Go through the Math in Focus Grade 6 Workbook Answer Key Chapter 3 Lesson 3.1 Dividing Fractions to finish your assignments.
Math in Focus Grade 6 Course 1 A Chapter 3 Lesson 3.1 Answer Key Dividing Fractions
Math in Focus Grade 6 Chapter 3 Lesson 3.1 Guided Practice Answer Key
Solve.
Question 1.
Rina cut 3 paper squares into a number of equal pieces. Each piece was \(\frac{1}{6}\) of a square. Into how many pieces did Rina cut the 3 paper squares?
The model shows that:
Number of one-sixths in 1 paper square = 
Number of one-sixths in 3 paper squares = ×
Answer:
Rina cut the 3 paper squares into 18 pieces.
Explanation:
Given that Rina cut 3 paper squares into a number of equal pieces and each piece was \(\frac{1}{6}\) of a square. So the number of many pieces did Rina cut the 3 paper squares is 3 ÷ \(\frac{1}{6}\)
= 3 × 6
= 18 pieces.
Divide.
Question 2.
3 ÷ \(\frac{1}{5}\) = 
Answer:
3 ÷ \(\frac{1}{5}\) = 15.
Explanation:
The division of 3 ÷ \(\frac{1}{5}\) is 3 × 5 = 15.
Question 3.
7 ÷ \(\frac{1}{4}\) =
Answer:
7 ÷ \(\frac{1}{4}\) = 28.
Explanation:
The division of 7 ÷ \(\frac{1}{4}\) is 7 × 4 = 28.
Question 4.
4 ÷ \(\frac{1}{2}\) = 
Answer:
4 ÷ \(\frac{1}{2}\) = 8.
Explanation:
The division of 4 ÷ \(\frac{1}{2}\) is 4 × 2 = 8.
Question 5.
5 ÷ \(\frac{1}{3}\) =
Answer:
5 ÷ \(\frac{1}{3}\) = 15.
Explanation:
The division of 5 ÷ \(\frac{1}{3}\) is 5 × 3 = 15.
Question 6.
6 ÷ \(\frac{1}{5}\) =
Answer:
6 ÷ \(\frac{1}{5}\) = 15.
Explanation:
The division of 6 ÷ \(\frac{1}{5}\) is 6 × 5 = 15.
Question 7.
8 ÷ \(\frac{1}{8}\) =
Answer:
8 ÷ \(\frac{1}{8}\) = 64.
Explanation:
The division of 8 ÷ \(\frac{1}{8}\) is 8 × 8 = 64.
Hands-On
Activity Materials:
- 5 paper strips
Dividing Whole Numbers By A Fraction
Use 5 paper strips of the same size and length. Each strip represents 1 whole.
Step 1.
Take 2 paper strips. Divide each of them into thirds using vertical lines and place them as shown. Then find 2 ÷ \(\frac{2}{3}\)
Refer to your model.
Complete:
There are 
two-thirds in the 2 paper strips.
So, 2 ÷ \(\frac{2}{3}\) = 
.
Step 2.
Divide each of the other 3 paper strips into fourths using vertical lines and place them as shown. Then find 3 ÷ \(\frac{3}{4}\).
Refer to your model.
Complete:
There are three-fourths in the 3 paper strips.
So, 3 ÷ \(\frac{3}{4}\) = .
Complete:
Question 8.
Find 7 ÷ \(\frac{3}{4}\)
Question 9.
Mrs. Johnson bought 6 pizzas. She cut them into many equal pieces for the students in her class. Each piece was \(\frac{3}{10}\) of a whole pizza. How many students were there in the class if each child received only one piece of pizza?
Answer:
There were 20 students in the class.
Explanation:
Given that Mrs. Johnson bought 6 pizzas and she cut them into many equal pieces for the students in her class. Each piece was \(\frac{3}{10}\) of a whole pizza. So the number of students were there in the class is 6 ÷ \(\frac{3}{10}\) which is 6 × \(\frac{10}{3}\)
= 2 × 10
= 20 students.
Divide. Express the quotient in simplest form.
Question 10.
4 ÷ \(\frac{4}{7}\)
Answer:
4 ÷ \(\frac{4}{7}\) = 7.
Explanation:
The division of 4 ÷ \(\frac{4}{7}\) is 4 × \(\frac{7}{4}\) = 7.
