McGraw Hill Math

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 15.2 Percents and Fractions existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 15.2 Percents and Fractions

Exercises

CONVERT

Convert the fractions to a simple percentage, or state that the fraction cannot be converted to a simple percentage.

Question 1.
\(\frac{1}{2}\) = ________________
Answer:
\(\frac{1}{2}\) = ?%
\(\frac{100}{2}\) = 50
1 x 50 = 50
\(\frac{1}{2}\) = 50%
Explanation:
The given fraction can be converted into simple percentage. Here the denominator of the given fraction 2 is evenly divided into 100. Divide 100 by 2 the quotient is equal to 50. Multiply the numerator 1 with the quotient 50 the product is equal to 50. Now add the percent sign. So\(\frac{1}{2}\) is equal to 50%.

Question 2.
\(\frac{3}{20}\) = ________________
Answer:
\(\frac{3}{20}\) = ?%
\(\frac{100}{20}\) = 5
3 x 5 = 15
\(\frac{3}{20}\) = 15%
Explanation:
The given fraction can be converted into simple percentage. Here the denominator of the given fraction 20 is evenly divided into 100. Divide 100 by 20 the quotient is equal to 5. Multiply the numerator 3 with the quotient 5 the product is equal to 15. Now add the percent sign. So\(\frac{3}{20}\) is equal to 15%.

Question 3.
\(\frac{7}{15}\) = ________________
Answer:
\(\frac{7}{15}\) = ?%
\(\frac{100}{15}\) = 6.66
7 x 6.66 = 46.7
\(\frac{7}{15}\) = 46.7%
Explanation:
The given fraction cannot be converted into simple percentage. Here the denominator of the given fraction 15 is not evenly divided into 100. Divide 100 by 15 the quotient is equal to 6.66. Multiply the numerator 7 with the quotient 6.66 the product is equal to 46.7. Now add the percent sign. So\(\frac{7}{15}\) is equal to 46.7%.

Question 4.
\(\frac{3}{10}\) = ________________
Answer:
\(\frac{3}{10}\) = ?%
\(\frac{100}{10}\) = 10
3 x 10= 30
\(\frac{3}{10}\) = 30%
Explanation:
The given fraction can be converted into simple percentage. Here the denominator of the given fraction 10 is evenly divided into 100. Divide 100 by 10 the quotient is equal to 10. Multiply the numerator 3 with the quotient 10 the product is equal to 30. Now add the percent sign. So\(\frac{3}{10}\) is equal to 30%.

Question 5.
\(\frac{2}{3}\) = ________________
Answer:
\(\frac{2}{3}\) = ?%
\(\frac{100}{3}\) = 33.3
2 x 33.3 = 66.6
\(\frac{2}{3}\) = 66.6%
Explanation:
The given fraction cannot be converted into simple percentage. Here the denominator of the given fraction 3 is not evenly divided into 100. Divide 100 by 3 the quotient is equal to 33.3. Multiply the numerator 2 with the quotient 33.3. the product is equal to 66.6. Now add the percent sign. So\(\frac{2}{3}\) is equal to 66.6%.

Question 6.
\(\frac{3}{4}\) = ________________
Answer:
\(\frac{3}{4}\) = ?%
\(\frac{100}{4}\) = 25
3 x 25 = 75
\(\frac{3}{4}\) = 75%
Explanation:
The given fraction can be converted into simple percentage. Here the denominator of the given fraction 4 is evenly divided into 100. Divide 100 by 4 the quotient is equal to 25. Multiply the numerator 3 with the quotient 25 the product is equal to 75. Now add the percent sign. So\(\frac{3}{4}\) is equal to 75%.

Question 7.
\(\frac{6}{11}\) = ________________
Answer:
\(\frac{6}{11}\) = ?%
\(\frac{100}{11}\) = 9.09
6 x 9.09 = 54.5
\(\frac{6}{11}\) = 54.5%
Explanation:
The given fraction cannot be converted into simple percentage. Here the denominator of the given fraction 11 is not evenly divided into 100. Divide 100 by 11 the quotient is equal to 9.09. Multiply the numerator 6 with the quotient 9.09 the product is equal to 54.5. Now add the percent sign. So\(\frac{6}{11}\) is equal to 54.5%.

Question 8.
1 = ________________
Answer:
\(\frac{1}{1}\) = ?%
\(\frac{100}{1}\) = 100
1 x 100 = 100
\(\frac{1}{1}\) = 100%
Explanation:
The given fraction can be converted into simple percentage. Here the denominator of the given fraction 1 is evenly divided into 100. Divide 100 by 1 the quotient is equal to 100. Multiply the numerator 1 with the quotient 100 the product is equal to 100. Now add the percent sign. So\(\frac{1}{1}\) is equal to 100%.

Question 9.
\(\frac{1}{32}\) = ________________
Answer:
\(\frac{1}{32}\) = ?%
\(\frac{100}{32}\) = 3.1
1 x 3.1 = 3.1
\(\frac{1}{32}\) = 3.1%
Explanation:
The given fraction cannot be converted into simple percentage. Here the denominator of the given fraction 32 is not evenly divided into 100. Divide 100 by 32 the quotient is equal to 3.1. Multiply the numerator 1 with the quotient 3.1 the product is equal to 3.1. Now add the percent sign. So\(\frac{1}{32}\) is equal to 3.1%.

Question 10.
\(\frac{4}{25}\) = ________________
Answer:
\(\frac{4}{25}\) = ?%
\(\frac{100}{25}\) = 4
4 x 4 = 16
\(\frac{4}{25}\) = 16%
Explanation:
The given fraction can be converted into simple percentage. Here the denominator of the given fraction 25 is evenly divided into 100. Divide 100 by 25 the quotient is equal to 4. Multiply the numerator 4 with the quotient 4 the product is equal to 16. Now add the percent sign. So\(\frac{4}{25}\) is equal to 16%.

Question 11.
\(\frac{19}{50}\) = ________________
Answer:
\(\frac{19}{50}\) = ?%
\(\frac{100}{50}\) = 2
19 x 2 = 38
\(\frac{19}{50}\) = 38%
Explanation:
The given fraction can be converted into simple percentage. Here the denominator of the given fraction 50 is evenly divided into 100. Divide 100 by 50 the quotient is equal to 2. Multiply the numerator 19 with the quotient 2 the product is equal to 38. Now add the percent sign. So\(\frac{19}{50}\) is equal to 38%.

