Chapter 1 Use Positive Rational Numbers
Section 1.6: Divide Mixed Numbers
Page 43 Exercise 1 Answer
A \(5 \frac{1}{2}\) inch strip of silver wire is cut into \(1 \frac{3}{8}\) inch pieces so we must divide \(5 \frac{1}{2}\) by \(1 \frac{3}{8}\).
\(5 \frac{1}{2} \div 1 \frac{3}{8}=\frac{11}{2} \div \frac{11}{8}=\frac{11}{2} \times \frac{8}{11}=\frac{11 \times 8}{2 \times 11}=\frac{88}{22}=4\)Result
She can make 4 pieces.
Page 43 Exercise 1 Answer
Use estimation to check whether the answer is reasonable, that is round up or round down the fractions and divide.
Round down both fractions, \(5 \frac{1}{2}\) to 5 and \(1 \frac{3}{8}\) to 1. The quotient 5 ÷ 1 is 5.
Round up both fractions, \(5 \frac{1}{2}\) to 6 and \(1 \frac{3}{8}\) to 2. The quotient 6 ÷ 2 is 3.
Thus, the answer must be greater than 3 and less than 5.
Since the answer is 4, it is reasonable.
Result
Rounding both fractions down gives \(5 \frac{1}{2} \div 1 \frac{3}{8} \approx 5 \div 1=5\) and rounding both up gives \(5 \frac{1}{2} \div 1 \frac{3}{8} \approx\) 6 ÷ 2 = 3 so the answer must be greater than 3 and less than 5. Since the answer is 4, it is reasonable.
Read And Learn More: enVisionmath 2.0 Grade 6 Volume 1 Solutions
Page 44 Exercise 1 Answer
To divide mixed numbers, rewrite the mixed numbers as improper fractions, rewrite as multiplication, and then multiply:
\(37 \frac{1}{2} \div 10 \frac{3}{4}=\frac{75}{2} \div \frac{43}{4}=\frac{75}{2} \times \frac{4}{43}=\frac{75 \times 4}{2 \times 43}=\frac{300}{86}=\frac{258}{86}+\frac{42}{86}=3 \frac{42}{86}=3 \frac{21}{43}\)The number of stickers must be a whole number so Damon can fit 3 medium bumper stickers on his car bumper.
Result
Damon can fit 3 medium bumper stickers on his car bumper.
Page 45 Exercise 2a Answer
20 ÷ \(2 \frac{2}{3}\)
First, estimate using compatible numbers.
21 ÷ 3 = 7
Write the whole number and mixed number as fractions and than multiply by the reciprocal of the divisor.
\(20 \div 2 \frac{2}{3}=\frac{20}{1} \div \frac{8}{3}=\frac{20}{1} \times \frac{3}{8}=\frac{20 \times 3}{1 \times 8}=\frac{60}{8}=\frac{56}{8}+\frac{4}{8}=7 \frac{4}{8}=7 \frac{1}{2}\)The estimate, 7, is close to the quotient, \(7 \frac{1}{2}\). The answer is reasonable.
Result
\(7 \frac{1}{2}\)Page 45 Exercise 2b Answer
\(12 \frac{1}{2}\) ÷ 6
First, estimate using compatible numbers.
12 ÷ 6 = 2
Write the whole number and mixed number as fractions and than multiply by the reciprocal of the divisor.
\(12 \frac{1}{2} \div 6=\frac{25}{2} \div \frac{6}{1}=\frac{25}{2} \times \frac{1}{6}=\frac{25 \times 1}{2 \times 6}=\frac{25}{12}=\frac{24}{12}+\frac{1}{12}=2 \frac{1}{12}\)The estimate, 2, is close to the quotient, \(2 \frac{1}{12}\). The answer is reasonable.
Result
\(2 \frac{1}{12}\)Page 46 Exercise 1 Answer
To divide with mixed numbers, write mixed numbers and any whole numbers as fractions. Use the reciprocal of the divisor to rewrite the problem as a multiplication problem and then multiply. You can use an estimate to check whether the answer is reasonable. Use compatible numbers to estimate.
