Question
\( \begin{array}{lll}\text { a) } 2 \div \frac{1}{2} & \text { b) } \frac{1}{2} \div \frac{1}{4} & \text { c) } \frac{5}{6} \div \frac{1}{6} \\ \text { d) } \frac{13}{20} \div \frac{4}{5} & \text { e) } \frac{2}{3} \div \frac{9}{16} & \text { f) } \frac{15}{4} \div \frac{3}{8} \\ \text { g) }\left(\frac{2}{3} \div \frac{1}{4}\right) \div \frac{7}{12} & \text { h) } \frac{2}{3} \div\left(\frac{1}{4} \div \frac{7}{12}\right) & \text { i) } \frac{32}{21} \div \frac{16}{7} \div \frac{18}{19} \\ \text { j) } 2 \frac{1}{4} \div \frac{7}{8} & \text { k) } 1 \frac{3}{4} \div 3 \frac{1}{4} & \text { l) } 4 \frac{4}{7} \div \frac{16}{15} \div 1 \frac{1}{14}\end{array} \)
Ask by Malone Evans. in Malaysia
Jan 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Here are the simplified answers for each division problem:
a) \( 4 \)
b) \( 2 \)
c) \( 5 \)
d) \( \frac{13}{16} \)
e) \( \frac{32}{27} \) or \( 1 \frac{5}{27} \)
f) \( 10 \)
g) \( 4 \frac{4}{7} \)
h) \( 1 \frac{5}{9} \)
i) \( \frac{19}{27} \)
j) \( 2 \frac{4}{7} \)
k) \( \frac{7}{13} \)
l) \( 4 \)
Solution
Let's solve each of the division problems step by step. Remember that dividing by a fraction is equivalent to multiplying by its reciprocal.
---
### **a) \( 2 \div \frac{1}{2} \)**
**Solution:**
\[
2 \div \frac{1}{2} = 2 \times \frac{2}{1} = 4
\]
**Answer:** \( 4 \)
---
### **b) \( \frac{1}{2} \div \frac{1}{4} \)**
**Solution:**
\[
\frac{1}{2} \div \frac{1}{4} = \frac{1}{2} \times \frac{4}{1} = \frac{4}{2} = 2
\]
**Answer:** \( 2 \)
---
### **c) \( \frac{5}{6} \div \frac{1}{6} \)**
**Solution:**
\[
\frac{5}{6} \div \frac{1}{6} = \frac{5}{6} \times \frac{6}{1} = \frac{30}{6} = 5
\]
**Answer:** \( 5 \)
---
### **d) \( \frac{13}{20} \div \frac{4}{5} \)**
**Solution:**
\[
\frac{13}{20} \div \frac{4}{5} = \frac{13}{20} \times \frac{5}{4} = \frac{65}{80} = \frac{13}{16} \quad (\text{simplified by dividing numerator and denominator by } 5)
\]
**Answer:** \( \frac{13}{16} \)
---
### **e) \( \frac{2}{3} \div \frac{9}{16} \)**
**Solution:**
\[
\frac{2}{3} \div \frac{9}{16} = \frac{2}{3} \times \frac{16}{9} = \frac{32}{27} = 1 \frac{5}{27}
\]
**Answer:** \( \frac{32}{27} \) or \( 1 \frac{5}{27} \)
---
### **f) \( \frac{15}{4} \div \frac{3}{8} \)**
**Solution:**
\[
\frac{15}{4} \div \frac{3}{8} = \frac{15}{4} \times \frac{8}{3} = \frac{120}{12} = 10
\]
**Answer:** \( 10 \)
---
### **g) \( \left(\frac{2}{3} \div \frac{1}{4}\right) \div \frac{7}{12} \)**
**Solution:**
1. First, divide \( \frac{2}{3} \) by \( \frac{1}{4} \):
\[
\frac{2}{3} \div \frac{1}{4} = \frac{2}{3} \times \frac{4}{1} = \frac{8}{3}
\]
2. Then, divide the result by \( \frac{7}{12} \):
\[
\frac{8}{3} \div \frac{7}{12} = \frac{8}{3} \times \frac{12}{7} = \frac{96}{21} = \frac{32}{7} = 4 \frac{4}{7}
\]
**Answer:** \( 4 \frac{4}{7} \)
---
### **h) \( \frac{2}{3} \div \left(\frac{1}{4} \div \frac{7}{12}\right) \)**
**Solution:**
1. First, divide \( \frac{1}{4} \) by \( \frac{7}{12} \):
\[