Question 12.
\(\frac{3}{50}\) = ________________
Answer:
\(\frac{3}{50}\) = ?%
\(\frac{100}{50}\) = 2
3 x 2 = 6
\(\frac{3}{50}\) = 6%
Explanation:
The given fraction can be converted into simple percentage. Here the denominator of the given fraction 50 is evenly divided into 100. Divide 100 by 50 the quotient is equal to 2. Multiply the numerator 3 with the quotient 2 the product is equal to 6. Now add the percent sign. So\(\frac{3}{50}\) is equal to 6%.

Question 13.
\(\frac{14}{10}\) = ________________
Answer:
\(\frac{14}{10}\) = ?%
\(\frac{100}{10}\) = 10
14 x 10 = 140
\(\frac{14}{10}\) = 140%
Explanation:
The given fraction can be converted into simple percentage. Here the denominator of the given fraction 10 is evenly divided into 100. Divide 100 by 10 the quotient is equal to 10. Multiply the numerator 14 with the quotient 10 the product is equal to 140. Now add the percent sign. So\(\frac{14}{10}\) is equal to 140%.

Question 14.
\(\frac{11}{20}\) = ________________
Answer:
\(\frac{11}{20}\) = ?%
\(\frac{100}{20}\) = 5
11 x 5 = 55
\(\frac{11}{20}\) = 55%
Explanation:
The given fraction can be converted into simple percentage. Here the denominator of the given fraction 20 is evenly divided into 100. Divide 100 by 20 the quotient is equal to 5. Multiply the numerator 11 with the quotient 5 the product is equal to 55. Now add the percent sign. So\(\frac{11}{20}\) is equal to 55%.

Question 15.
\(\frac{3}{25}\) = ________________
Answer:
\(\frac{3}{25}\) = ?%
\(\frac{100}{25}\) = 4
3 x 4 = 12
\(\frac{3}{25}\) = 12%
Explanation:
The given fraction can be converted into simple percentage. Here the denominator of the given fraction 25 is evenly divided into 100. Divide 100 by 25 the quotient is equal to 4. Multiply the numerator 3 with the quotient 4 the product is equal to 12. Now add the percent sign. So\(\frac{3}{25}\) is equal to 12%.

Question 16.
\(\frac{4}{9}\) = ________________
Answer:
\(\frac{4}{9}\) = ?%
\(\frac{100}{9}\) = 11.11
4 x 11.11 = 44.4
\(\frac{4}{9}\) = 44.4%
Explanation:
The given fraction cannot be converted into simple percentage. Here the denominator of the given fraction 9 is not evenly divided into 100. Divide 100 by 9 the quotient is equal to 11.11. Multiply the numerator 4 with the quotient 11.11 the product is equal to 44.4. Now add the percent sign. So\(\frac{4}{9}\) is equal to 44.4%.

Question 17.
\(\frac{7}{20}\) = ________________
Answer:
\(\frac{7}{20}\) = ?%
\(\frac{100}{20}\) = 5
7 x 5 = 35
\(\frac{7}{20}\) = 35%
Explanation:
The given fraction can be converted into simple percentage. Here the denominator of the given fraction 20 is evenly divided into 100. Divide 100 by 20 the quotient is equal to 5. Multiply the numerator 7 with the quotient 5 the product is equal to 35. Now add the percent sign. So\(\frac{7}{20}\) is equal to 35%.

Question 18.
200 = ______________
Answer:
\(\frac{200}{1}\) = ?%
\(\frac{100}{1}\) = 100
200 x 100 = 20000
\(\frac{200}{1}\) = 20000%
Explanation:
The given fraction can be converted into simple percentage. Here the denominator of the given fraction 1 is evenly divided into 100. Divide 100 by 1 the quotient is equal to 100. Multiply the numerator 200 with the quotient 100 the product is equal to 20000. Now add the percent sign. So\(\frac{200}{1}\) is equal to 20000%.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 12.4 Dividing Money existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 12.4 Dividing Money

Exercises Divide

Round to the nearest cent.

Question 1.

Answer:
$15÷$3 = $5.

Explanation:
The quotient of $15÷$3 is $5 and the nearest cent is $5.0.

Question 2.

Answer:
$56÷$5 is $11.20.

Explanation:
The quotient of $56÷$5 is $11.2 and the nearest cent is $11.20.

Question 3.

Answer:
$89÷$3.25 = $27.38.

Explanation:
The quotient of $89÷$3.25 is $27.384 and the nearest cent is $27.38.

Question 4.

Answer:
$10÷2.3 = $4.347.

Explanation:
The quotient of $10÷2.3 is $4.347 and the nearest cent is $4.35.

Question 5.

Answer:
$4.25÷5.5 = $0.772.

Explanation:
The quotient of $4.25÷5.5 is $0.772 and the nearest cent is $0.77.

Question 6.

Answer:
$25.25÷$4.50 is $5.611.

Explanation:
The quotient of $25.25÷$4.50 is $5.611 and the nearest cent is $5.61.

Question 7.

Answer:
$78.89÷2.1 is $37.566.

Explanation:
The quotient of $78.89÷2.1 is $37.566 and the nearest cent is $37.57.

Question 8.

Answer:
$42.50÷$8.25 = $5.151.

Explanation:
The quotient of $42.50÷$8.25 is $5.151 and the nearest cent is $5.15.

Question 9.

Answer:
$45.45÷5.5 is $8.263.

Explanation:
The quotient of $45.45÷5.5 is $8.263 and the nearest cent is $8.26.

Question 10.

Answer:
$5.01÷$2.33 is $2.150.

Explanation:
The quotient of $5.01÷$2.33 is $2.150 and the nearest cent is $2.15.

Question 11.

Answer:

Explanation:
The quotient of $15÷$3 is $5 and the nearest cent is

Question 12.

Answer:
$9800.12÷10.2 = $960.796.

Explanation:
The quotient of $9800.12÷10.2 is $960.796 and the nearest cent is $960.80.

Question 13.

Answer:
$96.65÷$5.55 = $17.414.

Explanation:
The quotient of $96.65÷$5.55 is $17.414 and the nearest cent is $17.41.

Question 14.

Answer:
$45.12÷$6.51 is $6.930.

Explanation:
The quotient of $45.12÷$6.51 is $6.930 and the nearest cent is $6.93.

