McGraw Hill Math Grade 7 Unit Test Lessons 6-8 Answer Key

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McGraw-Hill Math Grade 7 Unit Test Lessons 6-8 Answer Key

Change to mixed numbers.

Question 1.
\(\frac{17}{7}\)
Answer:
2\(\frac{3}{7}\)
Explanation:
Any fraction greater than 1 is an improper fraction can be be changed to mixed number,
which is a part of whole number and fraction.
\(\frac{17}{7}\)
= 2\(\frac{3}{7}\)

Question 2.
\(\frac{29}{6}\)
Answer:
4\(\frac{5}{6}\)
Explanation:
Any fraction greater than 1 is an improper fraction can be be changed to mixed number,
which is a part of whole number and fraction.
\(\frac{29}{6}\)
= 4\(\frac{5}{6}\)

Question 3.
\(\frac{102}{17}\)
Answer:
6
Explanation:
Any fraction greater than 1 is an improper fraction can be be changed to mixed number,
which is a part of whole number and fraction.
\(\frac{102}{17}\)
= 6

Question 4.
\(\frac{350}{33}\)
Answer:
10\(\frac{20}{33}\)
Explanation:
Any fraction greater than 1 is an improper fraction can be be changed to mixed number,
which is a part of whole number and fraction.
\(\frac{350}{33}\)
= 10\(\frac{20}{33}\)

Change to improper fractions.

Question 5.
7\(\frac{6}{11}\)
Answer:
\(\frac{83}{11}\)
Explanation:
To convert mixed fraction to improper fraction,
7\(\frac{6}{11}\)
Multiply the whole number by denominator of fraction.
7 x 11 = 77
Then add the numerator to the product.
77 + 6 = 83
Place the total over denominator,
\(\frac{83}{11}\)

Question 6.
5\(\frac{4}{13}\)
Answer:
\(\frac{69}{13}\)
Explanation:
To convert mixed fraction to improper fraction,
5\(\frac{4}{13}\)
Multiply the whole number by denominator of fraction.
5 x 13 = 65
Then add the numerator to the product.
65 + 4 = 69
Place the total over denominator,
\(\frac{69}{13}\)

Question 7.
4\(\frac{15}{19}\)
Answer:
\(\frac{91}{19}\)
Explanation:
To convert mixed fraction to improper fraction,
4\(\frac{15}{19}\)
Multiply the whole number by denominator of fraction.
4 x 19 = 76
Then add the numerator to the product.
76 + 15 = 91
Place the total over denominator,
\(\frac{91}{19}\)

Question 8.
7\(\frac{7}{16}\)
Answer:
\(\frac{119}{16}\)
Explanation:
To convert mixed fraction to improper fraction,
7\(\frac{7}{16}\)
Multiply the whole number by denominator of fraction.
7 x 16 = 112
Then add the numerator to the product.
112 + 7 = 119
Place the total over denominator,
\(\frac{119}{16}\)

Add or subtract, and reduce to simplest form.

Question 9.
1\(\frac{3}{4}\) + \(\frac{3}{4}\)
Answer:
2\(\frac{1}{2}\)
Explanation:
1\(\frac{3}{4}\) + \(\frac{3}{4}\)
= \(\frac{7}{4}\) + \(\frac{3}{4}\)
Add the numerators 7 + 3 = 10
Then place over denominators.
\(\frac{10}{4}\) = \(\frac{5}{2}\)
Reduce to the simplest form as,
= 2\(\frac{1}{2}\)

Question 10.
\(\frac{17}{49}\) – \(\frac{11}{49}\)
Answer:
\(\frac{6}{49}\)
Explanation:
\(\frac{17}{49}\) – \(\frac{11}{49}\)
Subtract the numerators 17 – 11 = 6
Then place over denominators.
\(\frac{6}{49}\)