Question 11.
6 ÷ \(\frac{2}{7}\)
Answer:
6 ÷ \(\frac{2}{7}\) = 21.
Explanation:
The division of 6 ÷ \(\frac{2}{7}\) is 6 × \(\frac{7}{2}\) which is 3 × 7 = 21.
Question 12.
9 ÷ \(\frac{3}{8}\)
Answer:
9 ÷ \(\frac{3}{8}\) = 24.
Explanation:
The division of 9 ÷ \(\frac{3}{8}\) is 9 × \(\frac{8}{3}\) which is 3 × 8 = 24.
Question 13.
5 ÷ \(\frac{10}{13}\)
Answer:
6\(\frac{1}{2}\).
Explanation:
The division of 5 ÷ \(\frac{10}{13}\) is 5 × \(\frac{13}{10}\) which is \(\frac{13}{2}\) = 6\(\frac{1}{2}\).
Question 14.
10 ÷ \(\frac{5}{14}\)
Answer:
10 ÷ \(\frac{5}{14}\) = 28.
Explanation:
The division of 10 ÷ \(\frac{5}{14}\) is 10 × \(\frac{14}{5}\) which is 2 × 14 = 28.
Question 15.
12 ÷ \(\frac{9}{10}\)
Answer:
12 ÷ \(\frac{9}{10}\) = 13 \(\frac{1}{3}\).
Explanation:
The division of 12 ÷ \(\frac{9}{10}\) is 12 × \(\frac{10}{9}\) which is \(\frac{40}{3}\) = 13 \(\frac{1}{3}\).
Hands-On Activity
Materials:
- 2 paper strips
Use 2 paper strips of the same size and length. Each strip represents 1 whole.
Step 1.
Take 1 paper strip and divide it into halves using vertical lines.
Then find \(\frac{1}{2}\) ÷ \(\frac{1}{4}\)
Refer to your model.
Complete:
There are 
fourths in a half.
So, \(\frac{1}{2}\) ÷ \(\frac{1}{4}\) =
Step 2.
Find \(\frac{1}{2}\) ÷ \(\frac{1}{4}\) by multiplication.
\(\frac{1}{2}\) ÷ \(\frac{1}{4}\) = 
Rewrite using the reciprocal of the divisor.
= Multiply.
Step 3.
Divide the other paper strip into one-thirds using vertical lines.
Then find \(\frac{2}{3}\) ÷ \(\frac{1}{6}\).
Refer to your model.
Complete.
Step 4.
Find \(\frac{2}{3}\) ÷ \(\frac{1}{6}\) by multiplication.
\(\frac{2}{3}\) ÷ \(\frac{1}{6}\) = 
Rewrite using the reciprocal of the divisor
= 
Multiply.
Hands-On Activity
Dividing Fractions with Remainder
A pitcher contains \(\frac{4}{5}\) quart of orange juice.
Step 1.
Copy the model and divide
Complete: \(\frac{4}{5}\) qt = 
qt
Step 2.
Use the model to answer this question.
Into how many glasses, each containing \(\frac{3}{10}\) quart, can the orange juice be poured 
.
How many quarts of orange juice will be left in the pitcher? 
qt
Step 3.
Now find the number of glasses by division. Express your answer as a mixed number.
The answer 2\(\frac{2}{3}\) means there are 2 glasses of orange juice, each containing \(\frac{3}{10}\) quart, and a remaining glass of orange juice that contains of \(\frac{2}{3}\) of \(\frac{3}{10}\) quart.
How many quarts of orange juice will be left in the pitcher. 
Complete.
Question 16.
Adam had \(\frac{5}{7}\) liter of water. He used the water to fill a few glasses completely. The capacity of each glass was \(\frac{2}{7}\) liter. How many glasses of water did Adam fill?
Answer:
Question 17.
Lina had \(\frac{2}{3}\) of a pizza. She cut it into pieces that were each \(\frac{1}{9}\) of the whole pizza. Into how many pieces did she cut it?
Answer:
Divide. Express the quotient in simplest form.
Question 18.
\(\frac{2}{3}\) ÷ \(\frac{1}{6}\)
Answer:
\(\frac{2}{3}\) ÷ \(\frac{1}{6}\)
Explanation:
The simplest form of \(\frac{2}{3}\) ÷ \(\frac{1}{6}\) is \(\frac{2}{3}\) × \(\frac{6}{1}\) = 4.
