Pick the model that represents this division equation. 1 3/4 ÷ 1 3/5 = ? Solve the equation.
Understand the Problem
The question is asking to identify the model that represents the division equation given, as well as solve the equation itself. This involves understanding how to visualize division using models.
Answer
$1 \frac{3}{32}$ or $\frac{35}{32}$
Answer for screen readers
The result of the equation $1 \frac{3}{4} \div 1 \frac{3}{5}$ is $\frac{35}{32}$ or $1 \frac{3}{32}$.
Steps to Solve
- Write the Division Equation as a Fraction
Convert the mixed number $1 \frac{3}{4}$ into an improper fraction.
The mixed number can be converted as follows:
$$ 1 \frac{3}{4} = \frac{4 \times 1 + 3}{4} = \frac{7}{4} $$
So, the division equation becomes:
$$ \frac{7}{4} \div 1 \frac{3}{5} $$
- Convert the Second Mixed Number
Now convert $1 \frac{3}{5}$ into an improper fraction:
$$ 1 \frac{3}{5} = \frac{5 \times 1 + 3}{5} = \frac{8}{5} $$
Now your division equation is:
$$ \frac{7}{4} \div \frac{8}{5} $$
- Use the Multiplication by Reciprocal
To divide fractions, multiply by the reciprocal of the divisor:
$$ \frac{7}{4} \div \frac{8}{5} = \frac{7}{4} \times \frac{5}{8} $$
- Multiply the Fractions
Now multiply the fractions:
$$ \frac{7 \times 5}{4 \times 8} = \frac{35}{32} $$
- Convert Back to a Mixed Number (if needed)
Finally, since $\frac{35}{32}$ is an improper fraction, you can convert it back to a mixed number:
$$ \frac{35}{32} = 1 \frac{3}{32} $$
The result of the equation $1 \frac{3}{4} \div 1 \frac{3}{5}$ is $\frac{35}{32}$ or $1 \frac{3}{32}$.
More Information
Dividing fractions involves converting any mixed numbers into improper fractions, then using the reciprocal and multiplying. It's important to convert back to a mixed number if required for easier understanding.
Tips
- Confusing division and multiplication of fractions.
- Not converting mixed numbers to improper fractions correctly.
- Forgetting to simplify the fraction if needed.
