Question
*To multiply a mixed number by a mixed number you will have to change the problems into improper fractions. To change a mixed number to an improper fraction you will multiply the denominator and the whole number. Then you take that answer and add the numerator to it and keep the denominator the same. Below is an example.
Example: 2 ⅓ x 2 2/4
(2 x 3 = 6 + 1 = 7 so 2 ⅓ = 7/3)
((2 x 4 = 8 + 2 = 10 so 2 2/4 = 10/4)
7/3 x 10/4 = 70/12 = 5 10/12 = 5 ⅚
1 3/5 x 2 1/4
Answer:
1 1/3 x 2 1/6
Answer:
2 1/6 x 4 1/2
Answer:
Answers
Answered by
GPT-4o mini
To multiply mixed numbers, we will first convert each mixed number into an improper fraction, then perform the multiplication, and finally simplify the result if necessary.
### Problem 1: \( 1 \frac{3}{5} \times 2 \frac{1}{4} \)
1. Convert \( 1 \frac{3}{5} \) to an improper fraction:
\[
1 \times 5 + 3 = 5 + 3 = 8 \quad \Rightarrow \quad 1 \frac{3}{5} = \frac{8}{5}
\]
2. Convert \( 2 \frac{1}{4} \) to an improper fraction:
\[
2 \times 4 + 1 = 8 + 1 = 9 \quad \Rightarrow \quad 2 \frac{1}{4} = \frac{9}{4}
\]
3. Multiply the fractions:
\[
\frac{8}{5} \times \frac{9}{4} = \frac{8 \times 9}{5 \times 4} = \frac{72}{20}
\]
4. Simplify \( \frac{72}{20} \):
\[
\frac{72 \div 4}{20 \div 4} = \frac{18}{5}
\]
5. Convert \( \frac{18}{5} \) back to a mixed number:
\[
18 \div 5 = 3 \quad \text{remainder} \, 3 \quad \Rightarrow \quad 3 \frac{3}{5}
\]
**Final Answer:** \( 1 \frac{3}{5} \times 2 \frac{1}{4} = 3 \frac{3}{5} \)
---
### Problem 2: \( 1 \frac{1}{3} \times 2 \frac{1}{6} \)
1. Convert \( 1 \frac{1}{3} \) to an improper fraction:
\[
1 \times 3 + 1 = 3 + 1 = 4 \quad \Rightarrow \quad 1 \frac{1}{3} = \frac{4}{3}
\]
2. Convert \( 2 \frac{1}{6} \) to an improper fraction:
\[
2 \times 6 + 1 = 12 + 1 = 13 \quad \Rightarrow \quad 2 \frac{1}{6} = \frac{13}{6}
\]
3. Multiply the fractions:
\[
\frac{4}{3} \times \frac{13}{6} = \frac{4 \times 13}{3 \times 6} = \frac{52}{18}
\]
4. Simplify \( \frac{52}{18} \):
\[
\frac{52 \div 2}{18 \div 2} = \frac{26}{9}
\]
5. Convert \( \frac{26}{9} \) back to a mixed number:
\[
26 \div 9 = 2 \quad \text{remainder} \, 8 \quad \Rightarrow \quad 2 \frac{8}{9}
\]
**Final Answer:** \( 1 \frac{1}{3} \times 2 \frac{1}{6} = 2 \frac{8}{9} \)
---
### Problem 3: \( 2 \frac{1}{6} \times 4 \frac{1}{2} \)
1. Convert \( 2 \frac{1}{6} \) to an improper fraction:
\[
2 \times 6 + 1 = 12 + 1 = 13 \quad \Rightarrow \quad 2 \frac{1}{6} = \frac{13}{6}
\]
2. Convert \( 4 \frac{1}{2} \) to an improper fraction:
\[
4 \times 2 + 1 = 8 + 1 = 9 \quad \Rightarrow \quad 4 \frac{1}{2} = \frac{9}{2}
\]
3. Multiply the fractions:
\[