Question 15.

Answer:
$99.50÷$7.55 = $13.178.

Explanation:
The quotient of $99.50÷$7.55 is $13.178 and the nearest cent is $13.18.

Question 16.

Answer:
$8.88÷4.1 is $2.165.

Explanation:
The quotient of $8.88÷4.1 is $2.165 and the nearest cent is $2.17.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 12.3 Dividing Decimals by Decimals existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 12.3 Dividing Decimals by Decimals

Exercises Divide

Round to the nearest ten-thousandth.

Question 1.

Answer:
11.2÷-4.5 = -002.488.

Explanation:
The quotient of 11.2÷-4.5 is -002.488, so the nearest ten thousand will be -2.4889.

Question 2.

Answer:
5.7÷2.5 is 2.28000.

Explanation:
The quotient of 5.7÷2.5 is 2.28000, so the nearest ten thousand will be 2.2800.

Question 3.

Answer:
88.3÷8.1 = 10.90123.

Explanation:
The quotient of 88.3÷8.1 is 10.90123, so the nearest ten thousand will be 10.9012.

Question 4.

Answer:
4.5÷2.1 = 02.14285.

Explanation:
The quotient of 4.5÷2.1 is 02.14285, so the nearest ten thousand will be 2.1429.

Question 5.

Answer:
5.98÷7.88 is 0.75888.

Explanation:
The quotient of 5.98÷7.88 is 0.75888, so the nearest ten thousand will be 0.7589.

Question 6.

Answer:
17.1÷2.33 is 7.33905.

Explanation:
The quotient of 17.1÷2.33 is 7.33905, so the nearest ten thousand will be 7.3390.

Question 7.

Answer:
8.56÷-2.3 = -3.72173.

Explanation:
The quotient of 8.56÷-2.3 is -3.72173, so the nearest ten thousand will be -3.7217.

Question 8.

Answer:
5.12÷2.222 = 02.30423.

Explanation:
The quotient of 5.12÷2.222 is 02.30423, so the nearest ten thousand will be 02.3042.

Question 9.

Answer:
4.6÷3.41 = 01.34897.

Explanation:
The quotient of 4.6÷3.41 is 01.34897, so the nearest ten thousand will be 1.3490.

Question 10.

Answer:
6.54÷-2.11 is -3.09952.

Explanation:
The quotient of 6.54÷-2.11 is -3.09952, so the nearest ten thousand will be -3.0995.

Question 11.

Answer:
6.01÷2.37 = 02.53586.

Explanation:
The quotient of 6.01÷2.37 is 02.53586, so the nearest ten thousand will be 02.5359.

Question 12.

Answer:
6.44÷5.55 = 1.16036.

Explanation:
The quotient of 6.44÷5.55 is 1.16036, so the nearest ten thousand will be 1.1603.

Question 13.

Answer:
9.1÷3.03 is 3.00330.

Explanation:
The quotient of 9.1÷3.03 is 3.00330, so the nearest ten thousand will be 3.0033.

Question 14.

Answer:
987.1÷2.1 is 470.04761.

Explanation:
The quotient of 987.1÷2.1 is 470.04761, so the nearest ten thousand will be 470.0476.

Question 15.

Answer:
8.89÷3.71 = 2.39622.

Explanation:
The quotient of 8.89÷3.71 is 2.39622, so the nearest ten thousand will be 2.3962.

Question 16.

Answer:
56.98÷-2.45 = -23.25714.

Explanation:
The quotient of 56.98÷-2.45 is -23.25714, so the nearest ten thousand will be -23.2571.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 4.4 Multiplying Mixed Numbers to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 4.4 Multiplying Mixed Numbers

Exercises Multiply

Question 1.
5\(\frac{1}{2}\) × 3\(\frac{3}{4}\)
Answer:
20\(\frac{5}{8}\),

Explanation:
We have 5\(\frac{1}{2}\) X 3\(\frac{3}{4}\),
Step 1:
Change the mixed number into improper fraction as
\(\frac{5 X 2  +  1}{2}\) = \(\frac{11}{2}\) and
3\(\frac{3}{4}\) = \(\frac{3 X 4 + 3}{4}\) = \(\frac{15}{4}\),
Step 2:
Multiplying the fractions as \(\frac{11}{2}\) X \(\frac{15}{4}\) = \(\frac{11 X 15}{2 X 4}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{165}{8}\) = \(\frac{20 X 8 + 5}{8}\) = 20\(\frac{5}{8}\).

Question 2.
2\(\frac{1}{3}\) × 2\(\frac{4}{5}\)
Answer:
6\(\frac{8}{15}\),

Explanation:
We have 2\(\frac{1}{3}\) X 2\(\frac{4}{5}\),
Step 1:
Change the mixed number into improper fraction as
\(\frac{6 X 3  +  1}{3}\) = \(\frac{2 X 5 + 4}{5}\),
Step 2:
Multiplying the fractions as \(\frac{7}{3}\) X \(\frac{14}{5}\) =
\(\frac{7 X 14}{3  X  5}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{98}{15}\) = \(\frac{15 X 6 + 8}{15}\) = 6\(\frac{8}{15}\).

Question 3.
8\(\frac{1}{5}\) × 3\(\frac{1}{7}\)
Answer:
25\(\frac{27}{35}\),

Explanation:
We have 8\(\frac{1}{5}\) X 3\(\frac{1}{7}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{8 X 5  +  1}{5}\) = \(\frac{41}{5}\) and
3\(\frac{1}{7}\) = \(\frac{3 X 7 + 1}{7}\) = \(\frac{22}{7}\),
Step 2:
Multiplying the fractions as \(\frac{41}{5}\) X \(\frac{22}{7}\) =
\(\frac{41 X 22}{5  X  7}\) = \(\frac{902}{35}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{902}{35}\) = \(\frac{25 X 35 + 27}{35}\) = 25\(\frac{27}{35}\).

Question 4.
1\(\frac{3}{4}\) × 12\(\frac{1}{3}\)
Answer:
21\(\frac{7}{12}\),

Explanation:
We have 1\(\frac{3}{4}\) X 12\(\frac{1}{3}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{1 X 4 + 3}{4}\) = \(\frac{7}{4}\) and
12\(\frac{1}{3}\) = \(\frac{12 X 3 + 1}{3}\) = \(\frac{37}{3}\),
Step 2:
Multiplying the fractions as \(\frac{7}{4}\) X \(\frac{37}{3}\) =
\(\frac{7 X 37}{4  X  3}\) = \(\frac{259}{12}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{259}{12}\) = \(\frac{21 X 12 + 7}{12}\) = 21\(\frac{7}{12}\).

