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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 \(\frac{180}{44}\).

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 5.4 Multiplying and Dividing with Negative Numbers existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 5.4 Multiplying and Dividing with Negative Numbers

Exercises Multiply or Divide

Question 1.
5 × (-3) = _________
Answer:
5 × (-3) = -15
Explanation:
The above two given numbers have different signs, one is positive and one is negative. So, there product is negative. Multiply 5 with -3 the product is equal to -15.

Question 2.
13 × (-10) = _________
Answer:
13 × (-10) = -130
Explanation:
The above two given numbers have different signs, one is positive and one is negative. So, there product is negative. Multiply 13 with -10 the product is equal to -130.

Question 3.
100 × (-1) = _________
Answer:
100 × (-1) = -100
Explanation:
The above two given numbers have different signs, one is positive and one is negative. So, there product is negative. Multiply 100 with -1 the product is equal to -100.

Question 4.
23 × (-3) = _________
Answer:
23 × (-3) = -69
Explanation:
The above two given numbers have different signs, one is positive and one is negative. So, there product is negative. Multiply 23 with -3 the product is equal to -69.

Question 5.
15 × (-15) = _________
Answer:
15 × (-15) = -225
Explanation:
The above two given numbers have different signs, one is positive and one is negative. So, there product is negative. Multiply 15 with -15 the product is equal to -225.

Question 6.
(-12) × 20 = _________
Answer:
(-12) × 20 = -240
Explanation:
The above two given numbers have different signs, one is negative and one is positive. So, there product is negative. Multiply -12 with 20 the product is equal to -240.

Question 7.
(-2) × (-4) = _________
Answer:
(-2) × (-4) = 8
Explanation:
The above two given numbers have same signs. So, there product is positive. Multiply -2 with -4 the product is equal to 8.

Question 8.
(-1) × 1 = _________
Answer:
(-1) × 1 = -1
Explanation:
The above two given numbers have different signs, one is negative and one is positive. So, there product is negative. Multiply -1 with 1 the product is equal to -1.

Question 9.
(-125) × (-1) = _________
Answer:
(-125) × (-1) = 125
Explanation:
The above two given numbers have same signs. So, there product is positive. Multiply -125 with -1 the product is equal to 125.

Question 10.
(-3) × 103 = _________
Answer:
(-3) × 103 = -309
Explanation:
The above two given numbers have different signs, one is negative and one is positive. So, there product is negative. Multiply -3 with 103 the product is equal to -309.

Question 11.
(-20) ÷ 20 = _________
Answer:
(-20) ÷ 20 = -1
Explanation:
The above two given numbers have different signs, one is negative and one is positive. So, there quotient is negative. Divide -20 by 20 the quotient is equal to -1

Question 12.
(-22) × 0 = _____
Answer:
(-22) × 0 = 0
Explanation:
Multiply -22 with 0 the product is equal to 0. Zero doesn’t have negative sign.

Question 13.
(-3) × (-1) = _____
Answer:
(-3) × (-1) = 3
Explanation:
The above two given numbers have same signs. So, there product is positive. Multiply -3 with -1 the product is equal to 3.

Question 14.
(-12) ÷ 4 = _____
Answer:
(-12) ÷ 4 = -3
Explanation:
The above two given numbers have different signs, one is negative and one is positive. So, there quotient is negative. Divide -12 by 4 the quotient is equal to -3.

Question 15.
15 ÷ (-3) = ____
Answer:
15 ÷ (-3) = -5
Explanation:
The above two given numbers have different signs, one is positive and one is negative. So, there quotient is negative. Divide 15 by -3 the quotient is equal to -5.

Question 16.
(-27) ÷ (-9 ÷ \(\frac{1}{9}\)) = ____
Answer:
(-27) ÷ (-9 ÷ \(\frac{1}{9}\)) = \(\frac{1}{3}\)
Explanation:
The above two given numbers have same signs. So, there quotient is positive. Divide (-27) by (-9 ÷ \(\frac{1}{9}\)) the quotient is equal to \(\frac{1}{3}\).

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 5.3 Adding and Subtracting with Negative Numbers existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 5.3 Adding and Subtracting with Negative Numbers

Exercises Add

Question 1.
17 + (-3) = ____
Answer:
17 + (-3) = 14
Explanation:
Perform addition operation on above given numbers. Add 17 to -3 the sum is equal to 14.

Question 2.
(-15) + 6 = _____
Answer:
(-15) + 6 = -9
Explanation:
Perform addition operation on above two given numbers. Add -15 with 6 the sum is equal to -9.

