the figure is a pentagon, a hexagon, a heptagon, or an octagon.

Question 1.

Answer: Hexagon
A hexagon is a polygon with six sides and six angles.

Question 2.

Answer: Pentagon
A pentagon is a polygon with five sides and five angles.

Question 3.

Answer: Heptagon
A polygon with seven sides and seven angles is called a heptagon.

Question 4.

Answer: Octagon
A polygon with eight sides and eight angles is called an Octagon.

Question 5.

Answer: Hexagon
A hexagon is a polygon with six sides and six angles.

Question 6.

Answer: Pentagon
A pentagon is a polygon with five sides and five angles.

Question 7.

Answer: Octagon
A polygon with eight sides and eight angles is called an Octagon.

Question 8.

Answer: Hexagon
A hexagon is a polygon with six sides and six angles.

Question 9.
Are these two figures congruent?

Answer: Yes
Explanation:
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
So, the above two figures are congruent.

Question 10.
Are these two figures congruent?

Answer: No
Explanation:
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
So, the above two figures are not congruent.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 3.5 Adding or Subtracting Mixed Numbers with Unlike Denominators to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 3.5 Adding or Subtracting Mixed Numbers with Unlike Denominators

Exercises Add

Question 1.
12\(\frac{1}{2}\) + 3\(\frac{3}{4}\)
Answer:
\(\frac{65}{4}\) or 16\(\frac{1}{4}\),

Explanation:
Given to add 12\(\frac{1}{2}\) + 3\(\frac{3}{4}\) as
both are in mixed fractions we convert into fractions as
12\(\frac{1}{2}\) = \(\frac{12 X 2 + 1}{2}\) = \(\frac{25}{2}\) and 3\(\frac{3}{4}\) = \(\frac{3 X 4 + 3}{4}\) = \(\frac{15}{4}\) both don’t have common denominators first we multiply \(\frac{25}{2}\) by 2 we get
\(\frac{25 X 2}{2 X 2}\) = \(\frac{50}{4}\) now we add numerators as \(\frac{50 + 15}{4}\) = \(\frac{65}{4}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{16 X 4 + 1}{4}\) = 16\(\frac{1}{4}\).

Question 2.
13\(\frac{3}{7}\) + 4\(\frac{3}{11}\)
Answer:
\(\frac{1,363}{77}\) or 17\(\frac{54}{77}\),

Explanation:
Given to add 13\(\frac{3}{7}\) + 4\(\frac{3}{11}\) as
both are in mixed fractions we convert into fractions as
13\(\frac{3}{7}\) = \(\frac{13 X 7 + 3}{7}\) = \(\frac{94}{7}\) and 4\(\frac{3}{11}\) = \(\frac{4 X 11 + 3}{11}\) = \(\frac{47}{11}\) both don’t have common denominators first we multiply \(\frac{94}{7}\) by 11 we get
\(\frac{94 X 11}{7 X 11}\) = \(\frac{1,034}{77}\) and
\(\frac{47}{11}\) by 7 we get
\(\frac{47 X 7}{11 X 7}\) = \(\frac{329}{77}\)
now we add numerators as \(\frac{1,034 + 329}{77}\) = \(\frac{1,363}{77}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{17 X 77 + 54}{77}\) = 17\(\frac{54}{77}\).

Question 3.
5\(\frac{2}{7}\) + 3\(\frac{3}{8}\)
Answer:
\(\frac{485}{56}\) or 8\(\frac{37}{56}\),

Explanation:
Given to add 5\(\frac{2}{7}\) + 3\(\frac{3}{8}\) as
both are in mixed fractions we convert into fractions as
5\(\frac{2}{7}\) = \(\frac{5 X 7 + 2}{7}\) = \(\frac{37}{7}\) and 3\(\frac{3}{8}\) = \(\frac{3 X 8 + 3}{8}\) = \(\frac{27}{8}\) both don’t have common denominators first we multiply \(\frac{37}{7}\) by 8 we get
\(\frac{37 X 8}{7 X 8}\) = \(\frac{296}{56}\) and
\(\frac{27}{8}\) by 7 we get
\(\frac{27 X 7}{8 X 7}\) = \(\frac{189}{56}\)
now we add numerators as \(\frac{296 + 189}{56}\) = \(\frac{485}{56}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{8 X 56 + 37}{56}\) = 8\(\frac{37}{56}\).

Question 4.
3\(\frac{1}{6}\) + 7\(\frac{1}{4}\)
Answer:
\(\frac{125}{12}\) or 10\(\frac{5}{12}\),

Explanation:
Given to add 3\(\frac{1}{6}\) + 7\(\frac{1}{4}\) as
both are in mixed fractions we convert into fractions as
3\(\frac{1}{6}\) = \(\frac{3 X 6 + 1}{6}\) = \(\frac{19}{6}\) and 7\(\frac{1}{4}\) = \(\frac{7 X 4 + 1}{4}\) = \(\frac{29}{4}\) both don’t have common denominators first we multiply \(\frac{19}{6}\) by 4 we get
\(\frac{19 X 4}{6 X 4}\) = \(\frac{76}{24}\) and
\(\frac{29}{4}\) by 6 we get
\(\frac{29 X 6}{4 X 6}\) = \(\frac{174}{24}\)
now we add numerators as \(\frac{76 + 174}{24}\) = \(\frac{250}{24}\) both goes in 2 which is \(\frac{125}{12}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{10 X 12 + 5}{12}\) = 10\(\frac{5}{12}\).

Question 5.
4\(\frac{3}{11}\) + 3\(\frac{1}{3}\)
Answer:
\(\frac{251}{33}\) or 7\(\frac{20}{33}\),

Explanation:
Given to add 4\(\frac{3}{11}\) + 3\(\frac{1}{3}\) as
both are in mixed fractions we convert into fractions as
4\(\frac{3}{11}\) = \(\frac{4 X 11 + 3}{11}\) = \(\frac{47}{11}\) and 3\(\frac{1}{3}\) = \(\frac{3 X 3 + 1}{3}\) = \(\frac{10}{3}\) both don’t have common denominators first we multiply \(\frac{47}{11}\) by 3 we get
\(\frac{47 X 3}{11 X 3}\) = \(\frac{141}{33}\) and
\(\frac{10}{3}\) by 11 we get
\(\frac{10 X 11}{3 X 11}\) = \(\frac{110}{33}\)
now we add numerators as \(\frac{141 + 110}{33}\) = \(\frac{251}{33}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{7 X 33 + 20}{33}\) = 7\(\frac{20}{33}\).

Question 6.
11\(\frac{1}{2}\) + 5\(\frac{2}{5}\)
Answer:
\(\frac{169}{10}\) or 16\(\frac{9}{10}\),

Explanation:
Given to add 11\(\frac{1}{2}\) + 5\(\frac{2}{5}\) as
both are in mixed fractions we convert into fractions as
11\(\frac{1}{2}\) = \(\frac{11 X 2 + 1}{10}\) = \(\frac{23}{2}\) and 5\(\frac{2}{5}\) = \(\frac{5 X 5 + 2}{5}\) = \(\frac{27}{5}\) both don’t have common denominators first we multiply \(\frac{23}{2}\) by 5 we get
\(\frac{23 X 5}{2 X 5}\) = \(\frac{115}{10}\) and
\(\frac{27}{5}\) by 2 we get
\(\frac{27 X 2}{5 X 2}\) = \(\frac{54}{10}\)
now we add numerators as \(\frac{115 + 54}{10}\) = \(\frac{169}{10}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{16 X 10 + 9}{10}\) = 16\(\frac{9}{10}\).

Question 7.
4\(\frac{7}{9}\) + 5\(\frac{2}{7}\)
Answer:
\(\frac{634}{63}\) or 10\(\frac{4}{63}\),

Explanation:
Given to add 4\(\frac{7}{9}\) + 5\(\frac{2}{7}\) as
both are in mixed fractions we convert into fractions as
4\(\frac{7}{9}\) = \(\frac{4 X 9 + 7}{9}\) = \(\frac{43}{9}\) and 5\(\frac{2}{7}\) = \(\frac{5 X 7 + 2}{7}\) = \(\frac{37}{7}\) both don’t have common denominators first we multiply \(\frac{43}{9}\) by 7 we get
\(\frac{43 X 7}{9 X 7}\) = \(\frac{301}{63}\) and
\(\frac{37}{7}\) by 9 we get
\(\frac{37 X 9}{7 X 9}\) = \(\frac{333}{63}\)
now we add numerators as \(\frac{301 + 333}{63}\) = \(\frac{634}{63}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{10 X 63 + 4}{63}\) = 10\(\frac{4}{63}\).

Question 8.
13\(\frac{3}{5}\) + 15\(\frac{7}{11}\)
Answer:
\(\frac{1,608}{55}\) or 29\(\frac{13}{55}\),

Explanation:
Given to add 13\(\frac{3}{5}\) + 15\(\frac{7}{11}\) as
both are in mixed fractions we convert into fractions as
13\(\frac{3}{5}\) = \(\frac{13 X 5 + 3}{5}\) = \(\frac{68}{5}\) and 15\(\frac{7}{11}\) = \(\frac{15 X 11 + 7}{11}\) = \(\frac{172}{11}\) both don’t have common denominators first we multiply \(\frac{68}{5}\) by 11 we get
\(\frac{68 X 11}{5 X 11}\) = \(\frac{748}{55}\) and
\(\frac{172}{11}\) by 5 we get
\(\frac{172 X 5}{11 X 5}\) = \(\frac{860}{55}\)
now we add numerators as \(\frac{748 + 860}{55}\) = \(\frac{1,608}{55}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{29 X 55 + 13}{55}\) = 29\(\frac{13}{55}\).