Question 19.
\(\frac{3}{5}\) ÷ \(\frac{1}{10}\)
Answer:
\(\frac{3}{5}\) ÷ \(\frac{1}{10}\) = 6.
Explanation:
The simplest form of \(\frac{3}{5}\) ÷ \(\frac{1}{10}\) is \(\frac{3}{5}\) × \(\frac{10}{1}\) which is 3 × 2 = 6.
Question 20.
\(\frac{3}{4}\) ÷ \(\frac{1}{2}\)
Answer:
\(\frac{3}{4}\) ÷ \(\frac{1}{2}\) = 1 \(\frac{1}{2}\).
Explanation:
The simplest form of
\(\frac{3}{4}\) ÷ \(\frac{1}{2}\) = \(\frac{3}{4}\) × \(\frac{2}{1}\) which is \(\frac{3}{2}\) = 1 \(\frac{1}{2}\).
Question 21.
\(\frac{1}{6}\) ÷ \(\frac{2}{3}\)
Answer:
\(\frac{1}{6}\) ÷ \(\frac{2}{3}\) = \(\frac{1}{4}\).
Explanation:
The simplest form of
\(\frac{1}{6}\) ÷ \(\frac{2}{3}\) = \(\frac{1}{6}\) × \(\frac{3}{2}\)
= \(\frac{1}{4}\).
Question 22.
\(\frac{5}{8}\) ÷ \(\frac{15}{16}\)
Answer:
\(\frac{5}{8}\) ÷ \(\frac{15}{16}\) = \(\frac{2}{3}\).
Explanation:
The simplest form of
\(\frac{5}{8}\) ÷ \(\frac{15}{16}\) = \(\frac{5}{8}\) × \(\frac{16}{15}\)
= \(\frac{2}{3}\).
Question 23.
\(\frac{7}{16}\) ÷ \(\frac{5}{12}\)
Answer:
\(\frac{7}{16}\) ÷ \(\frac{5}{12}\) = 1\(\frac{1}{20}\).
Explanation:
The simplest form of
\(\frac{7}{16}\) ÷ \(\frac{5}{12}\) = \(\frac{7}{16}\) × \(\frac{12}{5}\)
= \(\frac{21}{20}\)
= 1\(\frac{1}{20}\).
Complete.
Question 24.
Divide \(\frac{5}{9}\) by 4\(\frac{1}{3}\).
Answer:
Caution
Before finding the reciprocal of a whole number or a mixed number, you need to first write ¡t as an improper fraction.
Question 25.
Divide 2\(\frac{3}{5}\) by 1\(\frac{8}{9}\).
2\(\frac{3}{5}\) and 1\(\frac{8}{9}\) are both mixed numbers. Express the mixed numbers as improper fractions.
Answer:
Hands-On Activity
Division Involving Whole Numbers and Fractions
Work in pairs.
Step 1.
Find each quotient.
a) 4 ÷ \(\frac{2}{5}\) and \(\frac{2}{5}\) ÷ 4
Answer:
4 ÷ \(\frac{2}{5}\) = 10.
\(\frac{2}{5}\) ÷ 4 = \(\frac{1}{10}\).
Explanation:
The quotient of 4 ÷ \(\frac{2}{5}\) is
4 ÷ \(\frac{2}{5}\) = 4 × \(\frac{5}{2}\)
= 2 × 5
= 10.
And the quotient of \(\frac{2}{5}\) ÷ 4 is
\(\frac{2}{5}\) ÷ 4 = \(\frac{2}{5}\) × \(\frac{1}{4}\)
= \(\frac{1}{10}\).
b) \(\frac{1}{4}\) ÷ \(\frac{2}{3}\) and \(\frac{2}{3}\) ÷ \(\frac{1}{4}\)
Answer:
\(\frac{1}{4}\) ÷ \(\frac{2}{3}\) = \(\frac{3}{8}\).
\(\frac{2}{3}\) ÷ \(\frac{1}{4}\) = 2 \(\frac{2}{3}\).
Explanation:
The quotient of \(\frac{1}{4}\) ÷ \(\frac{2}{3}\) is
\(\frac{1}{4}\) ÷ \(\frac{2}{3}\) = \(\frac{1}{4}\) × \(\frac{3}{2}\)
= \(\frac{3}{8}\).