Question 11.
1\(\frac{5}{11}\) + \(\frac{3}{11}\)
Answer:
1\(\frac{8}{11}\)
Explanation:
1\(\frac{5}{11}\) + \(\frac{3}{11}\)
= \(\frac{16}{11}\) + \(\frac{3}{11}\)
Add the numerators 16 + 3 = 19
Then place over denominators.
\(\frac{19}{11}\)
Reduce to the simplest form as,
= 1\(\frac{8}{11}\)

Question 12.
2\(\frac{23}{39}\) + \(\frac{24}{39}\)
Answer:
3\(\frac{8}{39}\)
Explanation:
2\(\frac{23}{39}\) + \(\frac{24}{39}\)
= \(\frac{101}{39}\) + \(\frac{24}{39}\)
Add the numerators 101 + 24 = 125
Then place over denominators.
\(\frac{125}{39}\)
Reduce to the simplest form as,
= 3\(\frac{23}{39}\)

Question 13.
\(\frac{34}{41}\) – \(\frac{13}{41}\)
Answer:
\(\frac{21}{41}\)
Explanation:
\(\frac{34}{41}\) – \(\frac{13}{41}\)
Subtract the numerators 34 – 13 = 21
Then place over denominators.
\(\frac{21}{41}\)

Question 14.
\(\frac{11}{32}\) + \(\frac{19}{32}\)
Answer:
\(\frac{15}{16}\)
Explanation:
\(\frac{11}{32}\) + \(\frac{19}{32}\)
Add the numerators 11 + 19 = 30
Then place over denominators.
\(\frac{30}{32}\) = \(\frac{15}{16}\)

Question 15.
\(\frac{55}{93}\) – \(\frac{28}{93}\)
Answer:
\(\frac{9}{31}\)
Explanation:
\(\frac{55}{93}\) – \(\frac{28}{93}\)
Subtract the numerators 55 – 28 = 27
Then place over denominators.
\(\frac{27}{93}\) = \(\frac{9}{31}\)

Question 16.
\(\frac{36}{74}\) + \(\frac{33}{74}\)
Answer:
\(\frac{69}{74}\)
Explanation:
\(\frac{36}{74}\) + \(\frac{33}{74}\)
Add the numerators 36 + 33 = 69
Then place over denominators.
\(\frac{69}{74}\)

Question 17.
5\(\frac{3}{17}\) – 4\(\frac{2}{17}\)
Answer:
1\(\frac{1}{17}\)
Explanation:
5\(\frac{3}{17}\) – 4\(\frac{2}{17}\)
= \(\frac{88}{17}\) + \(\frac{70}{17}\)
Subtract the numerators 88 – 70 = 18
Then place over denominators.
\(\frac{18}{17}\)
Reduce to the simplest form as,
= 1\(\frac{1}{17}\)

Question 18.
4\(\frac{23}{33}\) + \(\frac{17}{24}\)
Answer:
5\(\frac{107}{264}\)
Explanation:
4\(\frac{23}{33}\) + \(\frac{17}{24}\)
= \(\frac{155}{33}\) + \(\frac{17}{24}\)
Find a common multiple for both the denominators is 264
Multiply both the numerator and denominator,
that will make the denominator equal to common multiple.
\(\frac{155 X 8}{33 X 8}\) + \(\frac{17 X 11}{24 X 11}\)
= \(\frac{1240}{264}\) + \(\frac{187}{264}\)
Add the numerators 1240 + 187 = 1427
Then place over denominators.
\(\frac{1427}{264}\)
Reduce to the simplest form as,
= 5\(\frac{107}{264}\)

Question 19.
\(\frac{4}{9}\) + \(\frac{4}{15}\)
Answer:
\(\frac{32}{45}\)
Explanation:
\(\frac{4}{9}\) + \(\frac{4}{15}\)
Find a common multiple for both the denominators is 135
Multiply both the numerator and denominator,
that will make the denominator equal to common multiple.
\(\frac{4 X 15}{9 X 15}\) + \(\frac{4 X 9}{15 X 9}\)
= \(\frac{60}{135}\) + \(\frac{32}{135}\)
Add the numerators 60 + 36 = 96
Then place over denominators.
\(\frac{96}{135}\)
Reduce to the simplest form as,
= \(\frac{32}{45}\)