Question 9.
22\(\frac{5}{6}\) + 27\(\frac{5}{13}\)
Answer:
\(\frac{3,917}{78}\) or 50\(\frac{17}{78}\),

Explanation:
Given to add 22\(\frac{5}{6}\) + 27\(\frac{5}{13}\) as
both are in mixed fractions we convert into fractions as
22\(\frac{5}{6}\) = \(\frac{22 X 6 + 5}{6}\) = \(\frac{137}{6}\) and 27\(\frac{5}{13}\) = \(\frac{27 X 13 + 5}{13}\) = \(\frac{356}{13}\) both don’t have common denominators first we multiply \(\frac{137}{6}\) by 13 we get
\(\frac{137 X 13}{6 X 13}\) = \(\frac{1,781}{78}\) and
\(\frac{356}{13}\) by 6 we get
\(\frac{356 X 6}{13 X 6}\) = \(\frac{2,136}{78}\)
now we add numerators as \(\frac{1,781 + 2,136}{78}\) = \(\frac{3,917}{78}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{50 X 78 + 17}{78}\) = 50\(\frac{17}{78}\).

Question 10.
1\(\frac{1}{11}\) + 7\(\frac{2}{5}\)
Answer:
\(\frac{467}{55}\) or 8\(\frac{27}{55}\),

Explanation:
Given to add 1\(\frac{1}{11}\) + 7\(\frac{2}{5}\) as
both are in mixed fractions we convert into fractions as
1\(\frac{1}{11}\) = \(\frac{1 X 11 + 1}{11}\) = \(\frac{12}{11}\) and 7\(\frac{2}{5}\) = \(\frac{7 X 5 + 2}{5}\) = \(\frac{37}{5}\) both don’t have common denominators first we multiply \(\frac{12}{11}\) by 5 we get
\(\frac{12 X 5}{11 X 5}\) = \(\frac{60}{55}\) and
\(\frac{37}{5}\) by 11 we get
\(\frac{37 X 11}{5 X 11}\) = \(\frac{407}{55}\)
now we add numerators as \(\frac{60 + 407}{55}\) = \(\frac{467}{55}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{8 X 55 + 27}{55}\) = 8\(\frac{27}{55}\).

Question 11.
44\(\frac{1}{2}\) + 14\(\frac{2}{9}\)
Answer:
\(\frac{1,053}{18}\) or \(\frac{117}{2}\) or
58\(\frac{1}{2}\),

Explanation:
Given to add 44\(\frac{1}{2}\) + 14\(\frac{2}{9}\) as
both are in mixed fractions we convert into fractions as
44\(\frac{1}{2}\) = \(\frac{44 X 2 + 1}{2}\) = \(\frac{89}{2}\) and 14\(\frac{2}{9}\) = \(\frac{14 X 9 + 2}{13}\) = \(\frac{128}{9}\) both don’t have common denominators first we multiply \(\frac{89}{2}\) by 9 we get
\(\frac{89 X 9}{2 X 9}\) = \(\frac{801}{18}\) and
\(\frac{128}{9}\) by 2 we get
\(\frac{128 X 2}{9 X 2}\) = \(\frac{252}{18}\)
now we add numerators as \(\frac{801 + 252}{18}\) = \(\frac{1,053}{18}\) both goes by 3 we divide by 3 we get
\(\frac{351}{6}\) still goes by 3 we get \(\frac{117}{2}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{58 X 2 + 1}{2}\) = 58\(\frac{1}{2}\).

Question 12.
9\(\frac{5}{7}\) + 10\(\frac{1}{3}\)
Answer:
\(\frac{421}{21}\) or 20\(\frac{1}{21}\),

Explanation:
Given to add 9\(\frac{5}{7}\) + 10\(\frac{1}{3}\) as
both are in mixed fractions we convert into fractions as
9\(\frac{5}{7}\) = \(\frac{9 X 7 + 5}{7}\) = \(\frac{68}{7}\) and 10\(\frac{1}{3}\) = \(\frac{10 X 3 + 1}{3}\) = \(\frac{31}{3}\) both don’t have common denominators first we multiply \(\frac{68}{7}\) by 3 we get
\(\frac{68 X 3}{7 X 3}\) = \(\frac{204}{21}\) and
\(\frac{31}{3}\) by 7 we get
\(\frac{31 X 7}{3 X 7}\) = \(\frac{217}{21}\)
now we add numerators as \(\frac{204 + 217}{21}\) = \(\frac{421}{21}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{20 X 21 + 1}{21}\) = 20\(\frac{1}{21}\).

Question 13.
4\(\frac{3}{7}\) + 4\(\frac{4}{9}\)
Answer:
\(\frac{559}{63}\) or 8\(\frac{55}{63}\),

Explanation:
Given to add 4\(\frac{3}{7}\) + 4\(\frac{4}{9}\) as
both are in mixed fractions we convert into fractions as
4\(\frac{3}{7}\) = \(\frac{4 X 7 + 3}{7}\) = \(\frac{31}{7}\) and 4\(\frac{4}{9}\) = \(\frac{4 X 9 + 4}{9}\) = \(\frac{40}{9}\) both don’t have common denominators first we multiply \(\frac{31}{7}\) by 9 we get
\(\frac{31 X 9}{7 X 9}\) = \(\frac{279}{63}\) and
\(\frac{40}{9}\) by 7 we get
\(\frac{40 X 7}{9 X 7}\) = \(\frac{280}{63}\)
now we add numerators as \(\frac{279 + 280}{63}\) = \(\frac{559}{63}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{8 X 63 + 55}{63}\) = 8\(\frac{55}{63}\).

Question 14.
5\(\frac{5}{8}\) + 3\(\frac{3}{7}\)
Answer:
\(\frac{507}{56}\) or 9\(\frac{3}{56}\),

Explanation:
Given to add 5\(\frac{5}{8}\) + 3\(\frac{3}{7}\) as
both are in mixed fractions we convert into fractions as
5\(\frac{5}{8}\) = \(\frac{5 X 8 + 5}{8}\) = \(\frac{45}{8}\) and 3\(\frac{3}{7}\) = \(\frac{3 X 7 + 3}{7}\) = \(\frac{24}{7}\) both don’t have common denominators first we multiply \(\frac{45}{8}\) by 7 we get
\(\frac{45 X 7}{8 X 7}\) = \(\frac{315}{56}\) and
\(\frac{24}{7}\) by 8 we get
\(\frac{24 X 8}{7 X 8}\) = \(\frac{192}{56}\)
now we add numerators as \(\frac{315 + 192}{56}\) = \(\frac{507}{56}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{9 X 56 + 3}{56}\) = 9\(\frac{3}{56}\).

Question 15.
46\(\frac{4}{7}\) + 44\(\frac{1}{2}\)
Answer:
\(\frac{1,275}{14}\) or 91\(\frac{1}{14}\),

Explanation:
Given to add 46\(\frac{4}{7}\) + 44\(\frac{1}{2}\) as
both are in mixed fractions we convert into fractions as
46\(\frac{4}{7}\) = \(\frac{46 X 7 + 4}{7}\) = \(\frac{326}{7}\) and 44\(\frac{1}{2}\) = \(\frac{44 X 2 + 1}{2}\) = \(\frac{89}{2}\) both don’t have common denominators first we multiply \(\frac{326}{7}\) by 2 we get
\(\frac{326 X 2}{7 X 2}\) = \(\frac{652}{14}\) and
\(\frac{89}{2}\) by 7 we get
\(\frac{89 X 7}{2 X 7}\) = \(\frac{623}{14}\)
now we add numerators as \(\frac{652 + 623}{14}\) = \(\frac{1,275}{14}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{91 X 14 + 1}{14}\) = 91\(\frac{1}{14}\).

Question 16.
4\(\frac{5}{8}\) + 3\(\frac{7}{9}\)
Answer:
\(\frac{605}{72}\) or 8\(\frac{29}{72}\),

Explanation:
Given to add 4\(\frac{5}{8}\) + 3\(\frac{7}{9}\) as
both are in mixed fractions we convert into fractions as
4\(\frac{5}{8}\) = \(\frac{4 X 8 + 5}{8}\) = \(\frac{37}{8}\) and 3\(\frac{7}{9}\) = \(\frac{3 X 9 + 7}{9}\) = \(\frac{34}{9}\) both don’t have common denominators first we multiply \(\frac{37}{8}\) by 9 we get
\(\frac{37 X 9}{8 X 9}\) = \(\frac{333}{72}\) and
\(\frac{34}{9}\) by 8 we get
\(\frac{34 X 8}{9 X 8}\) = \(\frac{272}{72}\)
now we add numerators as \(\frac{333 + 272}{72}\) = \(\frac{605}{72}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{8 X 72 + 29}{72}\) = 8\(\frac{29}{72}\).

Exercises Subtract

Question 1.
11\(\frac{5}{9}\) – 4\(\frac{9}{13}\)
Answer:
\(\frac{803}{117}\) or 6\(\frac{101}{13}\),

Explanation:
Given to subtract 11\(\frac{5}{9}\) – 4\(\frac{9}{13}\) as
both are in mixed fractions we convert into fractions as
11\(\frac{5}{9}\) = \(\frac{11 X 9 + 5}{9}\) = \(\frac{104}{9}\) and 4\(\frac{9}{13}\) = \(\frac{4 X 13 + 9}{13}\) = \(\frac{61}{13}\) both don’t have common denominators first we multiply \(\frac{104}{9}\) by 13 we get
\(\frac{104 X 13}{9 X 13}\) = \(\frac{1,352}{117}\) and
\(\frac{61}{13}\) by 9 we get
\(\frac{61 X 9}{13 X 9}\) = \(\frac{549}{117}\)
now we subtract numerators as \(\frac{1,352 – 549}{117}\) = \(\frac{803}{117}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{6 X 117 + 101}{117}\) = 6\(\frac{101}{117}\).