The quotient of \(\frac{2}{3}\) ÷ \(\frac{1}{4}\) is
\(\frac{2}{3}\) ÷ \(\frac{1}{4}\) = \(\frac{2}{3}\) × \(\frac{4}{1}\)
= \(\frac{8}{3}\)
= 2 \(\frac{2}{3}\).
c) \(\frac{4}{5}\) ÷ \(\frac{3}{10}\) and \(\frac{3}{10}\) ÷ \(\frac{4}{5}\)
Answer:
\(\frac{4}{5}\) ÷ \(\frac{3}{10}\) = 2\(\frac{2}{3}\).
\(\frac{3}{10}\) ÷ \(\frac{4}{5}\) = \(\frac{3}{8}\).
Explanation:
The quotient of \(\frac{4}{5}\) ÷ \(\frac{3}{10}\) is
\(\frac{4}{5}\) ÷ \(\frac{3}{10}\) = \(\frac{4}{5}\) × \(\frac{10}{3}\)
= \(\frac{8}{3}\)
= 2\(\frac{2}{3}\).
And the quotient of \(\frac{3}{10}\) ÷ \(\frac{4}{5}\) is
\(\frac{3}{10}\) ÷ \(\frac{4}{5}\) = \(\frac{3}{10}\) × \(\frac{5}{4}\)
= \(\frac{3}{8}\).
d) \(\frac{5}{8}\) ÷ \(\frac{3}{4}\) and \(\frac{3}{4}\) ÷ \(\frac{5}{8}\)
Answer:
\(\frac{5}{8}\) ÷ \(\frac{3}{4}\) = \(\frac{5}{6}\).
\(\frac{3}{4}\) ÷ \(\frac{5}{8}\) = 1\(\frac{1}{5}\).
Explanation:
The quotient of \(\frac{5}{8}\) ÷ \(\frac{3}{4}\) is
\(\frac{5}{8}\) ÷ \(\frac{3}{4}\) = \(\frac{5}{8}\) × \(\frac{4}{3}\)
= \(\frac{5}{6}\).
The quotient of \(\frac{3}{4}\) ÷ \(\frac{5}{8}\) is
\(\frac{3}{4}\) ÷ \(\frac{5}{8}\) = \(\frac{3}{4}\) × \(\frac{8}{5}\)
= \(\frac{6}{5}\)
= 1\(\frac{1}{5}\).
Step 2.
What do you observe about the products of each pair of quotients?
Step 3.
Given that \(\frac{6}{7}\) ÷ 9 = \(\frac{2}{21}\) and \(\frac{10}{11}\) ÷ \(\frac{5}{6}\) = \(\frac{12}{11}\), find the following quotients mentally.
a) 9 ÷ \(\frac{6}{7}\)
Answer:
9 ÷ \(\frac{6}{7}\) = 10\(\frac{1}{2}\).
Explanation:
The quotient of 9 ÷ \(\frac{6}{7}\) is
9 ÷ \(\frac{6}{7}\) = 9 × \(\frac{7}{6}\)
= \(\frac{21}{2}\)
= 10\(\frac{1}{2}\).
b) \(\frac{5}{6}\) ÷ \(\frac{10}{11}\)
Answer:
\(\frac{5}{6}\) ÷ \(\frac{10}{11}\) = \(\frac{11}{12}\).
Explanation:
The quotient of \(\frac{5}{6}\) ÷ \(\frac{10}{11}\) is
\(\frac{5}{6}\) ÷ \(\frac{10}{11}\) = \(\frac{5}{6}\) × \(\frac{11}{10}\)
= \(\frac{11}{12}\).
Math Journal Explain in words the meaning of each division statement.
a) 4 ÷ \(\frac{2}{5}\) and \(\frac{2}{5}\) ÷ 4
Answer:
4 ÷ \(\frac{2}{5}\) = 10.
\(\frac{2}{5}\) ÷ 4 = \(\frac{1}{10}\).
Explanation:
The quotient of 4 ÷ \(\frac{2}{5}\) is
4 ÷ \(\frac{2}{5}\) = 4 × \(\frac{5}{2}\)
= 2 × 5
= 10.