Question 5.
2\(\frac{1}{2}\) × 4\(\frac{2}{3}\)
Answer:
11\(\frac{2}{3}\),

Explanation:
We have 2\(\frac{1}{2}\) X 4\(\frac{2}{3}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{2 X 2 + 1}{2}\) = \(\frac{5}{2}\) and
4\(\frac{2}{3}\) = \(\frac{4 X 3 + 2}{3}\) = \(\frac{14}{3}\),
Step 2:
Multiplying the fractions as \(\frac{5}{2}\) X \(\frac{14}{3}\) =
\(\frac{5 X 14}{2 X 3}\) = \(\frac{70}{6}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{70}{6}\) = \(\frac{35}{3}\) = 11\(\frac{2}{3}\).

Question 6.
3\(\frac{1}{8}\) × 3\(\frac{1}{7}\)
Answer:
9\(\frac{23}{28}\),

Explanation:
We have 3\(\frac{1}{8}\) X 3\(\frac{1}{7}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{3 X 8 + 1}{8}\) = \(\frac{25}{8}\) and
3\(\frac{1}{7}\) = \(\frac{3 X 7 + 1}{7}\) = \(\frac{22}{7}\),
Step 2:
Multiplying the fractions as \(\frac{25}{2}\) X \(\frac{22}{7}\) =
\(\frac{25 X 22}{8 X 7}\) = \(\frac{550}{56}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{550}{56}\) = \(\frac{275}{28}\) =
9\(\frac{23}{28}\).

Question 7.
11\(\frac{1}{5}\) × 6\(\frac{2}{3}\)
Answer:
74\(\frac{2}{3}\),

Explanation:
We have 11\(\frac{1}{5}\) X 6\(\frac{2}{3}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{11 X 5 + 1}{5}\) = \(\frac{56}{5}\) and
6\(\frac{2}{3}\) = \(\frac{6 X 3 + 2}{3}\) = \(\frac{20}{3}\),
Step 2:
Multiplying the fractions as \(\frac{56}{5}\) X \(\frac{20}{3}\) =
\(\frac{56 X 20}{5 X 3}\) = \(\frac{1,120}{15}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{1,120}{15}\) = \(\frac{56 X 5 X 4}{5 X 3}\) = \(\frac{224}{3}\) = 74\(\frac{2}{3}\).

Question 8.
9\(\frac{1}{2}\) × 5\(\frac{1}{5}\)
Answer:
49\(\frac{2}{5}\),

Explanation:
We have 9\(\frac{1}{2}\) X 5\(\frac{1}{5}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{9 X 2 + 1}{2}\) = \(\frac{19}{2}\) and
5\(\frac{1}{5}\) = \(\frac{5 X 5 + 1}{5}\) = \(\frac{26}{5}\),
Step 2:
Multiplying the fractions as \(\frac{19}{2}\) X \(\frac{26}{5}\) =
\(\frac{19 X 26}{2 X 5}\) = \(\frac{494}{10}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{494}{10}\) = \(\frac{247 X 2}{5 X 2}\) = \(\frac{247}{5}\) = 49\(\frac{2}{5}\).

Question 9.
1\(\frac{2}{3}\) × 7\(\frac{1}{5}\)
Answer:
12,

Explanation:
We have 1\(\frac{2}{3}\) X 7\(\frac{1}{5}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{1 X 3 + 2}{3}\) = \(\frac{5}{3}\) and
7\(\frac{1}{5}\) = \(\frac{7 X 5 + 1}{5}\) = \(\frac{36}{5}\),
Step 2:
Multiplying the fractions as \(\frac{5}{3}\) X \(\frac{36}{5}\) =
\(\frac{5 X 36}{3 X 5}\) = \(\frac{180}{15}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{180}{15}\) = \(\frac{15 X 12 }{15}\)= 12.

Question 10.
8\(\frac{3}{4}\) × 3\(\frac{1}{2}\)
Answer:
23\(\frac{5}{8}\),

Explanation:
We have 8\(\frac{3}{4}\) X 3\(\frac{1}{2}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{8 X 4 + 3}{4}\) = \(\frac{27}{4}\) and
3\(\frac{1}{2}\) = \(\frac{3 X 2 + 1}{2}\) = \(\frac{7}{2}\),
Step 2:
Multiplying the fractions as \(\frac{27}{4}\) X \(\frac{7}{2}\) =
\(\frac{27 X 7}{4 X 2}\) = \(\frac{189}{8}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{189}{8}\) = \(\frac{23 X 8 + 5}{8}\) = 23\(\frac{5}{8}\).

Question 11.
3\(\frac{5}{8}\) × 5\(\frac{1}{4}\)
Answer:
19\(\frac{1}{32}\),

Explanation:
We have 3\(\frac{5}{8}\) X 5\(\frac{1}{4}\),
Step 1:
Change the mixed number into improper fraction as
\(\frac{3 X 8 + 5}{8}\) = \(\frac{29}{8}\) and
5\(\frac{1}{4}\) = \(\frac{5 X 4 + 1}{4}\) = \(\frac{21}{4}\),
Step 2:
Multiplying the fractions as \(\frac{29}{8}\) X \(\frac{21}{4}\) = \(\frac{29 X 21}{8 X 4}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{609}{32}\) = \(\frac{19 X 32 + 1}{32}\) = 19\(\frac{1}{32}\).

Question 12.
4\(\frac{2}{3}\) × 4\(\frac{1}{2}\)
Answer:
21,

Explanation:
We have 4\(\frac{2}{3}\) X 4\(\frac{1}{2}\),
Step 1:
Change the mixed number into improper fraction as
\(\frac{4 X 3 + 2}{3}\) = \(\frac{14}{3}\) and
4\(\frac{1}{2}\) = \(\frac{4 X 2 + 1}{2}\) = \(\frac{9}{2}\),
Step 2:
Multiplying the fractions as \(\frac{14}{3}\) X \(\frac{9}{2}\) = \(\frac{14 X 9}{3 X 2}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{126}{6}\) = 21.