For example:
\(4 \frac{1}{5} \div 1 \frac{2}{3}=\frac{21}{5} \div \frac{5}{3}=\frac{21}{5} \times \frac{3}{5}=\frac{21 \times 3}{5 \times 5}=\frac{63}{25}=\frac{50}{25}+\frac{13}{25}=2 \frac{13}{25}\)Estimate: 4 ÷ 2 = 2. The estimate, 2, is close to the quotient, \(2 \frac{13}{25}\). The answer is reasonable.
Result
To divide with mixed numbers, write mixed numbers and any whole numbers as fractions. Use the reciprocal of the divisor to rewrite the problem as a multiplication problem and then multiply.
Page 46 Exercise 2 Answer
When dividing mixed numbers, it is important to estimate the quotient to see if the answer is reasonable.
Page 46 Exercise 3 Answer
In Example 1, the length of Damon’s bumper was \(37 \frac{1}{2}\) inches and the length of each long bumper sticker is 15 inches.
To find how many long bumper stickers can fit on his bumper, we must then divide \(37 \frac{1}{2}\) and 15.
When dividing mixed numbers, first convert the mixed number to an improper fraction. Next, rewrite the division as multiplying by the reciprocal of the divisor and then multiply:
\(37 \frac{1}{2} \div 15=\frac{75}{2} \div \frac{15}{1}=\frac{75}{2} \times \frac{1}{15}=\frac{75 \times 1}{2 \times 15}=\frac{75}{30}=\frac{5}{2}=2 \frac{1}{2}\)The number of bumper stickers must be a whole number so we need to round the quotient down to the nearest whole number. He can then fit 2 long stickers on his bumper.
Since the quotient was not a whole number and needed to be rounded down, then there is uncovered space on his bumper.
Result
2 long stickers and there is uncovered space.
Page 46 Exercise 4 Answer
When dividing by fractions less than 1, the quotient is always greater than the dividend. For example, \(\frac{2}{7}\) ÷ \(\frac{1}{3}=\frac{2}{7} \times \frac{3}{1}=\frac{6}{7} \text { and } \frac{6}{7}>\frac{2}{7}\)
When dividing by a mixed number, the quotient is always less than the dividend. For example \(\frac{5}{7} \div 2 \frac{1}{3}=\)\(\frac{5}{7} \div \frac{7}{3}=\frac{5}{7} \times \frac{3}{7}=\frac{15}{49} \text { and } \frac{15}{49}<\frac{5}{7} .\)
Result
When dividing by fractions less than 1, the quotient is always greater than the dividend. When dividing by a mixed number, the quotient is always less than the dividend.
Page 46 Exercise 5 Answer
To divide with mixed numbers, write mixed numbers and any whole numbers as fractions. Use the reciprocal of the divisor to rewrite the problem as a multiplication problem. Finally, multiply and use the estimate to check whether the answer is reasonable. Use compatible numbers to estimate.
\(2 \frac{5}{8} \div 2 \frac{1}{4}=\frac{21}{8} \div \frac{9}{4}=\frac{21}{8} \times \frac{4}{9}=\frac{21 \times 4}{8 \times 9}=\frac{84}{72}=\frac{7}{6}=\frac{6}{6}+\frac{1}{6}=1 \frac{1}{6}\)Estimate: 2 ÷ 2 = 1. The estimate, 1, is close to the quotient, \(1 \frac{1}{6}\). The answer is reasonable.
Result
\(1 \frac{1}{6}\)
Page 46 Exercise 6 Answer
To divide with mixed numbers, write mixed numbers and any whole numbers as fractions. Use the reciprocal of the divisor to rewrite the problem as a multiplication problem. Finally, multiply and use the estimate to check whether the answer is reasonable. Use compatible numbers to estimate.
\(3 \div 4 \frac{1}{2}=\frac{3}{1} \div \frac{9}{2}=\frac{3}{1} \times \frac{2}{9}=\frac{3 \times 2}{1 \times 9}=\frac{6}{9}=\frac{2}{3}\)Estimate: 3 ÷ 5 = \(\frac{3}{5}\). The estimate, \(\frac{3}{5}\), is close to the quotient, \(\frac{2}{3}\). The answer is reasonable.