Question 2.
13\(\frac{1}{6}\) – 10\(\frac{2}{15}\)
Answer:
\(\frac{91}{30}\) or 3\(\frac{1}{30}\),

Explanation:
Given to subtract 13\(\frac{1}{6}\) – 10\(\frac{2}{15}\) as
both are in mixed fractions we convert into fractions as
13\(\frac{1}{6}\) = \(\frac{13 X 6 + 1}{6}\) = \(\frac{79}{6}\) and 10\(\frac{2}{15}\) = \(\frac{10 X 15 + 2}{15}\) = \(\frac{152}{15}\) both don’t have common denominators first we multiply \(\frac{79}{6}\) by 15 we get
\(\frac{79 X 15}{6 X 15}\) = \(\frac{1,185}{90}\) and
\(\frac{152}{15}\) by 6 we get
\(\frac{152 X 6}{15 X 6}\) = \(\frac{912}{90}\)
now we subtract numerators as \(\frac{1,185 – 912}{90}\) = \(\frac{273}{90}\) both goes by 3 we get \(\frac{91}{30}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{3 X 30 + 1}{30}\) = 3\(\frac{1}{30}\).

Question 3.
15\(\frac{2}{3}\) – 14\(\frac{1}{6}\)
Answer:
\(\frac{3}{2}\) or 1\(\frac{1}{2}\),

Explanation:
Given to subtract 15\(\frac{2}{3}\) – 14\(\frac{1}{6}\) as
both are in mixed fractions we convert into fractions as
15\(\frac{2}{3}\) = \(\frac{15 X 3 + 2}{3}\) = \(\frac{47}{3}\) and 14\(\frac{1}{6}\) = \(\frac{14 X 6 + 1}{6}\) = \(\frac{85}{6}\) both don’t have common denominators first we multiply \(\frac{47}{3}\) by 2 we get
\(\frac{47 X 2}{3 X 2}\) = \(\frac{94}{6}\)
now we subtract numerators as \(\frac{94 – 85}{6}\) = \(\frac{9}{6}\) both goes by 3 we get \(\frac{3}{2}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{1 X 2 + 1}{2}\) = 1\(\frac{1}{2}\).

Question 4.
20\(\frac{3}{4}\) – 11\(\frac{4}{9}\)
Answer:
\(\frac{335}{36}\) or 9\(\frac{11}{36}\),

Explanation:
Given to subtract 20\(\frac{3}{4}\) – 11\(\frac{4}{9}\) as
both are in mixed fractions we convert into fractions as
20\(\frac{3}{4}\) = \(\frac{20 X 4 + 3}{4}\) = \(\frac{83}{4}\) and 11\(\frac{4}{9}\) = \(\frac{11 X 9 + 4}{9}\) = \(\frac{103}{9}\) both don’t have common denominators first we multiply \(\frac{83}{4}\) by 9 we get
\(\frac{83 X 9}{4 X 9}\) = \(\frac{747}{36}\) and
\(\frac{103}{9}\) by 4 we get \(\frac{103 X 4}{9 X 4}\)=
\(\frac{412}{36}\) now we subtract numerators as \(\frac{747 – 412}{36}\) = \(\frac{335}{36}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{9 X 36 + 11}{36}\) = 9\(\frac{11}{36}\).

Question 5.
13\(\frac{5}{6}\) – 3\(\frac{5}{7}\)
Answer:
\(\frac{425}{42}\) or 10\(\frac{5}{42}\),

Explanation:
Given to subtract 13\(\frac{5}{6}\) – 3\(\frac{5}{7}\) as
both are in mixed fractions we convert into fractions as
13\(\frac{5}{6}\) = \(\frac{13 X 6 + 5}{6}\) = \(\frac{83}{6}\) and 3\(\frac{5}{7}\) = \(\frac{3 X 7 + 5}{7}\) = \(\frac{26}{7}\) both don’t have common denominators first we multiply \(\frac{83}{6}\) by 7 we get
\(\frac{83 X 7}{6 X 7}\) = \(\frac{581}{42}\) and
\(\frac{26}{7}\) by 6 we get \(\frac{26 X 6}{7 X 6}\)=
\(\frac{156}{42}\) now we subtract numerators as \(\frac{581 – 156}{42}\) = \(\frac{425}{42}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{10 X 42 + 5}{42}\) = 10\(\frac{5}{42}\).

Question 6.
23\(\frac{4}{5}\) – 19\(\frac{5}{11}\)
Answer:
\(\frac{239}{55}\) or 4\(\frac{19}{55}\),

Explanation:
Given to subtract 23\(\frac{4}{5}\) – 19\(\frac{5}{11}\) as
both are in mixed fractions we convert into fractions as
23\(\frac{4}{5}\) = \(\frac{23 X 5 + 4}{5}\) = \(\frac{119}{5}\) and 19\(\frac{5}{11}\) = \(\frac{19 X 11 + 5}{11}\) = \(\frac{214}{11}\) both don’t have common denominators first we multiply \(\frac{119}{5}\) by 11 we get
\(\frac{119 X 11}{5 X 11}\) = \(\frac{1,309}{55}\) and
\(\frac{214}{11}\) by 5 we get \(\frac{214 X 5}{11 X 5}\)=
\(\frac{1,070}{55}\) now we subtract numerators as \(\frac{1,309 – 1,070}{55}\) = \(\frac{239}{55}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{4 X 55 + 19}{55}\) = 4\(\frac{19}{55}\).

Question 7.
13\(\frac{4}{11}\) – 3\(\frac{1}{2}\)
Answer:
\(\frac{217}{22}\) or 9\(\frac{19}{22}\),

Explanation:
Given to subtract 13\(\frac{4}{11}\) – 3\(\frac{1}{2}\) as
both are in mixed fractions we convert into fractions as
13\(\frac{4}{11}\) = \(\frac{13 X 11 + 4}{11}\) = \(\frac{147}{11}\) and 3\(\frac{1}{2}\) = \(\frac{3 X 2 + 1}{2}\) = \(\frac{7}{2}\) both don’t have common denominators first we multiply \(\frac{147}{11}\) by 2 we get \(\frac{147 X 2}{11 X 2}\) = \(\frac{294}{22}\) and
\(\frac{7}{2}\) by 11 we get \(\frac{7 X 11}{2 X 11}\)=
\(\frac{77}{22}\) now we subtract numerators as \(\frac{294 – 77}{222}\) = \(\frac{217}{22}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{9 X 22 + 19}{22}\) = 9\(\frac{19}{22}\).

Question 8.
11\(\frac{2}{3}\) – 10\(\frac{7}{9}\)
Answer:
\(\frac{8}{9}\),

Explanation:
Given to subtract 11\(\frac{2}{3}\) – 10\(\frac{7}{9}\) as
both are in mixed fractions we convert into fractions as
11\(\frac{2}{3}\) = \(\frac{11 X 3 + 2}{3}\) = \(\frac{35}{3}\) and 10\(\frac{7}{9}\) = \(\frac{10 X 9 + 7}{9}\) = \(\frac{97}{9}\) both don’t have common denominators first we multiply \(\frac{35}{3}\) by 3 we get \(\frac{35 X 3}{3 X 3}\) = \(\frac{105}{9}\) and
\(\frac{97}{9}\), now we subtract numerators as \(\frac{105 – 97}{9}\) = \(\frac{8}{9}\).

Question 9.
77\(\frac{1}{3}\) – 41\(\frac{5}{17}\)
Answer:
\(\frac{1,838}{51}\) or 36\(\frac{2}{51}\),

Explanation:
Given to subtract 77\(\frac{1}{3}\) – 41\(\frac{5}{17}\) as
both are in mixed fractions we convert into fractions as
77\(\frac{1}{3}\) = \(\frac{77 X 3 + 1}{3}\) = \(\frac{232}{3}\) and 41\(\frac{5}{17}\) = \(\frac{41 X 17 + 5}{17}\) = \(\frac{702}{17}\) both don’t have common denominators first we multiply \(\frac{232}{3}\) by 17 we get
\(\frac{232 X 17}{3 X 17}\) = \(\frac{3,944}{51}\) and
\(\frac{702}{17}\) by 3 we get \(\frac{702 X 3}{17 X 3}\)=
\(\frac{2,106}{51}\) now we subtract numerators as \(\frac{3,944 – 2,106}{51}\) = \(\frac{1,838}{51}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{36 X 51 + 2}{51}\) = 36\(\frac{2}{51}\).

Question 10.
9\(\frac{5}{7}\) – 3\(\frac{3}{14}\)
Answer:
\(\frac{91}{14}\) or 6\(\frac{7}{14}\),

Explanation:
Given to subtract 9\(\frac{5}{7}\) – 3\(\frac{3}{14}\) as
both are in mixed fractions we convert into fractions as
9\(\frac{5}{7}\) = \(\frac{9 X 7 + 5}{7}\) = \(\frac{68}{7}\) and 3\(\frac{3}{14}\) = \(\frac{3 X 14 + 3}{14}\) = \(\frac{45}{14}\) both don’t have common denominators first we multiply \(\frac{68}{7}\) by 2 we get \(\frac{68 X 2}{7 X 2}\) = \(\frac{136}{14}\) now we subtract numerators as \(\frac{136 – 45}{14}\) = \(\frac{91}{14}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{6 X 14 + 7}{14}\) = 6\(\frac{7}{14}\).

Question 11.
31\(\frac{7}{8}\) – 12\(\frac{2}{5}\)
Answer:
\(\frac{779}{40}\) or 19\(\frac{19}{40}\),

Explanation:
Given to subtract 31\(\frac{7}{8}\) – 12\(\frac{2}{5}\) as
both are in mixed fractions we convert into fractions as
31\(\frac{7}{8}\) = \(\frac{31 X 8 + 7}{8}\) = \(\frac{255}{8}\) and 12\(\frac{2}{5}\) = \(\frac{12 X 5 + 2}{5}\) = \(\frac{62}{5}\) both don’t have common denominators first we multiply \(\frac{255}{8}\) by 5 we get \(\frac{255 X 5}{8 X 5}\) = \(\frac{1,275}{40}\) and \(\frac{62}{5}\) by 8 we get \(\frac{62 X 8}{5 X 8}\)= \(\frac{496}{40}\) now we subtract numerators as \(\frac{1,275 – 496}{40}\) = \(\frac{779}{40}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{19 X 40 + 19}{40}\) = 19\(\frac{19}{40}\).

