Let's solve the problem shown in the image step by step and explain the solution.
---
Problem:
$$
\frac{2}{5} \div \frac{3}{10}
$$
---
Step 1: Understand the Rule for Dividing Fractions
To divide fractions, we use the rule:
>
"Keep, Change, Flip"
> -
Keep the first fraction as it is.
> -
Change the division sign to multiplication.
> -
Flip (invert) the second fraction.
So:
$$
\frac{2}{5} \div \frac{3}{10} = \frac{2}{5} \times \frac{10}{3}
$$
This matches what’s shown in the image.
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Step 2: Multiply the Fractions
Now multiply the numerators and the denominators:
$$
\frac{2 \times 10}{5 \times 3} = \frac{20}{15}
$$
So far, so good — this matches the result shown in the image.
---
Step 3: Simplify the Fraction
Now simplify $\frac{20}{15}$.
Find the greatest common divisor (GCD) of 20 and 15.
- Factors of 20: 1, 2, 4, 5, 10, 20
- Factors of 15: 1, 3, 5, 15
- GCD = 5
Divide numerator and denominator by 5:
$$
\frac{20 \div 5}{15 \div 5} = \frac{4}{3}
$$
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Final Answer:
$$
\frac{2}{5} \div \frac{3}{10} = \frac{4}{3}
$$
Or as a mixed number: $1 \frac{1}{3}$
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✔ Correction:
The image shows $\frac{20}{15}$ as the final answer, but it should be
simplified to $\frac{4}{3}$.
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Summary:
- The method is correct: change division to multiplication and flip the second fraction.
- The multiplication is correct: $\frac{2}{5} \times \frac{10}{3} = \frac{20}{15}$
- But $\frac{20}{15}$ must be simplified to $\frac{4}{3}$
---
✔ Correct Final Answer:
$$
\boxed{\frac{4}{3}}
$$
Parent Tip: Review the logic above to help your child master the concept of dividing fractions.