Question 20.
\(\frac{14}{25}\) – \(\frac{13}{35}\)
Answer:
\(\frac{33}{175}\)
Explanation:
\(\frac{14}{25}\) – \(\frac{13}{35}\)
Find a common multiple for both the denominators is 175.
Multiply both the numerator and denominator,
that will make the denominator equal to common multiple.
\(\frac{14 X 7}{25 X 7}\) – \(\frac{13 X 5}{35 X 5}\)
= \(\frac{98}{175}\) – \(\frac{65}{175}\)
Subtract the numerators 98 – 65 = 33
Then place over denominators.
\(\frac{33}{175}\)

Question 21.
1\(\frac{5}{9}\) + \(\frac{3}{11}\)
Answer:
1\(\frac{82}{99}\)
Explanation:
1\(\frac{5}{9}\) + \(\frac{3}{11}\)
= \(\frac{14}{9}\) + \(\frac{3}{11}\)
Find a common multiple for both the denominators is 99.
Multiply both the numerator and denominator,
that will make the denominator equal to common multiple.
\(\frac{14 X 11}{9 X 11}\) + \(\frac{3 X 9}{11 X 9}\)
= \(\frac{154}{99}\) + \(\frac{27}{99}\)
Add the numerators 154 + 27 = 181
Then place over denominators.
\(\frac{181}{99}\)
Reduce to its simplest f form,
1\(\frac{82}{99}\)

Question 22.
1\(\frac{7}{19}\) – \(\frac{2}{7}\)
Answer:
1\(\frac{11}{133}\)
Explanation:
1\(\frac{7}{19}\) – \(\frac{2}{7}\)
= \(\frac{26}{19}\) – \(\frac{2}{7}\)
Find a common multiple for both the denominators is 133.
Multiply both the numerator and denominator,
that will make the denominator equal to common multiple.
\(\frac{26 X 7}{19 X 7}\) – \(\frac{2 X 19}{7 X 19}\)
= \(\frac{182}{133}\) – \(\frac{38}{133}\)
Subtract the numerators 182 – 38 = 144
Then place over denominators.
\(\frac{144}{133}\)
Reduce to its simplest f form,
1\(\frac{11}{133}\)

Question 23.
\(\frac{3}{4}\) – \(\frac{19}{41}\)
Answer:
\(\frac{47}{164}\)
Explanation:
\(\frac{3}{4}\) – \(\frac{19}{41}\)
Find a common multiple for both the denominators is 164.
Multiply both the numerator and denominator,
that will make the denominator equal to common multiple.
\(\frac{3 X 41}{4 X 41}\) – \(\frac{19 X 4}{41 X 4}\)
= \(\frac{123}{164}\) – \(\frac{76}{164}\)
Subtract the numerators 123 – 76 = 47
Then place over denominators.
\(\frac{47}{164}\)

Question 24.
2\(\frac{8}{13}\) + \(\frac{9}{17}\)
Answer:
3\(\frac{32}{221}\)
Explanation:
2\(\frac{8}{13}\) + \(\frac{9}{17}\)
= \(\frac{34}{13}\) + \(\frac{9}{17}\)
Find a common multiple for both the denominators is 221.
Multiply both the numerator and denominator,
that will make the denominator equal to common multiple.
\(\frac{34 X 17}{13 X 17}\) + \(\frac{9 X 13}{17 X 13}\)
= \(\frac{578}{221}\) + \(\frac{117}{221}\)
Add the numerators 578 + 117 = 695
Then place over denominators.
\(\frac{695}{117}\)
Reduce to its simplest f form,
3\(\frac{32}{221}\)

Estimate, then add or subtract.