Question 12.
45\(\frac{1}{3}\) – 32\(\frac{3}{7}\)
Answer:
\(\frac{271}{21}\) or 12\(\frac{19}{21}\),

Explanation:
Given to subtract 45\(\frac{1}{3}\) – 32\(\frac{3}{7}\) as
both are in mixed fractions we convert into fractions as
\(\frac{45 X  3 + 1}{3}\) = \(\frac{136}{3}\) and 32\(\frac{3}{7}\) = \(\frac{32 X 7 + 3}{7}\) = \(\frac{227}{7}\) both don’t have common denominators first we multiply \(\frac{136}{3}\) by 7 we get \(\frac{136 X 7}{3 X 7}\) = \(\frac{952}{21}\) and \(\frac{227}{7}\) by 3 we get \(\frac{227 X 3}{7 X 3}\)= \(\frac{681}{21}\) now we subtract numerators as \(\frac{952 – 681}{21}\) = \(\frac{271}{21}\) as numerator is greater than denominator we write in mixed fraction as \(\frac{12 X  21 + 19}{21}\) = 12\(\frac{19}{21}\).

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.

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

Exercises Add

Question 1.
\(\frac{3}{4}\) + \(\frac{3}{4}\)
Answer:
\(\frac{6}{4}\) 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.
\(\frac{1}{5}\) + \(\frac{4}{5}\)
Answer:
\(\frac{5}{5}\) 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.
\(\frac{5}{8}\) + \(\frac{5}{8}\)
Answer:
\(\frac{10}{8}\) 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.
\(\frac{7}{9}\) + \(\frac{4}{9}\)
Answer:
\(\frac{11}{9}\) 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.
\(\frac{4}{11}\) + \(\frac{3}{11}\)
Answer:
\(\frac{7}{11}\),

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.
\(\frac{15}{17}\) + \(\frac{5}{17}\)
Answer:
\(\frac{20}{17}\) 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.
\(\frac{7}{9}\) + \(\frac{14}{9}\)
Answer:
\(\frac{21}{9}\) 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.
\(\frac{2}{3}\) + \(\frac{5}{3}\)
Answer:
\(\frac{7}{3}\) 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.
\(\frac{6}{23}\) + \(\frac{14}{23}\)
Answer:
\(\frac{20}{23}\),

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.
\(\frac{13}{37}\) + \(\frac{24}{37}\)
Answer:
\(\frac{37}{37}\) 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.
\(\frac{1}{4}\) + \(\frac{7}{4}\)
Answer:
\(\frac{8}{4}\) 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.
\(\frac{3}{11}\) + \(\frac{7}{11}\)
Answer:
\(\frac{10}{11}\),

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.
\(\frac{13}{27}\) + \(\frac{11}{27}\)
Answer:
\(\frac{24}{27}\) 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.
\(\frac{11}{14}\) + \(\frac{13}{14}\)
Answer:
\(\frac{24}{14}\) 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.
\(\frac{13}{24}\) + \(\frac{16}{24}\)
Answer:
\(\frac{29}{24}\) 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.
\(\frac{13}{37}\) + \(\frac{11}{37}\)
Answer:
\(\frac{24}{37}\),

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.
Answer:
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?
Answer:
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.
\(\frac{3}{4}\) – \(\frac{1}{4}\)
Answer:
\(\frac{2}{4}\) 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.
\(\frac{3}{3}\) – \(\frac{2}{3}\)
Answer:
\(\frac{1}{3}\),

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.
\(\frac{8}{9}\) – \(\frac{5}{9}\)
Answer:
\(\frac{3}{9}\) 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.
\(\frac{7}{8}\) – \(\frac{1}{8}\)
Answer:
\(\frac{6}{8}\) 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.
\(\frac{5}{7}\) – \(\frac{3}{7}\)
Answer:
\(\frac{2}{7}\),

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.
\(\frac{1}{2}\) – \(\frac{1}{2}\)
Answer:
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.
\(\frac{2}{3}\) – \(\frac{1}{3}\)
Answer:
\(\frac{1}{3}\),

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.
\(\frac{5}{3}\) – \(\frac{2}{3}\)
Answer:
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.
\(\frac{7}{5}\) – \(\frac{4}{5}\)
Answer:
\(\frac{3}{5}\),

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.
\(\frac{4}{7}\) – \(\frac{1}{7}\)
Answer:
\(\frac{3}{7}\),

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.
\(\frac{9}{7}\) – \(\frac{6}{7}\)
Answer:
\(\frac{3}{7}\),

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.
\(\frac{11}{9}\) – \(\frac{2}{9}\)
Answer:
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.
\(\frac{6}{5}\) – \(\frac{3}{5}\)
Answer:
\(\frac{3}{5}\),

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.
\(\frac{12}{11}\) – \(\frac{9}{11}\)
Answer:
\(\frac{3}{11}\),

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.
\(\frac{31}{35}\) – \(\frac{1}{35}\)
Answer:
\(\frac{30}{35}\) 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.
\(\frac{21}{22}\) – \(\frac{17}{22}\)
Answer:
\(\frac{4}{22}\) 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?
Answer:
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?
Answer:
No, Ellen will not have enough flour,

Explanation:
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.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 5.3 Dividing Fractions by Fractions to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 5.3 Dividing Fractions by Fractions

Exercises Divide

Question 1.
\(\frac{6}{7}\) ÷ \(\frac{3}{8}\)
Answer:
\(\frac{16}{7}\),

Explanation:
\(\frac{6}{7}\) ÷ \(\frac{3}{8}\) = \(\frac{6}{7}\) ÷ \(\frac{3}{8}\) = \(\frac{6}{7}\) X \(\frac{8}{3}\) =\(\frac{6 X 8}{7 X 3}\) both goes by 3, So \(\frac{2 X 3 X 8}{7 X 3}\) = \(\frac{2 X 8}{7}\) = \(\frac{16}{7}\).

Question 2.
\(\frac{4}{14}\) ÷ \(\frac{2}{16}\)
Answer:
\(\frac{16}{7}\),

Explanation:
\(\frac{4}{14}\) ÷ \(\frac{2}{16}\) = \(\frac{4}{14}\) ÷ \(\frac{2}{16}\) = \(\frac{4}{14}\) X \(\frac{16}{2}\) = \(\frac{4 X 16}{14 X 2}\) = \(\frac{16}{7}\).

Question 3.
\(\frac{2}{9}\) ÷ \(\frac{3}{7}\)
Answer:
\(\frac{14}{27}\),

Explanation:
\(\frac{2}{9}\) ÷ \(\frac{3}{7}\) = \(\frac{2}{9}\) X \(\frac{7}{3}\) = \(\frac{2 X 7}{9 X 3}\) = \(\frac{14}{27}\).

Question 4.
\(\frac{1}{4}\) ÷ \(\frac{1}{8}\)
Answer:
2,

Explanation:
\(\frac{1}{4}\) ÷ \(\frac{1}{8}\) = \(\frac{1}{4}\) ÷ \(\frac{1}{8}\) = \(\frac{1}{4}\) X \(\frac{8}{1}\) = \(\frac{1 X 8}{4 X 1}\) = 2.

Question 5.
\(\frac{5}{13}\) ÷ \(\frac{5}{9}\)
Answer:
\(\frac{9}{13}\),

Explanation:
\(\frac{5}{13}\) ÷ \(\frac{5}{9}\) = \(\frac{5}{13}\) X \(\frac{9}{5}\) = \(\frac{5 X 9}{13 X 5}\) = \(\frac{9}{13}\).

Question 6.
\(\frac{7}{9}\) ÷ \(\frac{1}{7}\)
Answer:
\(\frac{49}{9}\) = 5\(\frac{4}{9}\),

Explanation:
\(\frac{7}{9}\) ÷ \(\frac{1}{7}\) = \(\frac{7}{9}\) X \(\frac{7}{1}\) = \(\frac{7 X 7}{1 X 9}\) = \(\frac{49}{9}\) as numerator is greater than denominator we write as \(\frac{5 X 9 + 4}{9}\).

Question 7.
\(\frac{1}{13}\) ÷ \(\frac{1}{3}\)
Answer:
\(\frac{3}{13}\),

Explanation:
\(\frac{1}{13}\) ÷ \(\frac{1}{3}\) = \(\frac{1}{13}\) X \(\frac{3}{1}\) = \(\frac{3}{13}\),

Question 8.
\(\frac{5}{17}\) ÷ \(\frac{2}{17}\)
Answer:
\(\frac{5}{2}\),

Explanation:
\(\frac{5}{17}\) ÷ \(\frac{2}{17}\) = \(\frac{5}{17}\) X \(\frac{17}{2}\) = \(\frac{5 X 17}{17 X 2}\) = \(\frac{5}{2}\).

Question 9.
\(\frac{4}{5}\) ÷ \(\frac{1}{4}\)
Answer:
\(\frac{16}{5}\),

Explanation:
\(\frac{4}{5}\) ÷ \(\frac{1}{4}\) = \(\frac{4}{5}\) X \(\frac{4}{1}\) = \(\frac{4 X 4}{5 X 1}\) = \(\frac{16}{5}\).

Question 10.
\(\frac{15}{24}\) ÷ \(\frac{5}{3}\)
Answer:
\(\frac{3}{8}\),

Explanation:
\(\frac{15}{24}\) ÷ \(\frac{5}{3}\) = \(\frac{15}{24}\) X \(\frac{3}{5}\) = \(\frac{15 X 3}{5 X 24}\) = \(\frac{3}{8}\).