Result
\(\frac{2}{3}\)Page 46 Exercise 7 Answer
To divide with mixed numbers, write mixed numbers and any whole numbers as fractions. Use the reciprocal of the divisor to rewrite the problem as a multiplication problem. Finally, multiply and use the estimate to check whether the answer is reasonable. Use compatible numbers to estimate.
\(18 \div 3 \frac{2}{3}=\frac{18}{1} \div \frac{11}{3}=\frac{18}{1} \times \frac{3}{11}=\frac{18 \times 3}{1 \times 11}=\frac{54}{11}=\frac{44}{11}+\frac{10}{11}=4 \frac{10}{11}\)Estimate: 18 ÷ 3 = 6. The estimate, 6, is close to the quotient, \(4 \frac{10}{11}\), which is actually closer to 5 then 4 since \(\frac{10}{11}\) is very close to 1 The answer is reasonable.
Result
\(4 \frac{10}{11}\)
Page 46 Exercise 8 Answer
To divide with mixed numbers, write mixed numbers and any whole numbers as fractions. Use the reciprocal of the divisor to rewrite the problem as a multiplication problem. Finally, multiply and use the estimate to check whether the answer is reasonable. Use compatible numbers to estimate.
\(1 \frac{2}{5} \div 7=\frac{7}{5} \div \frac{7}{1}=\frac{7}{5} \times \frac{1}{7}=\frac{7 \times 1}{5 \times 7}=\frac{7}{35}=\frac{1}{5}\)Estimate: 1 ÷ 7 = \(\frac{1}{7}\). The estimate, \(\frac{1}{7}\), is close to the quotient, \(\frac{1}{5}\), which is less than one so the answer is reasonable.
Result
\(\frac{1}{5}\)Page 46 Exercise 9 Answer
To divide with mixed numbers, write mixed numbers and any whole numbers as fractions. Use the reciprocal of the divisor to rewrite the problem as a multiplication problem. Finally, multiply and use the estimate to check whether the answer is reasonable. Use compatible numbers to estimate.
\(5 \div 6 \frac{2}{5}=\frac{5}{1} \div \frac{32}{5}=\frac{5}{1} \times \frac{5}{32}=\frac{5 \times 5}{1 \times 32}=\frac{25}{32}\)Estimate: 5 ÷ 6 = \(\frac{5}{6}\). The estimate, \(\frac{5}{6}\), is close to the quotient, \(\frac{25}{32}\), which is less than one so the answer is reasonable.
Result
\(\frac{25}{32}\)
Page 46 Exercise 10 Answer
To divide with mixed numbers, write mixed numbers and any whole numbers as fractions. Use the reciprocal of the divisor to rewrite the problem as a multiplication problem. Finally, multiply and use the estimate to check whether the answer is reasonable. Use compatible numbers to estimate.
\(8 \frac{1}{5} \div 3 \frac{3}{4}=\frac{41}{5} \div \frac{15}{4}=\frac{41}{5} \times \frac{4}{15}=\frac{41 \times 4}{5 \times 15}=\frac{164}{75}=\frac{150}{75}+\frac{14}{75}=2 \frac{14}{75}\)Estimate: 8 ÷ 4 = 2. The estimate, 2, is close to the quotient, \(2 \frac{14}{75}\). The answer is reasonable.
Result
\(2 \frac{14}{75}\)
Page 46 Exercise 11 Answer
To divide with mixed numbers, write mixed numbers and any whole numbers as fractions. Use the reciprocal of the divisor to rewrite the problem as a multiplication problem. Finally, multiply and use the estimate to check whether the answer is reasonable. Use compatible numbers to estimate.
\(2 \frac{1}{2} \div 4 \frac{1}{10}=\frac{5}{2} \div \frac{41}{10}=\frac{5}{2} \times \frac{10}{41}=\frac{5 \times 10}{2 \times 41}=\frac{50}{82}=\frac{25}{41}\)Estimate: 2 ÷ 4 = \(\frac{1}{2}\). The estimate, \(\frac{1}{2}\), is close to the quotient, \(\frac{25}{41}\), which is less than one so the answer is reasonable.