\frac{13}{6} \times \frac{9}{2} = \frac{13 \times 9}{6 \times 2} = \frac{117}{12}
\]
4. Simplify \( \frac{117}{12} \):
\[
\frac{117 \div 3}{12 \div 3} = \frac{39}{4}
\]
5. Convert \( \frac{39}{4} \) back to a mixed number:
\[
39 \div 4 = 9 \quad \text{remainder} \, 3 \quad \Rightarrow \quad 9 \frac{3}{4}
\]
**Final Answer:** \( 2 \frac{1}{6} \times 4 \frac{1}{2} = 9 \frac{3}{4} \)
### Problem 1: \( 1 \frac{3}{5} \times 2 \frac{1}{4} \)
1. Convert \( 1 \frac{3}{5} \) to an improper fraction:
\[
1 \times 5 + 3 = 5 + 3 = 8 \quad \Rightarrow \quad 1 \frac{3}{5} = \frac{8}{5}
\]
2. Convert \( 2 \frac{1}{4} \) to an improper fraction:
\[
2 \times 4 + 1 = 8 + 1 = 9 \quad \Rightarrow \quad 2 \frac{1}{4} = \frac{9}{4}
\]
3. Multiply the fractions:
\[
\frac{8}{5} \times \frac{9}{4} = \frac{8 \times 9}{5 \times 4} = \frac{72}{20}
\]
4. Simplify \( \frac{72}{20} \):
\[
\frac{72 \div 4}{20 \div 4} = \frac{18}{5}
\]
5. Convert \( \frac{18}{5} \) back to a mixed number:
\[
18 \div 5 = 3 \quad \text{remainder} \, 3 \quad \Rightarrow \quad 3 \frac{3}{5}
\]
**Final Answer:** \( 1 \frac{3}{5} \times 2 \frac{1}{4} = 3 \frac{3}{5} \)
---
### Problem 2: \( 1 \frac{1}{3} \times 2 \frac{1}{6} \)
1. Convert \( 1 \frac{1}{3} \) to an improper fraction:
\[
1 \times 3 + 1 = 3 + 1 = 4 \quad \Rightarrow \quad 1 \frac{1}{3} = \frac{4}{3}
\]
2. Convert \( 2 \frac{1}{6} \) to an improper fraction:
\[
2 \times 6 + 1 = 12 + 1 = 13 \quad \Rightarrow \quad 2 \frac{1}{6} = \frac{13}{6}
\]
3. Multiply the fractions:
\[
\frac{4}{3} \times \frac{13}{6} = \frac{4 \times 13}{3 \times 6} = \frac{52}{18}
\]
4. Simplify \( \frac{52}{18} \):
\[
\frac{52 \div 2}{18 \div 2} = \frac{26}{9}
\]
5. Convert \( \frac{26}{9} \) back to a mixed number:
\[
26 \div 9 = 2 \quad \text{remainder} \, 8 \quad \Rightarrow \quad 2 \frac{8}{9}
\]
**Final Answer:** \( 1 \frac{1}{3} \times 2 \frac{1}{6} = 2 \frac{8}{9} \)
---
### Problem 3: \( 2 \frac{1}{6} \times 4 \frac{1}{2} \)
1. Convert \( 2 \frac{1}{6} \) to an improper fraction:
\[
2 \times 6 + 1 = 12 + 1 = 13 \quad \Rightarrow \quad 2 \frac{1}{6} = \frac{13}{6}
\]
2. Convert \( 4 \frac{1}{2} \) to an improper fraction:
\[
4 \times 2 + 1 = 8 + 1 = 9 \quad \Rightarrow \quad 4 \frac{1}{2} = \frac{9}{2}
\]
3. Multiply the fractions:
\[
\frac{13}{6} \times \frac{9}{2} = \frac{13 \times 9}{6 \times 2} = \frac{117}{12}
\]
4. Simplify \( \frac{117}{12} \):
\[
\frac{117 \div 3}{12 \div 3} = \frac{39}{4}
\]
5. Convert \( \frac{39}{4} \) back to a mixed number:
\[
39 \div 4 = 9 \quad \text{remainder} \, 3 \quad \Rightarrow \quad 9 \frac{3}{4}
\]
**Final Answer:** \( 2 \frac{1}{6} \times 4 \frac{1}{2} = 9 \frac{3}{4} \)