Question 11.
\(\frac{6}{11}\) ÷ \(\frac{11}{7}\)
Answer:
\(\frac{42}{121}\),

Explanation:
\(\frac{6}{11}\) ÷ \(\frac{11}{7}\) = \(\frac{6}{11}\) X \(\frac{7}{11}\) = \(\frac{6 X 7}{11 X 11}\) = \(\frac{42}{121}\).

Question 12.
\(\frac{13}{17}\) ÷ \(\frac{26}{17}\)
Answer:
\(\frac{1}{2}\),

Explanation:
\(\frac{13}{17}\) ÷ \(\frac{26}{17}\) = \(\frac{13}{17}\) X \(\frac{17}{26}\) = \(\frac{13 X 17}{17 X 26}\) both goes by 13 and 17 as \(\frac{13 X 1 X 17}{17 X 13 X 2}\) = \(\frac{1}{2}\).

Question 13.
\(\frac{3}{11}\) ÷ \(\frac{22}{33}\)
Answer:
\(\frac{9}{22}\),

Explanation:
\(\frac{3}{11}\) ÷ \(\frac{22}{33}\) = \(\frac{3}{11}\) x \(\frac{33}{22}\) = \(\frac{3 X 33} X {11 X 22}\) = \(\frac{9}{22}\),

Question 14.
\(\frac{4}{7}\) ÷ \(\frac{4}{21}\)
Answer:
3,

Explanation:
\(\frac{4}{7}\) ÷ \(\frac{4}{21}\) = \(\frac{4}{7}\) ÷ \(\frac{4}{21}\) = \(\frac{4}{7}\) X \(\frac{21}{4}\) = \(\frac{3}{1}\) = 3.

Question 15.
\(\frac{9}{14}\) ÷ \(\frac{3}{7}\)
Answer:
\(\frac{3}{2}\),

Explanation:
\(\frac{9}{14}\) ÷ \(\frac{3}{7}\) = \(\frac{9}{14}\) X \(\frac{7}{3}\) = \(\frac{9 X 7}{14 X 3}\) = \(\frac{3}{2}\).

Question 16.
\(\frac{3}{5}\) ÷ \(\frac{5}{3}\)
Answer:
\(\frac{9}{25}\),

Explanation:
\(\frac{3}{5}\) ÷ \(\frac{5}{3}\) = \(\frac{3}{5}\) X \(\frac{3}{5}\) = \(\frac{3 X 3}{5 X 5}\) = \(\frac{9}{25}\).

Question 17.
A recipe calls for the use of \(\frac{1}{16}\) ounce of batter for each muffin. How many muffins can be made from \(\frac{7}{8}\) ounces of batter?
Answer:
14 muffins,

Explanation:
A recipe calls for the use of \(\frac{1}{16}\) ounce of batter for each muffin. Number of muffins can be made from \(\frac{7}{8}\) ounces of batter \(\frac{7}{8}\) ÷ \(\frac{1}{16}\) = \(\frac{7}{8}\) X \(\frac{16}{1}\) = \(\frac{7 X 16}{8}\) = 14.

Question 18.
How many miles can a go-cart travel on a full tank of gas if the gas tank holds \(\frac{15}{16}\) gallons and burns \(\frac{1}{8}\) gallons for each mile traveled?
Answer:
7\(\frac{1}{2}\),

Explanation:
A go-cart travel gas if the gas tank holds \(\frac{15}{16}\) gallons burns \(\frac{1}{8}\) gallons for each mile traveled, Total number of miles it can travel, \(\frac{15}{16}\) ÷ \(\frac{1}{8}\) = \(\frac{15}{16}\) X \(\frac{8}{1}\) = \(\frac{15 X 8}{16}\) = \(\frac{15}{2}\) = 7\(\frac{1}{2}\).

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 5.2 Dividing Whole Numbers by Fractions to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 5.2 Dividing Whole Numbers by Fractions

Exercises Divide

Question 1.
5 ÷ \(\frac{1}{10}\)
Answer:
50,

Explanation:
5 ÷ \(\frac{1}{10}\), Multiply the whole number by the reciprocal of the fraction. 5 x \(\frac{10}{1}\) = 50.

Question 2.
9 ÷ \(\frac{3}{5}\)
Answer:
15,

Explanation:
9 ÷ \(\frac{3}{5}\), Multiply the whole number by the reciprocal of the fraction.
9 x \(\frac{5}{3}\) = \(\frac{9 X 5}{3}\), \(\frac{45}{3}\) = 15.

Question 3.
14 ÷ \(\frac{7}{8}\)
Answer:
16,

Explanation:
14 ÷ \(\frac{7}{8}\), Multiply the whole number by the reciprocal of the fraction. 14 x \(\frac{8}{7}\) = \(\frac{14 X 8}{7}\),\(\frac{112}{7}\) = 16.

Question 4.
12 ÷ \(\frac{4}{9}\)
Answer:
27,

Explanation:
12 ÷ \(\frac{4}{9}\), Multiply the whole number by the reciprocal of the fraction. 12 x \(\frac{9}{4}\) = \(\frac{12 X 9}{4}\), \(\frac{108}{4}\) = 27.

Question 5.
12 ÷ \(\frac{3}{4}\)
Answer:
16,

Explanation:
12 ÷ \(\frac{3}{4}\),Multiply the whole number by the reciprocal of the fraction. 12 x \(\frac{4}{3}\) = \(\frac{12 X 4}{3}\), \(\frac{48}{3}\) = 16.

Question 6.
42 ÷ \(\frac{7}{9}\)
Answer:
54,

Explanation:
42 ÷ \(\frac{7}{9}\), Multiply the whole number by the reciprocal of the fraction. 42 x \(\frac{9}{7}\) = \(\frac{42 X 9}{7}\), \(\frac{378}{7}\) = 54.

Question 7.
45 ÷ \(\frac{5}{8}\)
Answer:
72,

Explanation:
45 ÷ \(\frac{5}{8}\), Multiply the whole number by the reciprocal of the fraction. 45 x \(\frac{8}{5}\) = \(\frac{45 X 8}{5}\), \(\frac{360}{5}\) = 72.

Question 8.
24 ÷ \(\frac{2}{7}\)
Answer:
84,

Explanation:
24 ÷ \(\frac{2}{7}\), Multiply the whole number by the reciprocal of the fraction. 24 x \(\frac{7}{2}\) = \(\frac{24 X 7}{2}\), \(\frac{168}{2}\) = 84.

Question 9.
16 ÷ \(\frac{2}{5}\)
Answer:
40,

Explanation:
16 ÷ \(\frac{2}{5}\), Multiply the whole number by the reciprocal of the fraction. 16 x \(\frac{5}{2}\) = \(\frac{16 X 5}{2}\), \(\frac{80}{2}\) = 40.

Question 10.
5 ÷ \(\frac{3}{8}\)
Answer:
13\(\frac{1}{3}\),

Explanation:
5 ÷ \(\frac{3}{8}\), Multiply the whole number by the reciprocal of the fraction.
5 x \(\frac{8}{3}\) = \(\frac{5 X 8}{3}\), latex]\frac{40}{3}[/latex] = 13\(\frac{1}{3}\).

Question 11.
16 ÷ \(\frac{4}{7}\)
Answer:
28,

Explanation:
16 ÷ \(\frac{4}{7}\), Multiply the whole number by the reciprocal of the fraction. 16 x \(\frac{7}{4}\) = \(\frac{16 X 7}{4}\), \(\frac{112}{4}\) = 28.

Question 12.
39 ÷ \(\frac{3}{11}\)
Answer:
143,

Explanation:
39 ÷ \(\frac{3}{11}\), Multiply the whole number by the reciprocal of the fraction. 39 x \(\frac{11}{3}\) = \(\frac{39 X 11}{3}\), \(\frac{429}{3}\) = 143.

Question 13.
15 ÷ \(\frac{3}{11}\)
Answer:
55,

Explanation:
15 ÷ \(\frac{3}{11}\), Multiply the whole number by the reciprocal of the fraction. 15 x \(\frac{11}{3}\) = \(\frac{15 X 11}{3}\), \(\frac{165}{3}\) = 55.

Question 14.
14 ÷ \(\frac{7}{4}\)
Answer:
8,

Explanation:
14 ÷ \(\frac{7}{4}\), Multiply the whole number by the reciprocal of the fraction. 14 x \(\frac{4}{7}\) = \(\frac{14 X 4}{7}\), \(\frac{56}{7}\) = 8.

Question 15.
27 ÷ \(\frac{3}{11}\)
Answer:
99,

Explanation:
27 ÷ \(\frac{3}{11}\), Multiply the whole number by the reciprocal of the fraction. 27 x \(\frac{11}{3}\) = \(\frac{27 X 11}{3}\), \(\frac{297}{3}\) = 99.

Question 16.
33 ÷ \(\frac{3}{8}\)
Answer:
88,

Explanation:
33 ÷ \(\frac{3}{8}\), Multiply the whole number by the reciprocal of the fraction. 33 x \(\frac{8}{3}\) = \(\frac{33 X 8}{3}\), \(\frac{264}{2}\) = 88.

Question 17.
Brandon worked with his community to provide aid packages for recent hurricane victims. Each package was to contain \(\frac{4}{15}\) pounds of sugar. How many packages could Brandon fill if he had 60 pounds of sugar to distribute?
Answer:
225 packages,

Explanation:
Brandon had 60 pounds of sugar to distribute. Each package was to contain \(\frac{4}{15}\) pounds of sugar.
60 ÷ \(\frac{4}{15}\), Multiply the whole number by the reciprocal of the fraction. 60 x \(\frac{15}{4}\) = \(\frac{60 X 15}{4}\), \(\frac{900}{4}\) = 225 packages.