Result
\(\frac{25}{41}\)
Page 46 Exercise 12 Answer
To divide with mixed numbers, write mixed numbers and any whole numbers as fractions. Use the reciprocal of the divisor to rewrite the problem as a multiplication problem. Finally, multiply and use the estimate to check whether the answer is reasonable. Use compatible numbers to estimate.
\(2 \frac{2}{3} \div 6=\frac{8}{3} \div \frac{6}{1}=\frac{8}{3} \times \frac{1}{6}=\frac{8 \times 1}{3 \times 6}=\frac{8}{18}=\frac{4}{9}\)Estimate: 3 ÷ 6 = \(\frac{1}{2}\). The estimate, \(\frac{1}{2}\), is close to the quotient, \(\frac{4}{9}\), which is less than one so the answer is reasonable.
Result
\(\frac{4}{9}\)Page 46 Exercise 13 Answer
To divide with mixed numbers, write mixed numbers and any whole numbers as fractions. Use the reciprocal of the divisor to rewrite the problem as a multiplication problem. Finally, multiply and use the estimate to check whether the answer is reasonable. Use compatible numbers to estimate.
\(6 \frac{5}{9} \div 1 \frac{7}{9}=\frac{59}{9} \div \frac{16}{9}=\frac{59}{9} \times \frac{9}{16}=\frac{59 \times 9}{9 \times 16}=\frac{531}{144}=\frac{59}{16}=\frac{48}{16}+\frac{11}{16}=3 \frac{11}{16}\)Estimate: 6 ÷ 2 = 3. The estimate, 3, is close to the quotient, \(3 \frac{11}{16}\). The answer is reasonable.
Result
\(3 \frac{11}{16}\)
Page 47 Exercise 14 Answer
To divide with mixed numbers, write mixed numbers and any whole numbers as fractions. Use the reciprocal of the divisor to rewrite the problem as a multiplication problem. Finally, multiply:
\(10 \div 2 \frac{1}{4}=\frac{10}{1} \div \frac{9}{4}=\frac{10}{1} \times \frac{4}{9}=\frac{10 \times 4}{1 \times 9}=\frac{40}{9}=\frac{36}{9}+\frac{4}{9}=4 \frac{4}{9}\)Result
\(4 \frac{4}{9}\)Page 47 Exercise 15 Answer
To divide with mixed numbers, write mixed numbers and any whole numbers as fractions. Use the reciprocal of the divisor to rewrite the problem as a multiplication problem. Finally, multiply:
\(9 \frac{1}{3} \div 6=\frac{28}{3} \div \frac{6}{1}=\frac{28}{3} \times \frac{1}{6}=\frac{28 \times 1}{3 \times 6}=\frac{28}{18}=\frac{18}{18}+\frac{10}{18}=1 \frac{10}{18}=1 \frac{5}{9}\)Result
\(1 \frac{5}{9}\)Page 47 Exercise 16 Answer
To divide with mixed numbers, write mixed numbers and any whole numbers as fractions. Use the reciprocal of the divisor to rewrite the problem as a multiplication problem. Finally, multiply:
\(1 \frac{3}{8} \div 4 \frac{1}{8}=\frac{11}{8} \div \frac{33}{8}=\frac{11}{8} \times \frac{8}{33}=\frac{11 \times 8}{8 \times 33}=\frac{88}{264}=\frac{1}{3}\)Result
\(\frac{1}{3}\)Page 47 Exercise 17 Answer
To divide with mixed numbers, write mixed numbers and any whole numbers as fractions. Use the reciprocal of the divisor to rewrite the problem as a multiplication problem. Finally, multiply:
\(2 \frac{2}{3} \div 8=\frac{8}{3} \div \frac{8}{1}=\frac{8}{3} \times \frac{1}{8}=\frac{8 \times 1}{3 \times 8}=\frac{8}{24}=\frac{1}{3}\)Result
\(\frac{1}{3}\)Page 47 Exercise 18 Answer
To divide with mixed numbers, write mixed numbers and any whole numbers as fractions. Use the reciprocal of the divisor to rewrite the problem as a multiplication problem. Finally, multiply:
\(4 \frac{1}{3} \div 3 \frac{1}{4}=\frac{13}{3} \div \frac{13}{4}=\frac{13}{3} \times \frac{4}{13}=\frac{13 \times 4}{3 \times 13}=\frac{52}{39}=\frac{4}{3}=\frac{3}{3}+\frac{1}{3}=1 \frac{1}{3}\)Result
\(1 \frac{1}{3}\)Page 47 Exercise 19 Answer
To divide with mixed numbers, write mixed numbers and any whole numbers as fractions. Use the reciprocal of the divisor to rewrite the problem as a multiplication problem. Finally, multiply:
\(1 \div 8 \frac{5}{9}=\frac{1}{1} \div \frac{77}{9}=\frac{1}{1} \times \frac{9}{77}=\frac{1 \times 9}{1 \times 77}=\frac{9}{77}\)Result
\(\frac{9}{77}\)Page 47 Exercise 20 Answer
To divide with mixed numbers, write mixed numbers and any whole numbers as fractions. Use the reciprocal of the divisor to rewrite the problem as a multiplication problem. Finally, multiply:
\(3 \frac{5}{6} \div 9 \frac{5}{6}=\frac{23}{6} \div \frac{59}{6}=\frac{23}{6} \times \frac{6}{59}=\frac{23 \times 6}{6 \times 59}=\frac{138}{354}=\frac{23}{59}\)Result
\(\frac{23}{59}\)Page 47 Exercise 21 Answer
To divide with mixed numbers, write mixed numbers and any whole numbers as fractions. Use the reciprocal of the divisor to rewrite the problem as a multiplication problem. Finally, multiply:
\(16 \div 2 \frac{2}{3}=\frac{16}{1} \div \frac{8}{3}=\frac{16}{1} \times \frac{3}{8}=\frac{16 \times 3}{1 \times 8}=\frac{48}{8}=6\)Result
6
Page 47 Exercise 22 Answer
To divide with mixed numbers, write mixed numbers and any whole numbers as fractions. Use the reciprocal of the divisor to rewrite the problem as a multiplication problem. Finally, multiply:
\(2 \frac{5}{8} \div 13=\frac{21}{8} \div \frac{13}{1}=\frac{21}{8} \times \frac{1}{13}=\frac{21 \times 1}{8 \times 13}=\frac{21}{104}\)Result
\(\frac{21}{104}\)Page 47 Exercise 23 Answer
To divide with mixed numbers, write mixed numbers and any whole numbers as fractions. Use the reciprocal of the divisor to rewrite the problem as a multiplication problem. Finally, multiply:
\(3 \frac{6}{7} \div 6 \frac{3}{4}=\frac{27}{7} \div \frac{27}{4}=\frac{27}{7} \times \frac{4}{27}=\frac{27 \times 4}{7 \times 27}=\frac{108}{189}=\frac{4}{7}\)Result
\(\frac{4}{7}\)Page 47 Exercise 24 Answer
To divide with mixed numbers, write mixed numbers and any whole numbers as fractions. Use the reciprocal of the divisor to rewrite the problem as a multiplication problem. Finally, multiply:
\(2 \frac{1}{3} \div 1 \frac{1}{3}=\frac{7}{3} \div \frac{4}{3}=\frac{7}{3} \times \frac{3}{4}=\frac{7 \times 3}{3 \times 4}=\frac{21}{12}=\frac{7}{4}=\frac{4}{4}+\frac{3}{4}=1 \frac{3}{4}\)Result
\(1 \frac{3}{4}\)Page 47 Exercise 25 Answer
To divide with mixed numbers, write mixed numbers and any whole numbers as fractions. Use the reciprocal of the divisor to rewrite the problem as a multiplication problem. Finally, multiply:
\(3 \frac{3}{4} \div 1 \frac{1}{2}=\frac{15}{4} \div \frac{3}{2}=\frac{15}{4} \times \frac{2}{3}=\frac{15 \times 2}{4 \times 3}=\frac{30}{12}=\frac{10}{4}=\frac{8}{4}+\frac{2}{4}=2 \frac{2}{4}=2 \frac{1}{2}\)Result
\(2 \frac{1}{2}\)Page 47 Exercise 26 Answer
If each step of the ladder is \(2 \frac{1}{3}\) feet wide and Beth has a rope that is 21 feet long, then the number of steps she can make is:
\(21 \div 2 \frac{1}{3}=\frac{21}{1} \div \frac{7}{3}=\frac{21}{1} \times \frac{3}{7}=\frac{21 \times 3}{1 \times 7}=\frac{63}{7}=9\)Result
Beth can make 9 steps from the rope.