Question 13.
3\(\frac{1}{5}\) × 2\(\frac{1}{10}\)
Answer:
6\(\frac{18}{25}\),

Explanation:
We have 3\(\frac{1}{5}\) X 2\(\frac{1}{10}\),
Step 1:
Change the mixed number into improper fraction as
\(\frac{3 X 5 + 1}{5}\) = \(\frac{16}{5}\) and
2\(\frac{1}{10}\) = \(\frac{2 X 10 + 1}{10}\) = \(\frac{21}{10}\),
Step 2:
Multiplying the fractions as \(\frac{16}{5}\) X \(\frac{21}{10}\) = \(\frac{16 X 21}{5 X 10}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{336}{50}\) = \(\frac{2 X 168}{2 X 25}\) = \(\frac{168}{25}\) = 6\(\frac{18}{25}\).

Question 14.
10\(\frac{4}{5}\) × 2\(\frac{1}{11}\)
Answer:
22\(\frac{32}{55}\),

Explanation:
We have 10\(\frac{4}{5}\) X 2\(\frac{1}{11}\),
Step 1:
Change the mixed number into improper fraction as
\(\frac{10 X 5 + 4}{5}\) = \(\frac{54}{5}\) and
2\(\frac{1}{11}\) = \(\frac{2 X 11 + 1}{11}\) = \(\frac{23}{11}\),
Step 2:
Multiplying the fractions as \(\frac{54}{5}\) X \(\frac{23}{11}\) = \(\frac{1,242}{55}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{1,242}{55}\) = \(\frac{22 X 55 + 32}{55}\) = 22\(\frac{32}{55}\).

Question 15.
22\(\frac{5}{9}\) × 1\(\frac{3}{5}\)
Answer:
36\(\frac{4}{45}\),

Explanation:
We have 22\(\frac{5}{9}\) X 1\(\frac{3}{5}\),
Step 1:
Change the mixed number into improper fraction as
\(\frac{22 X 9 + 5}{9}\) = \(\frac{203}{9}\) and
1\(\frac{3}{5}\) = \(\frac{1 X 5 + 3}{5}\) = \(\frac{8}{5}\),
Step 2:
Multiplying the fractions as \(\frac{203}{9}\) X \(\frac{8}{5}\) = \(\frac{203 X 8}{9 X 5}\) = \(\frac{1,624}{45}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{1,624}{45}\) = \(\frac{1,624}{45}\) = \(\frac{36 X 45 + 4}{45}\) = 36\(\frac{4}{45}\).

Question 16.
14\(\frac{3}{4}\) × 2\(\frac{5}{7}\)
Answer:
40\(\frac{1}{28}\),

Explanation:
We have 14\(\frac{3}{4}\) X 2\(\frac{5}{7}\),
Step 1:
Change the mixed number into improper fraction as
\(\frac{14 X 4 + 3}{4}\) = \(\frac{59}{4}\) and
2\(\frac{5}{7}\) = \(\frac{2 X 7 + 5}{7}\) = \(\frac{19}{7}\),
Step 2:
Multiplying the fractions as \(\frac{59}{4}\) X \(\frac{19}{7}\) = \(\frac{59 X 19}{4 X 7}\) = \(\frac{1,121}{28}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{1,121}{28}\) = \(\frac{40 X 28 + 1}{28}\) = 40\(\frac{1}{28}\).

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 4.3 Multiplying Fractions and Mixed Numbers to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 4.3 Multiplying Fractions and Mixed Numbers

Exercises Multiply

Question 1.
6\(\frac{3}{4}\) × \(\frac{1}{9}\)
Answer:
\(\frac{3}{4}\),

Explanation:
We have 6\(\frac{3}{4}\) X \(\frac{1}{9}\),
Step 1:
Change the mixed number into improper fraction as
\(\frac{6 X 4  +  3}{4}\) = \(\frac{27}{4}\),
Step 2:
Multiplying the fractions as \(\frac{27}{4}\) X \(\frac{1}{9}\) = \(\frac{27 X 1}{4  X  9}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{27}{36}\) = \(\frac{9 X 3}{9 X 4}\) = \(\frac{3}{4}\).

Question 2.
\(\frac{1}{10}\) × 4\(\frac{1}{6}\)
Answer:
\(\frac{5}{12}\),

Explanation:
We have \(\frac{1}{10}\) X 4\(\frac{1}{6}\),
Step 1:
Change the mixed number into improper fraction as
\(\frac{4 X 6  +  1}{6}\) = \(\frac{25}{6}\),
Step 2:
Multiplying the fractions as \(\frac{1}{10}\) X \(\frac{25}{6}\) = \(\frac{1 X 25}{10 X  6}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{25}{60}\) = \(\frac{5 X 5}{5 X 2 X 6}\) = \(\frac{5}{12}\).

Question 3.
12\(\frac{1}{4}\) × \(\frac{2}{7}\)
Answer:
14,

Explanation:
We have 12\(\frac{1}{4}\) X \(\frac{2}{7}\),
Step 1:
Change the mixed number into improper fraction as
\(\frac{12 X 4  +  1}{4}\) = \(\frac{49}{4}\),
Step 2:
Multiplying the fractions as \(\frac{49}{4}\) X \(\frac{2}{7}\) = \(\frac{49 X 4}{2 X 7}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{7 X 7 X 2 X 2}{2 X 7}\) = 7 X 2 = 14.

Question 4.
3\(\frac{1}{7}\) × \(\frac{14}{11}\)
Answer:
4,

Explanation:
We have 3\(\frac{1}{7}\) X \(\frac{14}{11}\),
Step 1:
Change the mixed number into improper fraction as
\(\frac{3 X 7  +  1}{7}\) = \(\frac{22}{7}\),
Step 2:
Multiplying the fractions as \(\frac{22}{7}\) X \(\frac{14}{11}\) = \(\frac{22 X 14}{7 X  11}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{308}{77}\) = \(\frac{4 X 11 X 7}{7 X 11}\) = 4.

Question 5.
\(\frac{2}{5}\) × 3\(\frac{3}{4}\)
Answer:
\(\frac{3}{2}\),

Explanation:
We have \(\frac{2}{5}\) X 3\(\frac{3}{4}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{3 X 4  +  3}{4}\) = \(\frac{15}{4}\),
Step 2:
Multiplying the fractions as \(\frac{2}{5}\) X \(\frac{15}{4}\) = \(\frac{2 X 15}{ X  11}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{308}{77}\) = \(\frac{4 X 11 X 7}{7 X 11}\) = 4.