Question 18.
Dahlia is planning a bike trip with her friends. Her plan is to ride for \(\frac{3}{5}\) hour and then rest for \(\frac{1}{5}\) hour. If the entire trip will take 20 hours to complete, how many rest stops will the team make during the ride?
Answer:
25 stops,

Explanation:
Dahlia plan to ride for \(\frac{3}{5}\) hour then rest for \(\frac{1}{5}\) hour. Number of hours of ride \(\frac{3}{5}\) + \(\frac{1}{5}\),
= \(\frac{4}{5}\), If the entire trip will take 20 hours to complete,
20 ÷ \(\frac{4}{5}\), Multiply the whole number by the reciprocal of the fraction. 20 X \(\frac{5}{4}\) = \(\frac{20 X 5}{4}\),
Number of rest stops will the team make during the ride \(\frac{100}{4}\) = 25 stops.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 5.1 Dividing Fractions by Whole Numbers to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 5.1 Dividing Fractions by Whole Numbers

Exercises Divide

Question 1.
\(\frac{3}{2}\) ÷ 4
Answer:
\(\frac{3}{8}\),

Explanation:
Multiply the denominator with the whole number 4, So we get \(\frac{3}{2 X 4}\) = \(\frac{3}{8}\).

Question 2.
\(\frac{6}{16}\) ÷ 4
Answer:
\(\frac{3}{32}\),

Explanation:
Multiply the denominator with the whole number 4 as \(\frac{6}{16}\) =
\(\frac{6}{16 X 4}\), Simplify both numerator and denominator with 2, So we get \(\frac{3}{32}\).

Question 3.
\(\frac{6}{27}\) ÷ 3
Answer:
\(\frac{2}{27}\),

Explanation:
Multiply the denominator with the whole number 3 as \(\frac{6}{27}\) = \(\frac{6}{27 X 3}\), Simplify both numerator and denominator with 3,
So we get \(\frac{2}{27}\).

Question 4.
\(\frac{1}{12}\) ÷ 4
Answer:
\(\frac{1}{48}\),

Explanation:
Multiply the denominator with the whole number 4 as \(\frac{1}{12}\) =
\(\frac{1}{12 X 4}\), So we get \(\frac{1}{48}\).

Question 5.
\(\frac{18}{57}\) ÷ 2
Answer:
\(\frac{3}{19}\),

Explanation:
Multiply the denominator with the whole number 2 as \(\frac{18}{57}\) =\(\frac{18}{114}\), Simplify both numerator and denominator with 6,
So we get \(\frac{3}{19}\).

Question 6.
\(\frac{14}{15}\) ÷ 7
Answer:
\(\frac{2}{15}\),

Explanation:
Multiply the denominator with the whole number 7 as \(\frac{14}{15}\) =
\(\frac{14}{105}\), Simplify both numerator and denominator with 7,
So we get \(\frac{2}{15}\).

Question 7.
\(\frac{4}{9}\) ÷ 9
Answer:
\(\frac{4}{81}\),

Explanation:
Multiply the denominator with the whole number 9 as \(\frac{4}{9}\) =
\(\frac{4}{9 X 9}\), So we get \(\frac{4}{81}\).

Question 8.
\(\frac{12}{18}\) ÷ 12
Answer:
\(\frac{1}{18}\),

Explanation:
Multiply the denominator with the whole number 12 as \(\frac{12}{18}\) =
\(\frac{12}{18 X 12}\), Simplify both numerator and denominator with 12,
So we get \(\frac{1}{18}\).

Question 9.
\(\frac{16}{22}\) ÷ 4
Answer:
\(\frac{2}{11}\),

Explanation:
Multiply the denominator with the whole number 4 as \(\frac{16}{22}\) =
\(\frac{16}{22 X 4}\) = \(\frac{16}{88}\), Simplify both numerator and denominator with 8, So we get \(\frac{2}{11}\).

Question 10.
\(\frac{15}{19}\) ÷ 3
Answer:
\(\frac{5}{19}\),

Explanation:
Multiply the denominator with the whole number 3 as \(\frac{15}{19}\) =
\(\frac{15}{57}\), Simplify both numerator and denominator with 3,
So we get \(\frac{5}{19}\).

Question 11.
\(\frac{12}{31}\) ÷ 6
Answer:
\(\frac{1}{8}\),

Explanation:
Multiply the denominator with the whole number 6 as \(\frac{12}{31}\) = \(\frac{12}{31 X 6}\) = \(\frac{12}{186}\), Simplify both numerator and denominator with 12, So we get \(\frac{1}{8}\).

Question 12.
\(\frac{55}{63}\) ÷ 20
Answer:
\(\frac{11}{252}\),

Explanation:
Multiply the denominator with the whole number 20 as \(\frac{55}{63}\),
Simplify both numerator and denominator with 5, So we get \(\frac{11}{252}\).

Question 13.
\(\frac{33}{477}\) ÷ 11
Answer:
\(\frac{1}{159}\),

Explanation:
Multiply the denominator with the whole number 11 as \(\frac{33}{477}\)
\(\frac{33}{5247}\), Simplify both numerator and denominator with 33,
So we get \(\frac{1}{159}\).

Question 14.
\(\frac{3}{14}\) ÷ 9
Answer:
\(\frac{1}{42}\),

Explanation:
Multiply the denominator with the whole number 9 as \(\frac{3}{14}\) =\(\frac{3}{126}\), Simplify both numerator and denominator with 3,
So we get \(\frac{1}{42}\).

Question 15.
\(\frac{15}{31}\) ÷ 5
Answer:
\(\frac{3}{31}\),

Explanation:
Multiply the denominator with the whole number 5 as \(\frac{5}{31}\) =
\(\frac{15}{155}\), Simplify both numerator and denominator with 5,
So we get \(\frac{3}{31}\).

Question 16.
\(\frac{16}{63}\) ÷ 4
Answer:
\(\frac{4}{63}\),

Explanation:
Multiply the denominator with the whole number 4 as \(\frac{16}{63}\) =\(\frac{16}{252}\), Simplify both numerator and denominator with 4,
So we get \(\frac{4}{63}\).

Question 17.
Julius receives \(\frac{3}{4}\) pounds of Swiss chocolate from his grandmother and wants to divide the chocolate evenly among his 8 friends. How much chocolate will each friend receive?
Answer:
\(\frac{3}{32}\) pounds,

Explanation:
Julius receives \(\frac{3}{4}\) pounds of Swiss chocolate from his grandmother,
She wants to divide the chocolate evenly among his 8 friends.
\(\frac{3}{4}\) ÷ 8 multiply the denominator with the whole number,
\(\frac{3}{4 X 8}\) = \(\frac{3}{32}\), Each friend will receive \(\frac{3}{32}\) pounds of chocolates.

Question 18.
Paola has \(\frac{18}{25}\) yard of yarn. She wants to cut the yarn into 3 equal pieces to make button loops. How long should she cut each piece?
Answer:
\(\frac{6}{25}\) yards,

Explanation:
Paola has \(\frac{18}{25}\) yard of yarn. She wants to cut the yarn into 3 equal pieces to make button loops. \(\frac{18}{25}\) ÷ 3 = \(\frac{18}{25 X 3}\) = \(\frac{18}{75}\), Simplify both numerator and denominator with 3,
So we get \(\frac{6}{25}\) yards.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 5.4 Dividing Mixed Numbers to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 5.4 Dividing Mixed Numbers

Exercises Divide

Question 1.
3\(\frac{1}{6}\) ÷ 2\(\frac{1}{3}\)
Answer:
\(\frac{19}{14}\),

Explanation:
3\(\frac{1}{6}\) ÷ 2\(\frac{1}{3}\) = \(\frac{18 + 1}{6}\) ÷ \(\frac{6 + 1}{3}\) = \(\frac{19}{6}\) ÷ \(\frac{7}{3}\) = \(\frac{19}{6}\) x \(\frac{3}{7}\) = \(\frac{19 X 3}{6 X 7}\) = \(\frac{19}{14}\).

Question 2.
4\(\frac{3}{7}\) ÷ 3\(\frac{3}{8}\)
Answer:
1\(\frac{59}{189}\),

Explanation:
4\(\frac{3}{7}\) ÷ 3\(\frac{3}{8}\) = \(\frac{28 + 3}{7}\) ÷ \(\frac{24 + 3}{8}\) = \(\frac{31}{7}\) ÷ \(\frac{27}{8}\) = \(\frac{31}{7}\) x \(\frac{8}{27}\) = \(\frac{31 X 8}{7 X 27}\) = \(\frac{248}{189}\) = 1\(\frac{59}{189}\).

Question 3.
5\(\frac{3}{7}\) ÷ 2\(\frac{2}{3}\)
Answer:
2\(\frac{1}{28}\),

Explanation:
5\(\frac{3}{7}\) ÷ 2\(\frac{2}{3}\) = \(\frac{35 + 5}{7}\) ÷ \(\frac{6 + 2}{3}\) = \(\frac{40}{7}\) ÷ \(\frac{8}{3}\) = \(\frac{40}{7}\) x \(\frac{3}{8}\) = \(\frac{40 X 3}{7 X 8}\) = \(\frac{15}{7}\).

Question 4.
5\(\frac{2}{9}\) ÷ 3\(\frac{2}{7}\)
Answer:
1\(\frac{122}{207}\),

Explanation:
5\(\frac{2}{9}\) ÷ 3\(\frac{2}{7}\) = \(\frac{45 + 2}{9}\) ÷ \(\frac{21 + 2}{7}\) = \(\frac{47}{9}\) ÷ \(\frac{23}{7}\) = \(\frac{47}{9}\) x \(\frac{7}{23}\) = \(\frac{47 X 7}{9 X 23}\)
= \(\frac{329}{207}\) =1\(\frac{122}{207}\).