Page 47 Exercise 27 Answer
The area of the rectangle is 257\(\frac{1}{4}\)in2 and the length of one side is 10\(\frac{1}{2}\)in. The width is then the area divided by the length:
\(w=257 \frac{1}{4} \div 10 \frac{1}{2}\)= \(\frac{1029}{4} \div \frac{21}{2}\) (Rewrite as improper fractions)
= \(\frac{1029}{4} \times \frac{2}{21}\) (Rewrite as a multiplication problem)
= \(\frac{1029 \times 2}{4 \times 21}\) (Multiply)
= \(\frac{2058}{84}\)
= \(\frac{2016}{84}+\frac{42}{84}\)
= \(24 \frac{42}{84}\)
= \(24 \frac{1}{2}\)
Result
w = \(24 \frac{1}{2}\)
Page 48 Exercise 28 Answer
The smaller room is \(20 \frac{4}{5}\) feet long and the longer room is twice as long, so we must find the product \(20 \frac{4}{5} \times 2\).
\(20 \frac{4}{5} \times 2=\frac{104}{5} \times 2=\frac{104}{5} \times \frac{2}{1}=\frac{104 \times 2}{5 \times 1}=\frac{208}{5}=\frac{205}{5}+\frac{3}{5}=41 \frac{3}{5}\)Result
The larger room is \(41 \frac{3}{5}\) feet long.
Page 48 Exercise 29 Answer
To find how long is each part if the smaller room is divided into four equal parts we need to find the quotient \(20 \frac{4}{5} \div 4\)
\(20 \frac{4}{5} \div 4=\frac{104}{5} \div \frac{4}{1}=\frac{104}{5} \times \frac{1}{4}=\frac{104 \times 1}{5 \times 4}=\frac{104}{20}=\frac{100}{20}+\frac{4}{20}=5 \frac{4}{20}=5 \frac{1}{5}\)Result
Each part is \(5 \frac{1}{5}\) feet long.
Page 48 Exercise 30 Answer
First, we must calculate how many pounds of meat he used to make those 6 burgers.
\(\frac{3}{8} \times 6=\frac{3}{8} \times \frac{6}{1}=\frac{3 \times 6}{8 \times 1}=\frac{18}{8}=\frac{9}{4}=\frac{8}{4}+\frac{1}{4}=2 \frac{1}{4}\)He used \(2 \frac{1}{4}\) pounds to make 6 burgers. We need to calculate how many pounds of meat he has left.
\(3-2 \frac{1}{4}=\frac{3}{1}-\frac{9}{4}=\frac{3 \times 4}{1 \times 4}-\frac{9}{4}=\frac{12}{4}-\frac{9}{4}=\frac{12-9}{4}=\frac{3}{4}\)He has left \(\frac{3}{4}\) pound of meat. Obviously, he can make three \(\frac{1}{4}\) pound burgers.
Result
Luis can make three \(\frac{1}{4}\) pound burgers.
Page 48 Exercise 31 Answer
\(9 \times \frac{n}{5}=9 \div \frac{n}{5}\)The only number by which we can multiply and divide the same number, in this case 9, and get the equal result is one. Thus, \(\frac{n}{5}\) must be equal to one. This is true when n is 5.
Result
n = 5
Page 48 Exercise 32 Answer
First, we must calculate the quotient \(1 \frac{3}{4} \div 12\) to find out how many teaspoons of vanilla Margaret puts in one cupcake.