Question 6.
4\(\frac{5}{7}\) × \(\frac{7}{11}\)
Answer:
3,

Explanation:
We have 4\(\frac{5}{7}\) X \(\frac{7}{11}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{4 X 7  +  5}{7}\) = \(\frac{33}{7}\),
Step 2:
Multiplying the fractions as \(\frac{33}{7}\) X \(\frac{7}{11}\) = \(\frac{221}{77}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{221}{77}\) = \(\frac{3 X 11 X 7}{7 X 11}\) = 3.

Question 7.
4\(\frac{2}{5}\) × \(\frac{3}{11}\)
Answer:
\(\frac{6}{5}\) = 1\(\frac{1}{5}\),

Explanation:
We have 4\(\frac{2}{5}\) X \(\frac{3}{11}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{4 X 5  + 2}{5}\) = \(\frac{22}{5}\),
Step 2:
Multiplying the fractions as \(\frac{22}{5}\) X \(\frac{3}{11}\) = \(\frac{66}{55}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{66}{55}\) = \(\frac{6 X 11}{5 X 11}\) = \(\frac{6}{5}\)
as numerator is greater than denominator \(\frac{1 X 5 + 1}{5}\) = 1\(\frac{1}{5}\).

Question 8.
3\(\frac{1}{4}\) × \(\frac{4}{13}\)
Answer:
1,

Explanation:
We have 3\(\frac{1}{4}\) X \(\frac{4}{13}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{3 X 4  +  1}{4}\) = \(\frac{13}{4}\),
Step 2:
Multiplying the fractions as \(\frac{13}{4}\) X \(\frac{4}{13}\) = 3.

Question 9.
3\(\frac{3}{5}\) × \(\frac{10}{9}\)
Answer:
4,

Explanation:
We have 3\(\frac{3}{5}\) X \(\frac{10}{9}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{3 X 5  +  3}{5}\) = \(\frac{18}{5}\),
Step 2:
Multiplying the fractions as \(\frac{18}{5}\) X \(\frac{10}{9}\) = \(\frac{180}{45}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{180}{45}\) = \(\frac{45 X 4}{45}\) = 4.

Question 10.
\(\frac{3}{13}\) × 4\(\frac{1}{3}\)
Answer:
1,

Explanation:
We have \(\frac{3}{13}\) X 4\(\frac{1}{3}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{4 X 3  +  1}{3}\) = \(\frac{13}{3}\),
Step 2:
Multiplying the fractions as \(\frac{3}{13}\) X \(\frac{13}{3}\) = 1.

Question 11.
3\(\frac{2}{3}\) × \(\frac{2}{11}\)
Answer:
\(\frac{2}{3}\),

Explanation:
We have 3\(\frac{2}{3}\) X \(\frac{2}{11}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{3 X 3  +  2}{3}\) = \(\frac{11}{3}\),
Step 2:
Multiplying the fractions as \(\frac{11}{3}\) X \(\frac{2}{11}\) = \(\frac{22}{33}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{22}{33}\) = \(\frac{2 X 11}{3 X 11}\) = \(\frac{2}{3}\).

Question 12.
5\(\frac{1}{5}\) × \(\frac{3}{13}\)
Answer:
\(\frac{6}{5}\),

Explanation:
We have 5\(\frac{1}{5}\) X \(\frac{3}{13}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{5 X 5 + 1}{5}\) = \(\frac{26}{5}\),
Step 2:
Multiplying the fractions as \(\frac{26}{5}\) X \(\frac{3}{13}\) = \(\frac{78}{65}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{78}{65}\) = \(\frac{6 X 13}{5 X 13}\) =\(\frac{6}{5}\).

Question 13.
5\(\frac{1}{4}\) × \(\frac{1}{3}\)
Answer:
\(\frac{7}{4}\),

Explanation:
We have 5\(\frac{1}{4}\) X \(\frac{1}{3}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{5 X 4  +  1}{4}\) = \(\frac{21}{4}\),
Step 2:
Multiplying the fractions as \(\frac{26}{5}\) X \(\frac{3}{13}\) = \(\frac{78}{65}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{78}{65}\) = \(\frac{6 X 13}{5 X 13}\) =\(\frac{6}{5}\).

Question 14.
2\(\frac{4}{5}\) × \(\frac{2}{7}\)
Answer:
\(\frac{4}{5}\),

Explanation:
We have 2\(\frac{4}{5}\) X \(\frac{2}{7}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{2 X 5  + 4}{5}\) = \(\frac{14}{5}\),
Step 2:
Multiplying the fractions as \(\frac{14}{5}\) X \(\frac{2}{7}\) = \(\frac{28}{35}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{28}{35}\) = \(\frac{7 X 4}{7 X 5}\) =\(\frac{4}{5}\).

Question 15.
2\(\frac{1}{4}\) × \(\frac{3}{10}\)
Answer:
\(\frac{27}{40}\),

Explanation:
We have 2\(\frac{1}{4}\) X \(\frac{3}{10}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{2 X 4  +  1}{4}\) = \(\frac{9}{4}\),
Step 2:
Multiplying the fractions as \(\frac{9}{4}\) X \(\frac{3}{10}\) = \(\frac{27}{40}\) as numerator is smaller we cannot reduce further.

Question 16.
3\(\frac{1}{3}\) × \(\frac{3}{5}\)
Answer:
2,

Explanation:
We have 3\(\frac{1}{3}\) X \(\frac{3}{5}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{3 X 3 + 1}{3}\) = \(\frac{10}{3}\),
Step 2:
Multiplying the fractions as \(\frac{10}{3}\) X \(\frac{3}{5}\) = 2.