Question 3.
1 + (-12) = ____
Answer:
1 + (-12) = -11
Explanation:
Perform addition operation on above two given numbers. Add 1 with -12 the sum is equal to -11.

Question 4.
75 + (-36) = ____
Answer:
75 + (-36) = 39
Explanation:
Perform addition operation on above two given numbers. Add 75 with -36 the sum is equal to 39.

Question 5.
110 + (-56) + 14 = ____
Answer:
110 + (-56) + 14 = 68
Explanation:
Perform addition operation on above three given numbers. Add 110 with -56 and 14 the sum is equal to 68.

Question 6.
95 + (-65) + (-1) = _______________
Answer:
95 + (-65) + (-1) = 29
Explanation:
Perform addition operation on above three given numbers. Add 95 with -65 and -1 the sum is equal to 29.

Question 7.
(-20) + (-20) + 7 = ___
Answer:
(-20) + (-20) + 7 = -33
Explanation:
Perform addition operation on above three given numbers. Add -20 with -20 and 7 the sum is equal to -33.

Question 8.
51 + (-33) + 20 = __________________
Answer:
51 + (-33) + 20 = 38
Explanation:
Perform addition operation on above three given numbers. Add 51 with -33 and 20 the sum is equal to 38.

Question 9.
30 + (-22) = __________
Answer:
30 + (-22) = 8
Explanation:
Perform addition operation on above two given numbers. Add 30 to -22 the sum is equal to 8.

Question 10.
18 + 18 + (-18) = ________________
Answer:
18 + 18 + (-18) = 18
Explanation:
Perform addition operation on above three given numbers. Add 18 with 18 and -18 the sum is equal to 18.

Question 11.
(-25) + 14 = ____
Answer:
(-25) + 14 = -11
Explanation:
Perform addition operation on above two given numbers. Add -25 to 14  the sum is equal to -11.

Question 12.
80 + 13 + 29 + (-100) = ___
Answer:
80 + 13 + 29 + (-100) = 22
Explanation:
Perform addition operation on above four given numbers. Add 80 to 13, 29 and -100 the sum is equal to 22.

Question 13.
57 + (-39) + 10 = __________
Answer:
57 + (-39) + 10 = 28
Explanation:
Perform addition operation on above three given numbers. Add 57 with -39 and 10 the sum is equal to 28.

Question 14.
(-23) + 63 + (-9) = ______
Answer:
(-23) + 63 + (-9) = 31
Explanation:
Perform addition operation on above three given numbers. Add -23 with 63 and -9 the sum is equal to 31.

Question 15.
4 + 2 + (-7) + (-1) = ____________
Answer:
4 + 2 + (-7) + (-1) = -2
Explanation:
Perform addition operation on above four given numbers. Add 4 with 2,-7 and -1 the sum is equal to -2.

Question 16.
1 + (-9) + 9 = ____
Answer:
1 + (-9) + 9 = 1
Explanation:
Perform addition operation on above three given numbers. Add 1 with -9 and 9 the sum is equal to 1.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 5.2 Absolute Value existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 5.2 Absolute Value

Exercises Solve

Question 1.
|-9| = ____
Answer:
|-9| = 9
The absolute value of |-9| is 9.
Explanation:
The absolute value of 9 doesn’t tell whether the number is positive or negative, it just means that the number is 9 away from zero.

Question 2.
|-567| = ____
Answer:
|-567| = 567
The absolute value of |-567| is 567.
Explanation:
The absolute value of 567 doesn’t tell whether the number is positive or negative, it just means that the number is 567 away from zero.

Question 3.
|48| = ___
Answer:
|48| = 48
The absolute value of |48| is 48.
Explanation:
The absolute value of 48 doesn’t tell whether the number is positive or negative, it just means that the number is 48 away from zero.

Question 4.
|-0.24| = ____
Answer:
|-0.24| = 0.24
The absolute value of |-0.24| is 0.24.
Explanation:
The absolute value of 0.24 doesn’t tell whether the number is positive or negative, it just means that the number is 0.24 away from zero.

Question 5.
|\(\frac{-7}{8}\)| = ____
Answer:
|\(\frac{-7}{8}\)| = \(\frac{7}{8}\)
The absolute value of |\(\frac{-7}{8}\)| is \(\frac{7}{8}\).
Explanation:
The absolute value of \(\frac{7}{8}\) doesn’t tell whether the number is positive or negative, it just means that the number is \(\frac{7}{8}\) away from zero.