Question 5.
7\(\frac{2}{5}\) ÷ 3\(\frac{3}{5}\)
Answer:
2\(\frac{1}{8}\),

Explanation:
7\(\frac{2}{5}\) ÷ 3\(\frac{3}{5}\) = \(\frac{35 + 2}{5}\) ÷ \(\frac{15 + 3}{5}\) = \(\frac{37}{5}\) ÷ \(\frac{18}{5}\) = \(\frac{37}{5}\) x \(\frac{5}{18}\) = \(\frac{37 X 5}{5 X 18}\)
= \(\frac{37}{18}\) = 2\(\frac{1}{8}\).

Question 6.
4\(\frac{1}{4}\) ÷ 2\(\frac{3}{7}\)
Answer:
1\(\frac{3}{4}\),

Explanation:
4\(\frac{1}{4}\) ÷ 2\(\frac{3}{7}\) = \(\frac{35 + 2}{5}\) ÷ \(\frac{15 + 3}{5}\) = \(\frac{37}{5}\) ÷ \(\frac{18}{5}\) = \(\frac{37}{5}\) x \(\frac{5}{18}\) = \(\frac{37 X 5}{5 X 18}\)
= \(\frac{37}{18}\) = 2\(\frac{1}{18}\).

Question 7.
3\(\frac{4}{9}\) ÷ 3\(\frac{2}{9}\)
Answer:
1\(\frac{2}{29}\),

Explanation:
3\(\frac{4}{9}\) ÷ 3\(\frac{2}{9}\) = \(\frac{27 + 4}{9}\) ÷ \(\frac{27 + 2}{9}\) = \(\frac{31}{9}\) ÷ \(\frac{29}{9}\) = \(\frac{31}{9}\) x \(\frac{9}{29}\) = \(\frac{31 X 9}{9 X 29}\) = \(\frac{31}{29}\) = 1\(\frac{2}{29}\).

Question 8.
3\(\frac{4}{11}\) ÷ 5\(\frac{1}{2}\)
Answer:
\(\frac{74}{121}\),

Explanation:
3\(\frac{4}{11}\) ÷ 5\(\frac{1}{2}\) = \(\frac{33 + 4}{11}\) ÷ \(\frac{10 + 1}{2}\) = \(\frac{37}{11}\) ÷ \(\frac{11}{2}\) = \(\frac{37}{11}\) x \(\frac{2}{11}\) = \(\frac{37 X 2}{11 X 11}\) = \(\frac{74}{121}\).

Question 9.
4\(\frac{7}{13}\) ÷ 2\(\frac{2}{3}\)
Answer:

1\(\frac{73}{104}\),

Explanation:

4\(\frac{7}{13}\) ÷ 2\(\frac{2}{3}\) = \(\frac{52 + 7}{13}\) ÷ \(\frac{6 + 2}{3}\) = \(\frac{59}{13}\) ÷ \(\frac{8}{3}\) = \(\frac{59}{13}\) x \(\frac{3}{8}\) =  \(\frac{59 X 3}{13 X 8}\)
= \(\frac{177}{104}\) = 1\(\frac{73}{104}\).

Question 10.
3\(\frac{7}{13}\) ÷ 1\(\frac{5}{8}\)
Answer:
2\(\frac{30}{169}\),

Explanation:
3\(\frac{7}{13}\) ÷ 1\(\frac{5}{8}\) = \(\frac{39 + 7}{13}\) ÷ \(\frac{8 + 5}{8}\) = \(\frac{46}{13}\) ÷ \(\frac{13}{8}\) = \(\frac{46}{13}\) x \(\frac{8}{13}\) =
\(\frac{46 X 8}{13 X 13}\) = \(\frac{368}{169}\) = 2\(\frac{30}{169}\).

Question 11.
1\(\frac{6}{7}\) ÷ 2\(\frac{2}{9}\)
Answer:
\(\frac{117}{140}\),

Explanation:
1\(\frac{6}{7}\) ÷ 2\(\frac{2}{9}\) = \(\frac{7 + 6}{7}\) ÷ \(\frac{18 + 2}{9}\) = \(\frac{13}{7}\) ÷ \(\frac{20}{9}\) = \(\frac{13}{7}\) X \(\frac{9}{20}\) = \(\frac{13 X 9}{7 X 20}\) = \(\frac{117}{140}\).

Question 12.
3\(\frac{5}{8}\) ÷ 1\(\frac{7}{8}\)
Answer:
1\(\frac{14}{15}\)

Explanation:
3\(\frac{5}{8}\) ÷ 1\(\frac{7}{8}\) = \(\frac{24 + 5}{8}\) ÷ \(\frac{8 + 7}{8}\) = \(\frac{29}{8}\) ÷ \(\frac{15}{8}\) = \(\frac{29}{8}\) x \(\frac{8}{15}\) = \(\frac{29 X 8}{8 X 15}\) = \(\frac{29}{15}\) = 1\(\frac{14}{15}\).

Question 13.
2\(\frac{4}{7}\) ÷ 4\(\frac{1}{3}\)
Answer:
\(\frac{54}{91}\),

Explanation:
2\(\frac{4}{7}\) ÷ 4\(\frac{1}{3}\) = \(\frac{14 + 4}{7}\) ÷ \(\frac{12 + 1}{3}\) = \(\frac{18}{7}\) ÷ \(\frac{13}{3}\) = \(\frac{18}{7}\) x \(\frac{3}{13}\) = \(\frac{18 X 3}{7 x 13}\) = \(\frac{54}{91}\).

Question 14.
6\(\frac{1}{2}\) ÷ 2\(\frac{1}{2}\)
Answer:
2\(\frac{3}{5}\),

Explanation:

6\(\frac{1}{2}\) ÷ 2\(\frac{1}{2}\) = \(\frac{12 + 1}{2}\) ÷ \(\frac{4 + 1}{2}\) = \(\frac{13}{2}\) ÷ \(\frac{5}{2}\) = \(\frac{13}{2}\) x \(\frac{2}{5}\) = \(\frac{13 X 2}{2 x 5}\) = \(\frac{13}{5}\) = 2\(\frac{3}{5}\).

Question 15.
7\(\frac{3}{5}\) ÷ 1\(\frac{4}{5}\)
Answer:
4\(\frac{2}{9}\),

Explanation:
7\(\frac{3}{5}\) ÷ 1\(\frac{4}{5}\) = \(\frac{35 + 3}{5}\) ÷ \(\frac{5 + 4}{5}\) = \(\frac{38}{5}\) ÷ \(\frac{9}{5}\) = \(\frac{38}{5}\) x \(\frac{5}{9}\) = \(\frac{38 X 5}{5 x 9}\) = \(\frac{38}{9}\) = 4\(\frac{2}{9}\).

Question 16.
1\(\frac{2}{9}\) ÷ 3\(\frac{1}{7}\)
Answer:
\(\frac{7}{18}\),

Explanation:
1\(\frac{2}{9}\) ÷ 3\(\frac{1}{7}\) = \(\frac{9 + 2}{9}\) ÷ \(\frac{21 + 1}{7}\) = \(\frac{11}{9}\) ÷ \(\frac{22}{7}\) = \(\frac{11}{9}\) x \(\frac{7}{22}\) =\(\frac{11 X 7}{9 x  22}\)  = \(\frac{7}{18}\).

Question 17.
Ursula ran for 1\(\frac{3}{4}\) hours. If she ran 3\(\frac{3}{4}\) miles in total, how fast did she run in miles per hour?
Answer:
2\(\frac{1}{7}\) miles/hour,

Explanation:
Speed = Distance ÷ Time, Speed = 3\(\frac{3}{4}\) ÷1\(\frac{3}{4}\) = \(\frac{12 + 3}{4}\) ÷ \(\frac{4 + 3}{4}\) = \(\frac{15}{4}\) ÷ \(\frac{7}{4}\) = \(\frac{15}{4}\) x \(\frac{4}{7}\)
= \(\frac{15 X 4}{4 x 7}\) =  \(\frac{15}{7}\) = 2\(\frac{1}{7}\).

Question 18.
Mason sorted 14\(\frac{5}{8}\) pounds of laundry into 2\(\frac{1}{2}\) loads. How many pounds were in each load?
Answer:
5\(\frac{17}{20}\) pounds,

Explanation:
14\(\frac{5}{8}\) ÷ 2\(\frac{1}{2}\) = \(\frac{112 + 5}{8}\) ÷ \(\frac{4 +1}{2}\) = \(\frac{117}{8}\) ÷ \(\frac{5}{2}\) = \(\frac{117}{8}\) x \(\frac{2}{5}\) = \(\frac{117 X 2}{8 x 5}\)
= \(\frac{117}{20}\) = 5\(\frac{17}{20}\).

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 4 Test are as per the latest syllabus guidelines.

McGraw-Hill Math Grade 5 Chapter 4 Test Answer Key

Estimate. Then multiply. You can use the grids to help.

Question 1.
1.3 × 2
Estimate ______
product ______
Answer:
Estimate: 3.
product: 2.6.

Explanation:
Given the expression is 1.3 × 2. So the product is 2.6, and the estimated product is 3.

Question 2.
4.5 × 3
Estimate ______
product ______
Answer:
Estimate: 14.
product: 13.5.

Explanation:
Given the expression is 4.5 × 3. So the product is 13.5, and the estimated product is 14.

Question 3.
13.2 × 8
Estimate ______
product ______
Answer:
Estimate: 106.
product: 105.6

Explanation:
Given the expression is 13.2 × 8. So the product is 105.6, and the estimated product is 106.

Question 4.
4.24 × 3
Estimate ______
product ______
Answer:
Estimate: 13.
product: 12.72.

Explanation:
Given the expression is 4.24 × 3. So the product is 12.72, and the estimated product is 13.

Question 5.
2.01 × 5
Estimate ______
product ______
Answer:
Estimate: 10.1
product: 10.05.

Explanation:
Given the expression is 2.01 × 5. So the product is 10.05, and the estimated product is 10.1.