Question 17.
Thomas can walk on his hands 20\(\frac{2}{5}\) yards in a minute. How far can he go in \(\frac{3}{4}\) minutes?
Answer:
Thomas can walk 15\(\frac{3}{10}\) minutes,

Explanation:
As Thomas can walk on his hands 20\(\frac{2}{5}\) yards in a minute.
Far can he go in \(\frac{3}{4}\) minutes is 20\(\frac{2}{5}\) X \(\frac{3}{5}\)
Step 1:
Change the mixed number into improper fraction as
\(\frac{20 X 5  + 2}{5}\) = \(\frac{102}{15}\),
Step 2:
Multiplying the fractions as \(\frac{102}{15}\) X \(\frac{3}{5}\) = \(\frac{306}{75}\),
Step 3:
Convert the improper fraction to a mixed number and reduce
\(\frac{306}{75}\) = \(\frac{153}{10}\) = 15\(\frac{3}{10}\).
Therefore, Thomas can walk 15\(\frac{3}{10}\) minutes,

Question 18.
Peyton plays a round of golf in 3\(\frac{3}{8}\) hours. How long would it take him to play \(\frac{2}{3}\) rounds of golf?
Answer:
Peyton took 2\(\frac{1}{4}\) rounds of golf’s,

Explanation:
Given Peyton plays a round of golf in 3\(\frac{3}{8}\) hours. Long would it take him to play \(\frac{2}{3}\) rounds of golf is 3\(\frac{3}{8}\) X \(\frac{2}{3}\), So \(\frac{3 X 8 + 3}{8}\) X \(\frac{2}{3}\) = \(\frac{27}{8}\) X \(\frac{2}{3}\) = \(\frac{27 X 2}{8 X 3}\) = \(\frac{54}{24}\) both goes by 6 we get \(\frac{6 X 9}{6 X 4}\) = \(\frac{9}{4}\) =
as numerator is more than denominator \(\frac{2 X 4 + 1}{4}\) = 2\(\frac{1}{4}\). Peyton took 2\(\frac{1}{4}\) rounds of golf’s.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 14.3 Unit Rate existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 14.3 Unit Rate

Exercises

SOLVE

The graph below shows the distance Isabella rides her bicycle over time.

Question 1.
Which coordinates (point) on the graph show the unit rate?
Answer:
The coordinate (1,10) shows the unit rate on the graph.

Question 2.
What is the unit rate shown in the graph?
Answer:
The unit rate shown in the graph is 10.
The value for y at which the x coordinate is equal to 1 is called the unit rate.

Question 3.
If the graph also included a line to show how far Isabella walked over time at a rate of 3 miles per hour, would that line be above or below the one on the graph?
Answer:
If the graph also included a line to show how far Isabella walked over time at a rate of 3 miles per hour then the line be below the one on the graph.

Question 4.
Are the quantities in the table above proportional?
Answer:
Yes, the quantities in the above table are proportional.

Question 5.
What is the unit rate?
Answer:
The unit rate shown in the above table is 3.00.
The value for price at which the gallons of milk is equal to 1 is called the unit rate.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 14.2 Graphing Relationships existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 14.2 Graphing Relationships

Exercises

SOLVE

Vicki can read 2 pages in 3 minutes. Bruce can read 4 pages in 3 minutes.

Question 1.
Complete the chart below to show this relationship.

Answer:

Pages read by Vicki in 1 minute:
3 minutes = 2 pages
1 minute = y pages
3 x y = 2 x 1
3y = 2
Divide both sides of the equation by 3.
3y/3 = 2/3
y = 2/3
Pages read by Vicki in 6 minute:
3 minutes = 2 pages
6 minute = z pages
3 x z = 6 x 2
3z = 12
Divide both sides of the equation by 3.
3z/3 = 12/3
z = 4
Pages read by Bruce in 1 minute:
3 minutes = 4 pages
1 minute = y pages
3 x y = 4 x 1
Divide both sides of the equation by 3.
3y/3 = 4/3
y = 4/3
Pages read by Bruce in 6 minute:
3 minutes = 4 pages
6 minute = z pages
3 x z = 6 x 4
3z = 24
Divide both sides of the equation by 3.
3z/3 = 24/3
z = 8

Question 2.
Graph the relationship on the grid. Label each axis. Be sure to use different colors or styles of line so that you can tell the difference. Include a legend to describe which hue is for which person.

Answer:

The time is represented in x-axis and pages read by Vicki and Bruce are represented in y-axis as we can observe in the above image.

Question 3.
Which of the following correctly describes the relationship?
(a) Vicki reads twice as fast as Bruce.
(b) Bruce reads twice as fast as Vicki.
(c) Vicki’s reading rate is one-third of Bruce’s.
(d) Bruce reads half as fast as Vicki.
Answer:
Option B, Bruce reads twice as fast as Vicki correctly describes the relationship.

Question 4.
A store sells 5 pounds of potatoes for $1.00. How much would 1 pound cost? Construct a graph for potato price on the grid below. Label each axis.

Answer:

A store sells 5 pounds of potatoes for $1.00.
5 pounds = $1.00
1 pound = s $
5 x s= $1 x 1
5s = $1
Divide both sides of the equation by 5.
s = $1/5
The cost of 1 pound potatoes are $0.2.
In the above graph we can see price of potatoes are represented in y axis and pounds are represented in x axis.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 14.1 Plotting Ordered Pairs existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 14.1 Plotting Ordered Pairs

Exercises

PLOT ORDERED PAIRS

Give the coordinates for each point on the graph.

A ______________
Answer:
The coordinates (2,3) represents point A on the above graph.

B ______________
Answer:
The coordinates (4,-4) represents point B on the above graph.

C ______________
Answer:
The coordinates (-6,-6) represents point C on the above graph.

D ______________
Answer:
The coordinates (5,3) represents point D on the above graph.

E ______________
Answer:
The coordinates (3,5) represents point E on the above graph.

F ______________
Answer:
The coordinates (1,2) represents point F on the above graph.

G ______________
Answer:
The coordinates (-2,2) represents point G on the above graph.

H ______________
Answer:
The coordinates (-5,4) represents point H on the above graph.

I ______________
Answer:
The coordinates (9,7) represents point I on the above graph.

J _______________
Answer:
The coordinates (-6,8) represents point J on the above graph.

Plot the following ordered pairs on the graph:

A (3, 2)
B (7, -7)
C (-7, -7)
D (-7, 7)
E (7, 7)
F (9, 2)
G (6, 7)
H (-8, -6)
I (-2, 2)
J (-5, -5)
K (3, -4)
L(-2, -2)
Answer:

The given order pairs are plotted on the provided graph as we can observe in the above image.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 13.3 Rates existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 13.3 Rates

Exercises Solve

Question 1.
The two rectangles are similar (proportional). Given the information about rectangle EFGH, what is the length of side CD?