Question 6.
|\(\frac{1}{3}\)| = ____
Answer:
|\(\frac{1}{3}\)| = \(\frac{1}{3}\)
The absolute value of |\(\frac{1}{3}\)| is \(\frac{1}{3}\).
Explanation:
The absolute value of \(\frac{1}{3}\) doesn’t tell whether the number is positive or negative, it just means that the number is \(\frac{1}{3}\) away from zero.

Compare using <, >, or =

Question 7.
|—2| ____ |—8|
Answer:
|-2| < |-8|
Explanation:
The absolute value of |-2|  is 2.
The absolute value of |-8|  is 8.
So, |-2| is less than |-8|.

Question 8.
|56| ___ |-56|
Answer:
|56| = |-56|
Explanation:
The absolute value of |56|  is 56.
The absolute value of |-56|  is 56.
So, |56| is equal to |-56|.

Question 9.
|-12| ___ |-3|
Answer:
|-12| > |-3|
The absolute value of |-12|  is 12.
The absolute value of |-3|  is 3.
So, |-12| is greater than |-3|.

Question 10.
|-4| _______ |567|
Answer:
|-4| < |567|
Explanation:
The absolute value of |-4| is 4.
The absolute value of |567| is 567.
So, |-4| is less than |567|.

Question 11.
|35| _______ |—98|
Answer:
|35| < |-98|
Explanation:
The absolute value of |35| is 35.
The absolute value of |-98| is 98.
So, |35| is less than |-98|.

Question 12.
|6789| _______ |6799|
Answer:
|6789| < |6799|
Explanation:
The absolute value of |6789| is 6789.
The absolute value of |6799| is 6799.
So, |6789| is less than |6799|.

Solve

Question 13.
If Kim’s bank account balance is $ -12.48, how much would she need to deposit in order to bring her balance to $100.00? _________________________________________
Answer:
Kim’s bank account balance is $ -12.48.
To bring her balance to $100.00. She need to deposit $112.48.
$-12.48 + $100.00 + $12.48 = $100.00

Question 14.
If gas prices were $1.20 above average in March and $1.36 below average in April, which month was further from its average price?
Answer:
April month was further from its average price.

Question 15.
Bela’s bank account balance is $15.00. If she spends $12.86 on a shirt and $3.24 on a bracelet, what is her new balance? _______________________________________________
Answer:
Bela’s bank account balance is $15.00.
She want to spend$12.86 on a shirt and $3.24 on a bracelet.
$15.00 – $12.86 – $3.24 = -$1.10
Bela’s new balance is -$1.10.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 5.1 Negative Numbers existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 5.1 Negative Numbers

Exercises Add

Question 1.
(-4) + 4 =
Answer:
(-4) + 4 = 0
Explanation:
Perform addition operation on above two given numbers. When we add a negative number to its inverse the total is 0. Add -4 to 4 the sum is equal to 0.

Question 2.
(-110) + 210 =
Answer:
(-110) + 210 = 100
Explanation:
Perform addition operation on above two given numbers. Add -110 to 210 the sum is equal to 100.

Question 3.
(-9) + 17 + 9 + (-17) =
Answer:
(-9) + 17 + 9 + (-17) = 0
Explanation:
Perform addition operation on above given numbers. When we add a negative number to its inverse the total is 0. Add – 9 with 17, 9 and -17 the sum is equal to 0.

Question 4.
145 + (-125) =
Answer:
145 + (-125) = 20
Explanation:
Perform addition operation on above two given numbers. Add 145 to -125 the sum is equal to 20.

Question 5.
48 + (-38) =
Answer:
48 + (-38) = 10
Explanation:
Perform addition operation on above two given numbers. Add 48 to -38 the sum is equal to 10.

Question 6.
(-75) + 55 + 732 + (-712) =
Answer:
(-75) + 55 + 732 + (-712) = 0
Explanation:
Perform addition operation on above given numbers. Add -75 to 55, 732 and -712 the sum is equal to 0.

Question 7.
\(\frac{1}{4}\) + \(\left(-\frac{1}{4}\right)\) =
Answer:
\(\frac{1}{4}\) + \(\left(-\frac{1}{4}\right)\) = 0
Explanation:
Perform addition operation on above two given numbers. When we add a negative number to its inverse the total is 0. Add 1/4 to -1/4 the sum is equal to 0.

Question 8.
541 + 641 + (-741) + (-641) =
Answer:
541 + 641 + (-741) + (-641) = – 200
Explanation:
Perform addition operation on above given numbers. Add 541 with 641, -741 and -641 the sum is equal to -200.