And the quotient of \(\frac{2}{5}\) ÷ 4 is
\(\frac{2}{5}\) ÷ 4 = \(\frac{2}{5}\) × \(\frac{1}{4}\)
= \(\frac{1}{10}\).
b) \(\frac{1}{4}\) ÷ \(\frac{2}{3}\) and \(\frac{2}{3}\) ÷ \(\frac{1}{4}\)
Answer:
\(\frac{1}{4}\) ÷ \(\frac{2}{3}\) = \(\frac{3}{8}\).
\(\frac{2}{3}\) ÷ \(\frac{1}{4}\) = 2\(\frac{2}{3}\).
Explanation:
The quotient of \(\frac{1}{4}\) ÷ \(\frac{2}{3}\) is
\(\frac{1}{4}\) ÷ \(\frac{2}{3}\) = \(\frac{1}{4}\) × \(\frac{3}{2}\)
= \(\frac{3}{8}\).
And the quotient of \(\frac{2}{3}\) ÷ \(\frac{1}{4}\) is
\(\frac{2}{3}\) ÷ \(\frac{1}{4}\) = \(\frac{2}{3}\) × \(\frac{4}{1}\)
= \(\frac{8}{3}\)
= 2\(\frac{2}{3}\).
Math in Focus Course 1A Practice 3.1 Answer Key
Divide. Express the quotient ¡n simplest form. Use models to help you.
Question 1.
1 ÷ \(\frac{1}{4}\)
Answer:
1 ÷ \(\frac{1}{4}\) = 4.
Explanation:
The simplest form of 1 ÷ \(\frac{1}{4}\) is
1 ÷ \(\frac{1}{4}\) = 1 × \(\frac{4}{1}\)
= 4.
Question 2.
3 ÷ \(\frac{3}{5}\)
Answer:
3 ÷ \(\frac{3}{5}\) = 5.
Explanation:
The simplest form of 3 ÷ \(\frac{3}{5}\) is
3 ÷ \(\frac{3}{5}\) = 3 × \(\frac{5}{3}\)
= 5.
Question 3.
\(\frac{3}{4}\) ÷ \(\frac{1}{8}\)
Answer:
\(\frac{3}{4}\) ÷ \(\frac{1}{8}\) = 6.
Explanation:
The simplest form of \(\frac{3}{4}\) ÷ \(\frac{1}{8}\) is
\(\frac{3}{4}\) ÷ \(\frac{1}{8}\) = \(\frac{3}{4}\) × \(\frac{8}{1}\)
= 6.
Question 4.
\(\frac{2}{3}\) ÷ \(\frac{2}{9}\)
Answer:
\(\frac{2}{3}\) ÷ \(\frac{2}{9}\) = 3.
Explanation:
The simplest form of \(\frac{2}{3}\) ÷ \(\frac{2}{9}\) is
\(\frac{2}{3}\) ÷ \(\frac{2}{9}\) = \(\frac{2}{3}\) × \(\frac{9}{2}\)
= 3.
Draw a model to find each quotient.
Question 5.
1 ÷ \(\frac{1}{5}\)
Answer:
1 ÷ \(\frac{1}{5}\) = 5.
Explanation:
The quotient of 1 ÷ \(\frac{1}{5}\) is
1 ÷ \(\frac{1}{5}\) = 1 × \(\frac{5}{1}\)
= 5.
Question 6.
4 ÷ \(\frac{8}{9}\)
Answer:
4 ÷ \(\frac{8}{9}\) = 4\(\frac{1}{2}\).
Explanation:
The quotient of 4 ÷ \(\frac{8}{9}\) is
4 ÷ \(\frac{8}{9}\) = 4 × \(\frac{9}{8}\)
= \(\frac{9}{2}\)
= 4\(\frac{1}{2}\).
Question 7.
\(\frac{2}{5}\) ÷ \(\frac{3}{10}\)
Answer:
\(\frac{2}{5}\) ÷ \(\frac{3}{10}\) = 1\(\frac{1}{3}\).
Explanation:
The quotient of \(\frac{2}{5}\) ÷ \(\frac{3}{10}\) is
\(\frac{2}{5}\) ÷ \(\frac{3}{10}\) = \(\frac{2}{5}\) × \(\frac{10}{3}\)
= \(\frac{4}{3}\)
= 1\(\frac{1}{3}\).
Question 8.
\(\frac{3}{4}\) ÷ \(\frac{3}{16}\)
Answer:
\(\frac{3}{4}\) ÷ \(\frac{3}{16}\) = 4.