Question 25.
2\(\frac{14}{25}\) – 1\(\frac{17}{21}\)
Answer:
\(\frac{394}{525}\)
Explanation:
2\(\frac{14}{25}\) – 1\(\frac{17}{21}\)
= \(\frac{(2 X 25) + 14}{25}\) – \(\frac{(1 X 21) + 17}{21}\)
= \(\frac{64}{25}\) – \(\frac{38}{21}\)
= \(\frac{(64 X 21) – (38 X 25)}{525}\)
= \(\frac{1344 – 950}{525}\)
\(\frac{394}{525}\)

Question 26.
9\(\frac{22}{63}\) + 25\(\frac{43}{63}\)
Answer:
35\(\frac{2}{63}\)
Explanation:
9\(\frac{22}{63}\) + 25\(\frac{43}{63}\)
= 9\(\frac{(9 X 63) + 22}{63}\) + 25\(\frac{(25 x 63) + 43}{63}\)
= \(\frac{589}{63}\) + \(\frac{1618}{63}\)
= \(\frac{2207}{63}\)
= 35\(\frac{2}{63}\)

Question 27.
12\(\frac{23}{29}\) + 11\(\frac{17}{29}\)
Answer:
24\(\frac{11}{29}\)
Explanation:
12\(\frac{23}{29}\) + 11\(\frac{17}{29}\)
= latex]\frac{(12 X 29) + 23}{29}[/latex] + latex]\frac{(11 X 29) + 17}{29}[/latex]
= latex]\frac{371}{29}[/latex] + latex]\frac{336}{29}[/latex]
= latex]\frac{371 + 336}{29}[/latex]
= latex]\frac{707}{29}[/latex]
= 24\(\frac{11}{29}\)

Question 28.
18\(\frac{3}{7}\) + 5\(\frac{1}{4}\)
Answer:
23\(\frac{19}{28}\)
Explanation:
18\(\frac{3}{7}\) + 5\(\frac{1}{4}\)
= \(\frac{(7 X 18) + 3}{7}\) + \(\frac{(4 X 5) + 1}{4}\)
= \(\frac{129}{7}\) + \(\frac{21}{4}\)
= \(\frac{(129 X 4) + 21 x 7}{28}\)
= \(\frac{516 + 147 }{28}\)
= \(\frac{663}{28}\)
= 23\(\frac{19}{28}\)

Multiply or divide, and reduce to simplest form.

Question 29.
3 × 3\(\frac{2}{11}\)
Answer:
9\(\frac{6}{11}\)
Explanation:
3 × 3\(\frac{2}{11}\)
convert mixed fraction to improper fraction,
3 × \(\frac{35}{11}\)
Multiply the whole number by numerator,
3 × 35 = 105
Place your answer over denominator.
= \(\frac{105}{11}\)
Reduce to the simplest form,
9\(\frac{6}{11}\)

Question 30.
\(\frac{1}{2}\) × 55
Answer:
27\(\frac{1}{2}\)
Explanation:
\(\frac{1}{2}\) x 55
Multiply the whole number by numerator,
1 × 55 = 55
Place your answer over denominator.
= \(\frac{55}{2}\)
Reduce to the simplest form,
27\(\frac{1}{2}\)

Question 31.
\(\frac{3}{4}\) × 24
Answer:
18
Explanation:
\(\frac{3}{4}\) x 24
Multiply the whole number by numerator,
3 × 24 = 72
Place your answer over denominator.
= \(\frac{72}{4}\)
Reduce to the simplest form as 18.

Question 32.
\(\frac{14}{18}\) × \(\frac{11}{28}\)
Answer:
\(\frac{11}{36}\)
Explanation:
\(\frac{14}{18}\) x \(\frac{11}{28}\)
Multiply the numerators and denominators,
14 x 11 = 154
18 x 28 = 504
Place your answer over denominator.
= \(\frac{154}{504}\)
Reduce to the simplest form,
\(\frac{11}{36}\)

Question 33.
\(\frac{1}{3}\) × 4\(\frac{7}{9}\)
Answer:
1\(\frac{16}{27}\)
Explanation:
\(\frac{1}{3}\) x 4\(\frac{7}{9}\)
Convert mixed fraction into improper fraction,
\(\frac{1}{3}\) x \(\frac{43}{9}\)
Multiply the numerators and denominators,
1 x 43 = 43
3 x 9 = 27
Place your answer over denominator.
= \(\frac{43}{117}\)
Reduce to the simplest form,
1\(\frac{16}{27}\)