Question 6.
0.3 × 0.3
Estimate ______
product ______
Answer:
Estimate: 0.10.
product: 0.09

Explanation:
Given the expression is 0.3 × 0.3. So the product is 0.09, and the estimated product is 0.10.

Question 7.
0.4 × 0.6
Estimate ______
product ______
Answer:
Estimate: 0.2.
product: 0.24.

Explanation:
Given the expression is 0.4 × 0.6. So the product is 0.24, and the estimated product is 0.2.

Question 8.
0.3 × 0.8
Estimate ______
product ______
Answer:
Estimate: 0.2.
product: 0.24.

Explanation:
Given the expression is 0.3 × 0.8. So the product is 0.24, and the estimated product is 0.2.

Question 9.
0.6 × 0.8
Estimate ______
product ______
Answer:
Estimate: 0.5
product: 0.48

Explanation:
Given the expression is 0.6 × 0.8. So the product is 0.48, and the estimated product is 0.5.

Question 10.
1.2 × 0.4
Estimate ______
product ______
Answer:
Estimate: 0.5.
product: 0.48

Explanation:
Given the expression is 1.2 × 0.4. So the product is 0.48, and the estimated product is 0.5.

Estimate. Then divide.

Question 11.
1.2 ÷ 6
Estimate ______
Quotient ______
Answer:
Estimate: 0.1
Quotient: 0.2

Explanation:
Given that the expression is 1.2 ÷ 6. So the quotient is 0.2 and the estimated is 0.1.

Question 12.
4.4 ÷ 2
Estimate ______
Quotient ______
Answer:
Estimate: 0.1
Quotient: 0.2

Explanation:
Given that the expression is 1.2 ÷ 6. So the quotient is 0.2 and the estimated is 0.1.

Question 13.
5.6 ÷ 8
Estimate ______
Quotient ______
Answer:
Estimate: 1
Quotient: 0.7

Explanation:
Given that the expression is 5.6 ÷ 8. So the quotient is 0.7 and the estimated is 1.

Question 14.
35.7 ÷ 7
Estimate ______
Quotient ______
Answer:
Estimate: 5.
Quotient: 5.1.

Explanation:
Given that the expression is 35.7 ÷ 7. So the quotient is 5.1 and the estimated is 5.

Question 15.
3.9 ÷ 3
Estimate ______
Quotient ______
Answer:
Estimate: 1.
Quotient: 1.3

Explanation:
Given that the expression is 3.9 ÷ 3. So the quotient is 1.3 and the estimated is 1.

Question 16.
15 ÷ 0.5
Estimate ______
Quotient ______
Answer:
Estimate: 30.
Quotient: 30.

Explanation:
Given that the expression is 15 ÷ 0.5. So the quotient is 30 and the estimated is 30.

Question 17.
66 ÷ 0.03
Estimate ______
Quotient ______
Answer:
Estimate: 2000.
Quotient: 2200.

Explanation:
Given that the expression is 66 ÷ 0.03. So the quotient is 2200 and the estimated is 2000.

Question 18.
56 ÷ 0.8
Estimate ______
Quotient ______
Answer:
Estimate: 100.
Quotient: 70.

Explanation:
Given that the expression is 56 ÷ 0.8. So the quotient is 70 and the estimated is 100.

Question 19.
284 ÷ 0.4
Estimate ______
Quotient ______
Answer:
Estimate: 700.
Quotient: 710.

Explanation:
Given that the expression is 284 ÷ 0.4. So the quotient is 710 and the estimated is 700.

Question 20.
396 ÷ 0.33
Estimate ______
Quotient ______
Answer:
Estimate: 1000.
Quotient: 1200.

Explanation:
Given that the expression is 396 ÷ 0.33. So the quotient is 1200 and the estimated is 1000.

Estimate. Then multiply or divide.

Question 21.
10.66 × 10³ Estimate: _________________
Product: ___________________
Answer:
Estimate: 11,000.
Product: 10,660.

Explanation:
Given the expression is 10.66 × 10³ which is
= 10.66 × 10 × 10 × 10
= 10,660.

Question 22.
11.95 × 10² Estimate: _________________
Product: ___________________
Answer:
Estimate: 12,000.
Product: 11,195.

Explanation:
Given the expression is 11.95 × 10² which is
= 11.95 × 10 × 10
= 1,195.

Question 23.
14.92 × 10¹ Estimate: _________________
Product: ___________________
Answer:
Estimate: 150.
Product: 149.2.

Explanation:
Given the expression is 14.92 × 10¹ which is
= 14.92 × 10
= 149.2.

Question 24.
81.52 × 10⁰ Estimate: _________________
Product: ___________________
Answer:
Estimate: 82
Product: 81.52.

Explanation:
Given the expression is 81.52 × 10⁰ which is
= 81.52 × 1
= 81.52.

Question 25.
19.99 × 10³ Estimate: _________________
Product: ___________________
Answer:
Estimate: 20,000.
Product: 19,990

Explanation:
Given the expression is 19.99 × 10³ which is
= 19.99 × 10 × 10 × 10
=  19,990.

Question 26.
11.55 × 10² Estimate: _________________
Product: ___________________
Answer:
Estimate: 1,200.
Product: 1,155.

Explanation:
Given the expression is 11.55 × 10² which is
= 11.55 × 10 × 10
= 1,155.

Estimate. Then multiply and describe your strategy.

Question 27.
Estimate: 0.7 × 5 _________________________________
Multiply: 0.7 × 5 = _________________________________
Strategy: __________________________________________
Answer:
Estimate: 0.7 × 5 = 4
Multiply: 0.7 × 5 = 3.5

Explanation:
Given the expression is 0.7 × 5 which is
0.7 × 5 = 3.5

Solve. List the related multiplication and division facts.

Question 28.
5 ÷ 0.1 = ______________________________
Answer:
5 ÷ 0.1 = 50.

Explanation:
The division of 5 ÷ 0.1 is 50.

Solve.

Question 29.
The following amounts were added to a number: 7.2 × 10², 4.6 × 10², 2.7 × 10², and 6.2 × 10². After the amounts were added, the total was 34.4 × 10². What was the original number? Work backward to solve.
Answer:
7.2 × 10² = 720,
4.6 × 10² = 460,
2.7 × 10² = 270,
6.2 × 10² = 620.

Explanation:
The given expressions are 7.2 × 10², 4.6 × 10², 2.7 × 10², and 6.2 × 10² which is
7.2 × 10² = 720,
4.6 × 10² = 460,
2.7 × 10² = 270,
6.2 × 10² = 620.

Question 30.
An average adult should drink about 2 liters of water a day. How many 1-liter bottles of water are needed a day for 1,000 adults?
A case of 1-liter bottles of water holds 24 bottles. How many are needed for 1,000 people per day?
Answer:
The number of liters is 2,000 liters.

Explanation:
Given that an average adult should drink about 2 liters of water a day. So for 1,000 adults, it will be 1,000×2 = 2,000 liters. As a case of 1-liter bottles of water holds 24 bottles. The number of bottles needed for 1,000 people per day is 1,000÷24 which is 42 bottles.

Question 31.
A table shows a population of 10⁴ people for a community. How many people are in the community?
_______________________

Answer:
10,000 people.

Explanation:
The number of people in the community is 10×10×10×10 which is 10,000 people.

If each person in the community was given 0.3 pounds of rice each day for a week, how much rice was needed?
___________________

Answer:
The rice needed is 21,000 pounds.

Explanation:
As 0.3 pounds of rice each day for a week which means 0.3×7 = 2.1. The rice needed is 2.1×10000 which is 21,000 pounds.

A pound of rice is 16 ounces. How many ounces of rice are in 0.3 pounds?
___________________
Answer:
The number of ounces is 4.8 ounces.

Explanation:
As 1 pound of rice is 16 ounces, so the number of ounces of rice in 0.3 pounds is 0.3×16 which is 4.8 ounces.

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 3 Lesson 8 Division are as per the latest syllabus guidelines.

McGraw-Hill Math Grade 5 Answer Key Chapter 3 Lesson 8 Division

Solve

Find the answer, and tell what strategy you used.

Question 1.
147 ÷ 7 21
Strategy: _______________________________
Answer:
147 ÷ 7 = 21.

Explanation:
By dividing 147 ÷ 7 we will get 21. The strategy used is fact family division, as it is a set of four related multiplication and division facts that uses the same three numbers which is
147 ÷ 7 = 21,
147 ÷ 21 = 7,
21 × 7 = 147,
7 × 21 = 147,

Question 2.
156 ÷ 3 _______
Strategy: __________
Answer:
156 ÷ 3 = 52.

Explanation:
By dividing 156 ÷ 3 we will get 52. The strategy used is long division.

Question 3.
207 ÷ 9 _______
Strategy: __________
Answer:
207 ÷ 9 = 23.

Explanation:
By dividing 207 ÷ 9 we will get 23. The strategy used is long division.

Question 4.
136 ÷ 8 _____
Strategy: ___________________
Answer:
136 ÷ 8 = 17.

Explanation:
By dividing 136 ÷ 8 we will get 17. The strategy used is fact family division, as it is a set of four related multiplication and division facts that uses the same three numbers which is
136 ÷ 8 = 17,
136 ÷ 17 = 8,
17 × 8 = 136,
8 × 17 = 136.

Question 5.
119 ÷ 7 ________
Strategy: __________
Answer:
119 ÷ 7 = 17.

Explanation:
By dividing 119 ÷ 7 we will get 17. The strategy used is fact family division, as it is a set of four related multiplication and division facts that uses the same three numbers which is
119 ÷ 7 = 17,
119 ÷ 17 = 7,
17 × 7 = 119,
7 × 17 = 119.

Question 6.
332 ÷ 4 ________
Strategy: ________________________________
Answer:
332 ÷ 4 = 83.

Explanation:
By dividing 332 ÷ 4 we will get 83. The strategy used is long division.