Question 9.
44 + (-77) + 0 =
Answer:
44 + (-77) + 0 = -33
Explanation:
Perform addition operation on above given numbers. Add 44 to -77 and 0 the sum is equal to -33.

Question 10.
16 + \(\frac{1}{4}\) + \(\left(-\frac{1}{4}\right)\) + (-10) =
Answer:
16 + \(\frac{1}{4}\) + \(\left(-\frac{1}{4}\right)\) + (-10) = 6
Explanation:
Perform addition operation on above given numbers. Add 16 to 1/4, -1/4 and -10 the sum is equal to 6.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 4.4 Zero Property, Equality Properties existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 4.4 Zero Property, Equality Properties

Exercises Solve

Question 1.
5 × 0 =
Answer:
5 × 0 = 0 
Explanation:
Any number multiplied with zero is equal to zero. This property is called as zero property of multiplication.

Question 2.
0(1 + 4) =
Answer:
0(1 + 4)
= (0 x 1) + (0 x 4)
= 0 + 0
= 0
0(1 + 4) = 0
Explanation:
Zero property of addition and multiplication states that any addend + 0 will not change the total and any number multiplied with 0 is equal to 0.

Question 3.
0 × 1.111 =
Answer:
0 × 1.111 = 0 
Explanation:
Any number multiplied with zero is equal to zero. This property is called as zero property of multiplication.

Question 4.
7(0 + 5) =
Answer:
7(0 + 5)
= (7 x 0) + (7 x 5)
= 0 + 35
= 35
7(0 + 5) = 35
Explanation:
Zero property of addition and multiplication states that any addend + 0 will not change the total and any number multiplied with 0 is equal to 0.

Question 5.
0 × 0 × 3 × 9 =
Answer:
0 × 0 × 3 × 9 = 0
Explanation:
Any number multiplied with zero is equal to zero. This property is called as zero property of multiplication.

Question 6.
233.31 × 0 =
Answer:
233.31 × 0 = 0
Explanation:
Any number multiplied with zero is equal to zero. This property is called as zero property of multiplication.

Question 7.
0 × 200.893 =
Answer:
0 × 200.893 = 0
Explanation:
Any number multiplied with zero is equal to zero. This property is called as zero property of multiplication.

Question 8.
0 × 0 + 2 =
Answer:
0 × 0 + 2 = 0 + 2 = 2
Explanation:
Multiply 0 with 0 the product is equal to 0. Add 0 with 2 the sum is equal to 2.

Question 9.
0 (2 + 0) =
Answer:
0 (2 + 0) = (0 x 2) + (0 x 0) = 0
0 (2 + 0) = 0
Explanation:
Zero property of addition and multiplication states that any addend + 0 will not change the total and any number multiplied with 0 is equal to 0.

For questions 10-13, answer yes or no and briefly explain your answer.

Question 10.
If 8 + 1 = 6 + 3, then does 4(8 + 1) = 4(6 + 3)?
Answer:
Yes, If 8 + 1 = 6 + 3, then 4(8 + 1) = 4(6 + 3).
Explanation:
In equality property of multiplication the equation is equal if we multiply both sides by the same number. Here we are multiplying both sides by 4. So the answer is yes.

Question 11.
If 6 × 9 = 54, then does 4 + (6 × 9) = 54 + 4?
Answer:
Yes, If 6 × 9 = 54, then 4 + (6 × 9) = 54 + 4.
Explanation:
In equality property of addition the equation is equal if we add both sides by the same number. Here we are adding both sides by 4. So the answer is yes.

Question 12.
If \(\frac{1}{5}\) = \(\frac{3}{15}\), then does \(\frac{1}{5}\) – 5 = \(\frac{3}{15}\) – 5 ?
Answer:
Yes, If \(\frac{1}{5}\) = \(\frac{3}{15}\), then \(\frac{1}{5}\) – 5 = \(\frac{3}{15}\) – 5.
Explanation:
In equality property of subtraction the equation is equal if we subtract both sides by the same number. Here we are subtracting both sides by 5. So the answer is yes.

Question 13.
If 5 – 1 = 20 × .2, then does \(\frac{(5-1)}{22}\) = \(\frac{(20 \times .2)}{22}\)?
Answer:
Yes, If 5 – 1 = 20 × .2, then does \(\frac{(5-1)}{22}\) = \(\frac{(20 \times .2)}{22}\).
Explanation:
In equality property of division the equation is equal if we divide both sides by the same number. Here we are dividing both sides by 22. So the answer is yes.