Explanation:
The quotient of \(\frac{3}{4}\) ÷ \(\frac{3}{16}\) is
\(\frac{3}{4}\) ÷ \(\frac{3}{16}\) = \(\frac{3}{4}\) × \(\frac{16}{3}\)
= 4.
Find each quotient. Express your answer in its simplest form.
Question 9.
4 ÷ \(\frac{1}{7}\)
Answer:
4 ÷ \(\frac{1}{7}\) = 28.
Explanation:
The quotient of 4 ÷ \(\frac{1}{7}\) is
4 ÷ \(\frac{1}{7}\) = 4 × \(\frac{7}{1}\)
= 28.
Question 10.
12 ÷ \(\frac{1}{3}\)
Answer:
12 ÷ \(\frac{1}{3}\) = 36.
Explanation:
The quotient of 12 ÷ \(\frac{1}{3}\) is
12 ÷ \(\frac{1}{3}\) = 12 × \(\frac{3}{1}\)
= 36.
Question 11.
9 ÷ \(\frac{3}{4}\)
Answer:
9 ÷ \(\frac{3}{4}\) = 12.
Explanation:
The quotient of 9 ÷ \(\frac{3}{4}\) is
9 ÷ \(\frac{3}{4}\) = 9 × \(\frac{4}{3}\)
= 3 × 4
= 12.
Question 12.
10 ÷ \(\frac{4}{5}\)
Answer:
10 ÷ \(\frac{4}{5}\) = 12\(\frac{1}{2}\).
Explanation:
The quotient of 10 ÷ \(\frac{4}{5}\) is
10 ÷ \(\frac{4}{5}\) = 10 × \(\frac{5}{4}\)
= \(\frac{25}{2}\)
= 12\(\frac{1}{2}\).
Question 13.
\(\frac{1}{2}\) ÷ \(\frac{1}{8}\)
Answer:
\(\frac{1}{2}\) ÷ \(\frac{1}{8}\) = 4.
Explanation:
The quotient of \(\frac{1}{2}\) ÷ \(\frac{1}{8}\) is
\(\frac{1}{2}\) ÷ \(\frac{1}{8}\) = \(\frac{1}{2}\) × \(\frac{8}{1}\)
= 4.
Question 14.
\(\frac{1}{4}\) ÷ \(\frac{1}{2}\)
Answer:
\(\frac{1}{4}\) ÷ \(\frac{1}{2}\) = \(\frac{1}{2}\).
Explanation:
The quotient of \(\frac{1}{4}\) ÷ \(\frac{1}{2}\) is
\(\frac{1}{4}\) ÷ \(\frac{1}{2}\) = \(\frac{1}{4}\) × \(\frac{2}{1}\)
= \(\frac{1}{2}\).
Question 15.
\(\frac{3}{5}\) ÷ \(\frac{11}{15}\)
Answer:
\(\frac{3}{5}\) ÷ \(\frac{11}{15}\) = 1\(\frac{4}{11}\).
Explanation:
The quotient of \(\frac{3}{5}\) ÷ \(\frac{11}{15}\) is
\(\frac{3}{5}\) ÷ \(\frac{11}{15}\) = \(\frac{3}{5}\) × \(\frac{15}{11}\)
= \(\frac{15}{11}\)
= 1\(\frac{4}{11}\).
Question 16.
\(\frac{2}{3}\) ÷ \(\frac{10}{13}\)
Answer:
\(\frac{2}{3}\) ÷ \(\frac{10}{13}\) = \(\frac{13}{15}\).
Explanation:
The quotient of \(\frac{2}{3}\) ÷ \(\frac{10}{13}\) is
\(\frac{2}{3}\) ÷ \(\frac{10}{13}\) = \(\frac{2}{3}\) × \(\frac{13}{10}\)
= \(\frac{13}{15}\).
Question 17.
\(\frac{5}{6}\) ÷ \(\frac{7}{12}\)
Answer:
\(\frac{5}{6}\) ÷ \(\frac{7}{12}\) = 1\(\frac{3}{7}\).
Explanation:
The quotient of \(\frac{5}{6}\) ÷ \(\frac{7}{12}\) is
\(\frac{5}{6}\) ÷ \(\frac{7}{12}\) = \(\frac{5}{6}\) × \(\frac{12}{7}\)
= \(\frac{10}{7}\)
= 1\(\frac{3}{7}\).