\frac{1}{4} \div \frac{7}{12} = \frac{1}{4} \times \frac{12}{7} = \frac{12}{28} = \frac{3}{7}
\]
2. Then, divide \( \frac{2}{3} \) by \( \frac{3}{7} \):
\[
\frac{2}{3} \div \frac{3}{7} = \frac{2}{3} \times \frac{7}{3} = \frac{14}{9} = 1 \frac{5}{9}
\]
**Answer:** \( 1 \frac{5}{9} \)
---
### **i) \( \frac{32}{21} \div \frac{16}{7} \div \frac{18}{19} \)**
**Solution:**
1. First, divide \( \frac{32}{21} \) by \( \frac{16}{7} \):
\[
\frac{32}{21} \div \frac{16}{7} = \frac{32}{21} \times \frac{7}{16} = \frac{224}{336} = \frac{2}{3} \quad (\text{simplified by dividing numerator and denominator by } 112)
\]
2. Then, divide \( \frac{2}{3} \) by \( \frac{18}{19} \):
\[
\frac{2}{3} \div \frac{18}{19} = \frac{2}{3} \times \frac{19}{18} = \frac{38}{54} = \frac{19}{27} \quad (\text{simplified by dividing numerator and denominator by } 2)
\]
**Answer:** \( \frac{19}{27} \)
---
### **j) \( 2 \frac{1}{4} \div \frac{7}{8} \)**
**Solution:**
1. Convert the mixed number to an improper fraction:
\[
2 \frac{1}{4} = \frac{9}{4}
\]
2. Divide by \( \frac{7}{8} \):
\[
\frac{9}{4} \div \frac{7}{8} = \frac{9}{4} \times \frac{8}{7} = \frac{72}{28} = \frac{18}{7} = 2 \frac{4}{7}
\]
**Answer:** \( 2 \frac{4}{7} \)
---
### **k) \( 1 \frac{3}{4} \div 3 \frac{1}{4} \)**
**Solution:**
1. Convert the mixed numbers to improper fractions:
\[
1 \frac{3}{4} = \frac{7}{4}, \quad 3 \frac{1}{4} = \frac{13}{4}
\]
2. Divide:
\[
\frac{7}{4} \div \frac{13}{4} = \frac{7}{4} \times \frac{4}{13} = \frac{28}{52} = \frac{7}{13} \quad (\text{simplified by dividing numerator and denominator by } 4)
\]
**Answer:** \( \frac{7}{13} \)
---
### **l) \( 4 \frac{4}{7} \div \frac{16}{15} \div 1 \frac{1}{14} \)**
**Solution:**
1. Convert the mixed numbers to improper fractions:
\[
4 \frac{4}{7} = \frac{32}{7}, \quad 1 \frac{1}{14} = \frac{15}{14}
\]
2. Perform the divisions step by step:
- First, divide \( \frac{32}{7} \) by \( \frac{16}{15} \):
\[
\frac{32}{7} \div \frac{16}{15} = \frac{32}{7} \times \frac{15}{16} = \frac{480}{112} = \frac{30}{7}
\]
- Then, divide \( \frac{30}{7} \) by \( \frac{15}{14} \):
\[
\frac{30}{7} \div \frac{15}{14} = \frac{30}{7} \times \frac{14}{15} = \frac{420}{105} = 4
\]
**Answer:** \( 4 \)
---
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Simplify this solution Beyond the Answer
Did you know that division can be visualized with everyday scenarios? For example, when dividing by a fraction, you can think of it as sharing a pizza. If you have 2 pizzas and cut each into halves, you end up with 4 slices! It’s a great way to grasp dividing fractions more intuitively. If you’re looking to avoid common mistakes while dividing fractions, remember: always convert mixed numbers to improper fractions first! This lets you work with whole numbers and simplifies the problem, reducing potential errors. Also, don’t forget to "flip and multiply"—that's right! Change the division sign to a multiplication sign and use the reciprocal of the second fraction. Happy calculating!