\(1 \frac{3}{4} \div 12=\frac{7}{4} \div \frac{12}{1}=\frac{7}{4} \times \frac{1}{12}=\frac{7 \times 1}{4 \times 12}=\frac{7}{48}\)Margaret uses \(\frac{7}{48}\) teaspoon of vanilla to make one cupcake.
\(\frac{7}{48} \times 30=\frac{7}{48} \times \frac{30}{1}=\frac{7 \times 30}{48 \times 1}=\frac{210}{48}=\frac{192}{48}+\frac{18}{48}=4 \frac{18}{48}=4 \frac{3}{8}\)Result
Margaret will use \(4 \frac{3}{8}\) teaspoons to make 30 cupcakes.
Page 48 Exercise 33 Answer
If the diamond was \(1 \frac{1}{2}\) pounds and was cut into 6 equal pieces, then the weight of each piece was:
\(1 \frac{1}{2} \div 6=\frac{3}{2} \div \frac{6}{1}=\frac{3}{2} \times \frac{1}{6}=\frac{3 \times 1}{2 \times 6}=\frac{3}{12}=\frac{1}{4}\)Result
Each piece would weigh \(\frac{1}{4}\) pound.
Page 48 Exercise 34 Answer
To find out how many aquariums did the owner fill we must calculate the quotient \(17 \frac{1}{2} \div 5 \frac{5}{6}\)
\(17 \frac{1}{2} \div 5 \frac{5}{6}=\frac{35}{2} \div \frac{35}{6}=\frac{35}{2} \times \frac{6}{35}=\frac{35 \times 6}{2 \times 35}=\frac{6}{2}=3\)Result
He filled 3 aquariums.
Page 48 Exercise 35 Answer
To estimate the quotient \(17 \frac{1}{5} \div 3 \frac{4}{5}\) we must round both numbers to closest whole compatible numbers. For \(17 \frac{1}{5}\) we can use 18 and for \(3 \frac{4}{5}\) we can use 3, thus the estimate would be 18 ÷ 3 which is equal to 6.
\(17 \frac{1}{5} \div 3 \frac{4}{5}=\frac{86}{5} \div \frac{19}{5}=\frac{86}{5} \times \frac{5}{19}=\frac{86 \times 5}{5 \times 19}=\frac{86}{19}=\frac{76}{19}+\frac{10}{19}=4 \frac{10}{19}\)The estimate was correct, the answer \(4 \frac{10}{19}\) is close to 4.
Result
To estimate the quotient \(17 \frac{1}{5} \div 3 \frac{4}{5}\) we must round both numbers to closest whole compatible numbers. For \(17 \frac{1}{5}\) we can use 18 and for \(3 \frac{4}{5}\) we can use 3, thus the estimate would be 18 ÷ 3 which is equal to 6.
Page 48 Exercise 36a Answer
Since the restaurant has \(15 \frac{1}{5}\) pounds of ground beef and each meat loaf requires \(2 \frac{3}{8}\) pounds of meat, to answer the question how many meat loaves can be made find the quotient \(15 \frac{1}{5} \div 2 \frac{3}{8}\)
\(15 \frac{1}{5} \div 2 \frac{3}{8}=\frac{76}{5} \div \frac{19}{8}=\frac{76}{5} \times \frac{8}{19}=\frac{76 \times 8}{5 \times 19}=\frac{608}{95}=\frac{570}{95}+\frac{38}{95}=6 \frac{2}{5}\)The restaurant can make 6 meat loaves.
Result
The restaurant can make 6 meat loaves.
Page 48 Exercise 36b Answer
\(15 \frac{1}{5} \div 1 \frac{3}{5}=\frac{76}{5} \div \frac{8}{5}=\frac{76}{5} \times \frac{5}{8}=\frac{76 \times 5}{5 \times 8}=\frac{380}{40}=\frac{360}{40}+\frac{20}{40}=9 \frac{1}{2}\)The restaurant can make 9 smaller size meat loaves. Since the restaurant can make 6 bigger meat loaves, thus they can make 3 more meat laoves more if they choose to make them smaller.
Result
The restaurant can make 3 more meat loaves.