Question 18.
\(\frac{3}{4}\) ÷ \(\frac{9}{16}\)
Answer:
\(\frac{3}{4}\) ÷ \(\frac{9}{16}\) = 1\(\frac{1}{3}\).
Explanation:
The quotient of \(\frac{3}{4}\) ÷ \(\frac{9}{16}\) is
\(\frac{3}{4}\) ÷ \(\frac{9}{16}\) = \(\frac{3}{4}\) × \(\frac{16}{9}\)
= \(\frac{4}{3}\)
= 1\(\frac{1}{3}\).
Find each quotient. Express your answer in its simplest form.
Question 19.
\(\frac{1}{3}\) ÷ \(\frac{7}{4}\)
Answer:
\(\frac{1}{3}\) ÷ \(\frac{7}{4}\) = \(\frac{4}{21}\).
Explanation:
The quotient of \(\frac{1}{3}\) ÷ \(\frac{7}{4}\) is
\(\frac{1}{3}\) ÷ \(\frac{7}{4}\) = \(\frac{1}{3}\) × \(\frac{4}{7}\)
= \(\frac{4}{21}\).
Question 20.
\(\frac{1}{2}\) ÷ \(\frac{8}{4}\)
Answer:
\(\frac{1}{2}\) ÷ \(\frac{8}{4}\) = \(\frac{1}{4}\).
Explanation:
The quotient of \(\frac{1}{2}\) ÷ \(\frac{8}{4}\) is
\(\frac{1}{2}\) ÷ \(\frac{8}{4}\) = \(\frac{1}{2}\) × \(\frac{4}{8}\)
= \(\frac{1}{4}\).
Question 21.
\(\frac{1}{9}\) ÷ \(\frac{14}{3}\)
Answer:
\(\frac{1}{9}\) ÷ \(\frac{14}{3}\) = \(\frac{1}{42}\).
Explanation:
The quotient of \(\frac{1}{9}\) ÷ \(\frac{14}{3}\) is
\(\frac{1}{9}\) ÷ \(\frac{14}{3}\) = \(\frac{1}{9}\) × \(\frac{3}{14}\)
= \(\frac{1}{42}\).
Question 22.
\(\frac{5}{8}\) ÷ \(\frac{21}{4}\)
Answer:
\(\frac{5}{8}\) ÷ \(\frac{21}{4}\) = \(\frac{5}{42}\).
Explanation:
The quotient of \(\frac{5}{8}\) ÷ \(\frac{21}{4}\) is
\(\frac{5}{8}\) ÷ \(\frac{21}{4}\) = \(\frac{5}{8}\) × \(\frac{4}{21}\)
= \(\frac{5}{42}\).
Question 23.
3\(\frac{1}{2}\) ÷ 2\(\frac{1}{8}\)
Answer:
3\(\frac{1}{2}\) ÷ 2\(\frac{1}{8}\) = 1 \(\frac{11}{17}\).
Explanation:
The quotient of 3\(\frac{1}{2}\) ÷ 2\(\frac{1}{8}\) is
3\(\frac{1}{2}\) ÷ 2\(\frac{1}{8}\) = \(\frac{7}{2}\) ÷ \(\frac{17}{8}\)
= \(\frac{7}{2}\) × \(\frac{8}{17}\)
= \(\frac{28}{17}\)
= 1 \(\frac{11}{17}\).
Question 24.
5\(\frac{1}{4}\) ÷ 3\(\frac{1}{2}\)
Answer:
5\(\frac{1}{4}\) ÷ 3\(\frac{1}{2}\) = \(\frac{3}{2}\).
Explanation:
The quotient of 5\(\frac{1}{4}\) ÷ 3\(\frac{1}{2}\) is
5\(\frac{1}{4}\) ÷ 3\(\frac{1}{2}\) = \(\frac{21}{4}\) ÷ \(\frac{7}{2}\)
= \(\frac{21}{4}\) × \(\frac{2}{7}\)
= \(\frac{3}{2}\).
Question 25.
7\(\frac{3}{5}\) ÷ 8\(\frac{11}{15}\)
Answer:
7\(\frac{3}{5}\) ÷ 8\(\frac{11}{15}\) = \(\frac{114}{131}\).
