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Answer :
Louise made an error when she found the product of [tex]\(\frac{4}{5} \times 6\)[/tex] to be [tex]\(\frac{24}{30}\)[/tex]. Let's go through the correct steps to find the product and identify her mistake.
1. Understand the Multiplication:
- Louise is multiplying a fraction by a whole number: [tex]\(\frac{4}{5} \times 6\)[/tex].
- We can rewrite the whole number as a fraction: [tex]\(6 = \frac{6}{1}\)[/tex].
2. Multiply the Numerators:
- Multiply the numerators of the two fractions: [tex]\(4 \times 6 = 24\)[/tex].
3. Multiply the Denominators:
- Multiply the denominators of the two fractions: [tex]\(5 \times 1 = 5\)[/tex].
4. Form the New Fraction:
- After multiplying, the fraction formed is [tex]\(\frac{24}{5}\)[/tex].
5. Simplify or Convert to a Mixed Number (if necessary):
- [tex]\(\frac{24}{5}\)[/tex] is already in its simplest form because 24 and 5 have no common factors other than 1.
- However, it can be expressed as a mixed number: [tex]\(24 \div 5 = 4\)[/tex] with a remainder of 4. So, [tex]\(\frac{24}{5}\)[/tex] is equivalent to [tex]\(4 \frac{4}{5}\)[/tex].
Louise’s error was in simplifying the fraction. She obtained [tex]\(\frac{24}{30}\)[/tex], which is not the correct product as she incorrectly formed the denominator. The correct product of [tex]\(\frac{4}{5} \times 6\)[/tex] is [tex]\(\frac{24}{5}\)[/tex], which is also expressed as the mixed number [tex]\(4 \frac{4}{5}\)[/tex].
1. Understand the Multiplication:
- Louise is multiplying a fraction by a whole number: [tex]\(\frac{4}{5} \times 6\)[/tex].
- We can rewrite the whole number as a fraction: [tex]\(6 = \frac{6}{1}\)[/tex].
2. Multiply the Numerators:
- Multiply the numerators of the two fractions: [tex]\(4 \times 6 = 24\)[/tex].
3. Multiply the Denominators:
- Multiply the denominators of the two fractions: [tex]\(5 \times 1 = 5\)[/tex].
4. Form the New Fraction:
- After multiplying, the fraction formed is [tex]\(\frac{24}{5}\)[/tex].
5. Simplify or Convert to a Mixed Number (if necessary):
- [tex]\(\frac{24}{5}\)[/tex] is already in its simplest form because 24 and 5 have no common factors other than 1.
- However, it can be expressed as a mixed number: [tex]\(24 \div 5 = 4\)[/tex] with a remainder of 4. So, [tex]\(\frac{24}{5}\)[/tex] is equivalent to [tex]\(4 \frac{4}{5}\)[/tex].
Louise’s error was in simplifying the fraction. She obtained [tex]\(\frac{24}{30}\)[/tex], which is not the correct product as she incorrectly formed the denominator. The correct product of [tex]\(\frac{4}{5} \times 6\)[/tex] is [tex]\(\frac{24}{5}\)[/tex], which is also expressed as the mixed number [tex]\(4 \frac{4}{5}\)[/tex].
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