Question 34.
16 × \(\frac{3}{11}\)
Answer:
4\(\frac{4}{11}\)
Explanation:
16 × \(\frac{3}{11}\)
Multiply the whole number by numerator,
16 × 3 = 48
Place your answer over denominator.
= \(\frac{48}{11}\)
Reduce to the simplest form,
4\(\frac{4}{11}\)

Question 35.
\(\frac{16}{29}\) ÷ 48
Answer:
\(\frac{1}{87}\)
Explanation:
\(\frac{16}{29}\) ÷ 48
Multiply the whole number by denominator,
48 x 29 = 1392
place the numerator over denominator,
\(\frac{16}{1392}\)
Reduce to the simplest form,
\(\frac{1}{87}\)

Question 36.
\(\frac{51}{47}\) ÷ 17
Answer:
\(\frac{3}{47}\)
Explanation:
\(\frac{51}{47}\) ÷ 17
Multiply the whole number by denominator,
17 x 47 = 799
place the numerator over denominator,
\(\frac{51}{799}\)
Reduce to the simplest form,
\(\frac{3}{47}\)

Question 37.
\(\frac{7}{3}\) ÷ 42
Answer:
\(\frac{1}{18}\)
Explanation:
\(\frac{7}{3}\) ÷ 42
Multiply the whole number by denominator,
42 x 3 = 126
place the numerator over denominator,
\(\frac{7}{126}\)
Reduce to the simplest form,
\(\frac{1}{18}\)

Question 38.
\(\frac{4}{27}\) ÷ 3
Answer:
\(\frac{4}{81}\)
Explanation:
\(\frac{4}{27}\) ÷ 3
Multiply the whole number by denominator,
27 x 3 = 81
place the numerator over denominator,
\(\frac{4}{81}\)

Question 39.
\(\frac{75}{83}\) ÷ 15
Answer:
\(\frac{5}{83}\)
Explanation:
\(\frac{75}{83}\) ÷ 15
Multiply the whole number by denominator,
83 x 15 = 1245
place the numerator over denominator,
\(\frac{75}{1245}\)
Reduce to the simplest form,
\(\frac{5}{83}\)

Question 40.
39 ÷ \(\frac{6}{7}\)
Answer:
45\(\frac{1}{2}\)
Explanation:
39 ÷ \(\frac{6}{7}\)
Multiply the whole number by denominator,
39 x 7 = 273
place the numerator over denominator,
\(\frac{6}{273}\)
Reduce to the simplest form,
45\(\frac{1}{2}\)

Question 41.
125 ÷ \(\frac{25}{44}\)
Answer:
220
Explanation:
125 ÷ \(\frac{25}{44}\)
Multiply the whole number by denominator,
125 x 44 = 5500
place the numerator over denominator,
\(\frac{25}{5500}\) = 220

Question 42.
\(\frac{3}{4}\) ÷ \(\frac{16}{27}\)
Answer:
1\(\frac{17}{64}\)
Explanation:
\(\frac{3}{4}\) ÷ \(\frac{16}{27}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{3}{4}\) x \(\frac{27}{16}\)
Multiply the numerators and denominators,
3 x 27 = 81
4 x 16 = 64
place the numerator over denominator,
\(\frac{81}{64}\)
Reduce to the simplest form,
1\(\frac{17}{64}\)

Question 43.
\(\frac{24}{17}\) ÷ \(\frac{17}{24}\)
Answer:
1
Explanation:
\(\frac{24}{17}\) ÷ \(\frac{17}{24}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{24}{17}\) x \(\frac{24}{17}\)
Multiply the numerators and denominators,
24 x 17 = 408
24 x 17 = 408
place the numerator over denominator,
\(\frac{408}{408}\) = 1