Answer:
The above two rectangles ABDC and EFGH are similar (proportional).
Consider length of the side CD = x
BD/CD = FG/ GH
30/x = 6/16
To find the x value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
30 × 16 = 6 × x
480 = 6x
Divide both sides of the equation by 6.
480/6 = 6x/6
80 cm = x
Length of the side CD is equal to 80 cm.

Question 2.
George likes to sweeten his ice tea. When he drinks a 20-ounce ice tea, he puts in two teaspoons of sugar. If he is making a gallon of ice tea, how many teaspoons of sugar should he add?
Answer:
We know that 1 gallon is equal to 128 ounces.
20/2 = 128/x
To find the x value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
20 × x = 128 × 2
20 x = 256
Divide both sides of the equation by 20.
20x/20 = 256/20
x = 12.8 teaspoons
If George makes a gallon of ice tea, he will add 12.8 teaspoons of sugar.

Question 3.
The two triangles are similar. Calculate the length of side s.

Answer:
The above two triangles are similar.
3/9 = 2/s
To find the s value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
3 × s = 2 × 9
3s = 18
Divide both sides of the equation by 3.
3s/3 = 18/3
s = 6
Length of the side s is equal to 6.

Question 4.
Chuck took a long hike where he started at point B and followed the path in the diagram shown. If Chuck wants to take a shorter hike where he starts at B and walks 4 miles east, turns and walks 3 miles north and then returns to point B, how long B would his last leg be? Solve this problem using proportions even though you can solve it using the Pythagorean Theorem.

Answer:
Consider chuck last leg as x.
6.25/5 = x/4
To find the x value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
6.25 × 4 = x × 5
25 = 5x
Divide both sides of the equation by 5.
25/5 = 5x/5
x = 5

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 13.2 Proportions and Cross-Multiplying existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 13.2 Proportions and Cross-Multiplying

Exercises
Cross-Multiply
Round to the hundredths place.

Question 1.
\(\frac{x}{5}\) = \(\frac{30}{15}\)
Answer:
Given equation is \(\frac{x}{5}\) = \(\frac{30}{15}\)
To find the x value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
15x = 30 × 5
15x = 150
Divide both sides of the equation by 15.
\(\frac{15x}{15}\) = \(\frac{150}{15}\)
x = 10

Question 2.
\(\frac{z}{3}\) = \(\frac{24}{6}\)
Answer:
Given equation is \(\frac{z}{3}\) = \(\frac{24}{6}\)
To find the z value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
6z = 24 × 3
6z = 72
Divide both sides of the equation by 6.
\(\frac{6z}{6}\) = \(\frac{72}{6}\)
z = 12

Question 3.
\(\frac{14}{z}\) = \(\frac{100}{50}\)
Answer:
Given equation is \(\frac{14}{z}\) = \(\frac{100}{50}\)
To find the z value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
14 × 50 = 100 × z
700 = 100z
Divide both sides of the equation by 100.
\(\frac{700}{100}\) = \(\frac{100z}{100}\)
7 = z

Question 4.
\(\frac{56}{4}\) = \(\frac{y}{20}\)
Answer:
Given equation is \(\frac{56}{4}\) = \(\frac{y}{20}\)
To find the y value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
56 × 20 = y × 4
1120 = 4y
Divide both sides of the equation by 4.
\(\frac{1120}{4}\) = \(\frac{4y}{4}\)
280 = y

Question 5.
\(\frac{45}{9}\) = \(\frac{w}{3}\)
Answer:
Given equation is\(\frac{45}{9}\) = \(\frac{w}{3}\)
To find the w value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
45 × 3 = w × 9
135 = 9w
Divide both sides of the equation by 9.
\(\frac{135}{9}\) = \(\frac{9w}{9}\)
15 = w

Question 6.
\(\frac{14}{x}\) = \(\frac{70}{10}\)
Answer:
Given equation is \(\frac{14}{x}\) = \(\frac{70}{10}\)
To find the x value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
14 ×10 = 70 × x
140 = 70x
Divide both sides of the equation by 70.
\(\frac{140}{70}\) = \(\frac{70x}{70}\)
2 = x

Question 7.
\(\frac{33}{r}\) = \(\frac{11}{3}\)
Answer:
Given equation is \(\frac{33}{r}\) = \(\frac{11}{3}\)
To find the r value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
33 × 3= 11 × r
99 = 11r
Divide both sides of the equation by 11.
\(\frac{99}{11}\) = \(\frac{11r}{11}\)
9 = r

Question 8.
\(\frac{72}{9}\) = \(\frac{24}{z}\)
Answer:
Given equation is \(\frac{72}{9}\) = \(\frac{24}{z}\)
To find the z value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
72 × z = 24 × 9
72z = 216
Divide both sides of the equation by 72.
\(\frac{72z}{72}\) = \(\frac{216}{72}\)
z = 3

Question 9.
\(\frac{3}{2}\) = \(\frac{x}{5}\)
Answer:
Given equation is \(\frac{3}{2}\) = \(\frac{x}{5}\)
To find the x value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
3 × 5 = x × 2
15 = 2x
Divide both sides of the equation by 2.
\(\frac{15}{2}\) = \(\frac{2x}{2}\)
7.5 = x

Question 10.
\(\frac{700}{50}\) = \(\frac{35}{w}\)
Answer:
Given equation is \(\frac{700}{50}\) = \(\frac{35}{w}\)
To find the w value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
700 × w = 35 × 50
700w = 1750
Divide both sides of the equation by 700.
\(\frac{700w}{700}\) = \(\frac{1750}{700}\)
w = 2.5

Question 11.
\(\frac{36}{4}\) = \(\frac{x}{6}\)
Answer:
Given equation is \(\frac{36}{4}\) = \(\frac{x}{6}\)
To find the x value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
36 × 6 = x × 4
216 = 4x
Divide both sides of the equation by 4.
\(\frac{216}{4}\) = \(\frac{4x}{4}\)
54 = x

Question 12.
\(\frac{84}{12}\) = \(\frac{q}{4}\)
Answer:
Given equation is \(\frac{84}{12}\) = \(\frac{q}{4}\)
To find the q value we have to perform cross multiplication. Multiply the numerator of the first fraction by the denominator of the second fraction and write product on left hand side of the equation. Next multiply the denominator of the first fraction by the numerator of the second fraction and write the product on the right side of the equation.
84 × 4 = q × 12
336 = 12q
Divide both sides of the equation by 12.
\(\frac{336}{12}\) = \(\frac{12q}{12}\)
28 = q