Explanation:
The quotient of 7\(\frac{3}{5}\) ÷ 8\(\frac{11}{15}\) is
7\(\frac{3}{5}\) ÷ 8\(\frac{11}{15}\) =\(\frac{38}{5}\) ÷ \(\frac{131}{15}\)
= \(\frac{38}{5}\) × \(\frac{15}{131}\)
= \(\frac{114}{131}\).
Question 26.
12\(\frac{2}{3}\) ÷ 5\(\frac{11}{13}\)
Answer:
12\(\frac{2}{3}\) ÷ 5\(\frac{11}{13}\) = 2\(\frac{1}{6}\).
Explanation:
The quotient of 12\(\frac{2}{3}\) ÷ 5\(\frac{11}{13}\) is
12\(\frac{2}{3}\) ÷ 5\(\frac{11}{13}\) = \(\frac{26}{3}\) ÷ \(\frac{76}{13}\)
= \(\frac{38}{3}\) × \(\frac{13}{76}\)
= \(\frac{13}{6}\)
= 2\(\frac{1}{6}\).
Solve. Show your work.
Question 27.
6 pizzas were shared equally among a group of children. Each child got \(\frac{1}{9}\) of a pizza. How many children were in the group?
Answer:
The number of children were in the group is 54 children.
Explanation:
Given that 6 pizzas were shared equally among a group of children and each child got \(\frac{1}{9}\) of a pizza. So the number of children were in the group is 6 ÷ \(\frac{1}{9}\)
= 6 × 9
= 54 children.
Question 28.
A rectangle has an area of 15 square meters. It ¡s divided into parts, each with an area of \(\frac{3}{8}\) square meter. Into how many parts has the rectangle been divided?
Answer:
The number of parts has the rectangle been divided is 40 square meters.
Explanation:
Given that a rectangle has an area of 15 square meters and it ¡s divided into parts, each with an area of \(\frac{3}{8}\) square meter. So the number of parts has the rectangle been divided is 15 ÷ \(\frac{3}{8}\)
= 15 × \(\frac{8}{3}\)
= 5 × 8
= 40 square meters.
Question 29.
How many \(\frac{3}{8}\)-cup servings are in a pitcher containing 6\(\frac{3}{4}\) cups of orange juice?
Answer:
The number of serving pitchers be 18 cups.
Explanation:
Given that 1 cup contains \(\frac{3}{8}\) servings are in a pitcher containing and the total is 6\(\frac{3}{4}\) which is \(\frac{27}{4}\). So the number of serving pitchers be \(\frac{27}{4}\) ÷ \(\frac{3}{8}\)
= \(\frac{27}{4}\) × \(\frac{8}{3}\)
= 9 × 2
= 18 cups.
Question 30.
Maria buys 8\(\frac{1}{3}\) pounds of beef to make tacos for a party. She uses \(\frac{5}{9}\) pound of beef for each taco. How many tacos can Maria make?
Answer:
The number of tacos can Maria make is 15 tacos.
Explanation:
Given that Maria buys 8\(\frac{1}{3}\) pounds of beef to make tacos for a party which is \(\frac{25}{3}\) and she uses \(\frac{5}{9}\) pound of beef for each taco. So the number of tacos can Maria make is \(\frac{25}{3}\) ÷ \(\frac{5}{9}\)
= \(\frac{25}{3}\) × \(\frac{9}{5}\)
= 5 × 3
= 15.
The capacity of a large milk carton is 1\(\frac{1}{2}\) liters. A dozen large cartons are poured into a container and then poured into small cartons that each hold \(\frac{3}{10}\) liter. How many small cartons of milk can be filled?
Answer:
The number of small cartons of milk that can be filled is 60 cartons.
Explanation:
Given that the capacity of a large milk carton is 1\(\frac{1}{2}\) liters which is \(\frac{3}{2}\), so in pounds, it will be 12 × \(\frac{3}{2}\)
= 6 × 3
= 18.
And a dozen large cartons are poured into a container and then poured into small cartons that each hold \(\frac{3}{10}\) liter. Here, the total number of small cartons of milk can be filled = Total number of pounds of a dozen large cartons ÷ small carton capacity which is
= 18 ÷ \(\frac{3}{10}\)
= 18 × \(\frac{10}{3}\)
= 6 × 10
= 60.
The number of small cartons of milk that can be filled is 60 cartons.