Question 44.
\(\frac{39}{76}\) ÷ \(\frac{52}{57}\)
Answer:
\(\frac{9}{16}\)
Explanation:
\(\frac{39}{76}\) ÷ \(\frac{52}{57}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{39}{76}\) x \(\frac{57}{52}\)
Multiply the numerators and denominators,
39 x 57 = 2223
76 x 52 = 3952
place the numerator over denominator,
\(\frac{2223}{3952}\)
Reduce to the simplest form,
1\(\frac{9}{16}\)

Question 45.
Elena jogs at a constant rate of 5\(\frac{1}{3}\) miles per hour. How far does she jog in 3 hours?
Answer:
16 miles
Explanation:
Elena jogs at a constant rate of 5\(\frac{1}{3}\) miles per hour.
she jog in 3 hours = 3 x 5\(\frac{1}{3}\)
= 3 × \(\frac{16}{3}\)
Multiply the whole number by numerator,
16 × 3 = 48
Place your answer over denominator.
= \(\frac{48}{3}\)
= 16 miles.

Question 46.
To plant his vegetable garden, Randy needs to dig 24 holes that are each 4\(\frac{1}{2}\) inches deep.
How many total inches does he have to dig?
Answer:
108 inches.
Explanation:
Randy needs to dig 24 holes that are each 4\(\frac{1}{2}\) inches deep.
Total inches he need to dig,
24 x 4\(\frac{1}{2}\)
convert mixed fraction to improper fraction,
24 x \(\frac{9}{2}\)
Multiply the whole number by numerator,
24 x 9 = 216
place the numerator over denominator,
\(\frac{216}{2}\)
= 108 inches.

Question 47.
Cassie has \(\frac{5}{6}\) pound of sunflower seeds. She wants to divide the seeds among 3 people.
How many pounds will each person get?
Answer:
\(\frac{5}{18}\) pounds.
Explanation:
Cassie has \(\frac{5}{6}\) pound of sunflower seeds.
She wants to divide the seeds among 3 people.
Number of pounds will each person get,
\(\frac{5}{6}\) ÷ 3
Multiply the whole number by denominator,
6 x 3 = 18
place the numerator over denominator,
\(\frac{5}{18}\) pounds.

Question 48.
The temperature on Tuesday was -3°F.On Wednesday the temperature was 4°F.What is the average temperature for the two days? On which day was the temperature closer to 0°F?
Answer:
\(\frac{1}{2}\)°F;
Tuesday.
Explanation:
The temperature on Tuesday was -3°F.
On Wednesday the temperature was 4°F.
The average temperature for the two days,
\(\frac{ -3 + 4}{2}\)
= \(\frac{1}{2}\)°F.

Question 49.
A cookie recipe calls for \(\frac{3}{4}\) cup of sugar. If Aaron wants to make one half batches of cookies, how many cups of sugar will he need?
Answer:
1\(\frac{1}{8}\) cups
Explanation:
A cookie recipe calls for \(\frac{3}{4}\) cup of sugar.
If Aaron wants to make one half batches of cookies,
how many cups of sugar will he need
\(\frac{3}{4}\) + 1\(\frac{1}{2}\)
= \(\frac{3}{4}\) + 1\(\frac{2}{4}\)
= \(\frac{3}{4}\) + \(\frac{6}{4}\)
= \(\frac{9}{8}\)
= 1\(\frac{1}{8}\) cups.

Question 50.
Vivi steps off a 10-foot-high diving board and goes 7\(\frac{3}{8}\) feet below the surface of the swimming pool, then back up to the surface. How far does she travel together?
Answer:
24\(\frac{3}{4}\)
Explanation:
10 + 7\(\frac{3}{8}\) + 7\(\frac{3}{8}\)
= 10 + \(\frac{59}{8}\) + \(\frac{59}{8}\)
= 10 + \(\frac{118}{8}\)
= \(\frac{80 +118}{8}\)
= \(\frac{198}{8}\)
= 24 \(\frac{6}{8}\)
= 24 \(\frac{3}{4}\)