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Answer :
Sure! Let's tackle each part of the question step-by-step:
1. Problem 2:
We are given the multiplication [tex]\(\frac{6}{8} \cdot 7 = \frac{42}{56}\)[/tex].
To understand this:
- Start with the fraction [tex]\(\frac{6}{8}\)[/tex].
- Multiply [tex]\(\frac{6}{8}\)[/tex] by 7.
- This results in the new fraction [tex]\(\frac{42}{56}\)[/tex], which is already in its simplest form as given in the problem.
2. Problem 3:
We need to find the missing numerator in the equation [tex]\(\frac{6}{7} = \frac{}{42}\)[/tex].
To solve for the missing numerator:
- Set up a proportion: [tex]\(\frac{6}{7} = \frac{x}{42}\)[/tex].
- Multiply both sides by 42 to solve for [tex]\(x\)[/tex]:
- [tex]\(x = \frac{6 \times 42}{7}\)[/tex].
- Calculate [tex]\(x\)[/tex], which equals 36. So, [tex]\(\frac{6}{7} = \frac{36}{42}\)[/tex].
3. Problem 5:
We are given the equation [tex]\(\frac{1}{2} = \frac{8}{16}\)[/tex].
To check this:
- Simplify [tex]\(\frac{8}{16}\)[/tex] to find that it reduces to [tex]\(\frac{1}{2}\)[/tex].
- Therefore, both fractions are equivalent as shown in the problem.
4. Problem 6:
We need to find the missing denominator in the equation [tex]\(\frac{9}{?} = \frac{27}{30}\)[/tex].
To solve for the missing denominator:
- Set up a proportion: [tex]\(\frac{9}{y} = \frac{27}{30}\)[/tex].
- Solve for [tex]\(y\)[/tex] by cross-multiplying:
- [tex]\(9 \times 30 = 27 \times y\)[/tex].
- Solve for [tex]\(y\)[/tex]:
- [tex]\(y = \frac{9 \times 30}{27}\)[/tex].
- Calculate [tex]\(y\)[/tex], which equals 10. So, [tex]\(\frac{9}{10} = \frac{27}{30}\)[/tex].
These are the detailed solutions for each part of the question.
1. Problem 2:
We are given the multiplication [tex]\(\frac{6}{8} \cdot 7 = \frac{42}{56}\)[/tex].
To understand this:
- Start with the fraction [tex]\(\frac{6}{8}\)[/tex].
- Multiply [tex]\(\frac{6}{8}\)[/tex] by 7.
- This results in the new fraction [tex]\(\frac{42}{56}\)[/tex], which is already in its simplest form as given in the problem.
2. Problem 3:
We need to find the missing numerator in the equation [tex]\(\frac{6}{7} = \frac{}{42}\)[/tex].
To solve for the missing numerator:
- Set up a proportion: [tex]\(\frac{6}{7} = \frac{x}{42}\)[/tex].
- Multiply both sides by 42 to solve for [tex]\(x\)[/tex]:
- [tex]\(x = \frac{6 \times 42}{7}\)[/tex].
- Calculate [tex]\(x\)[/tex], which equals 36. So, [tex]\(\frac{6}{7} = \frac{36}{42}\)[/tex].
3. Problem 5:
We are given the equation [tex]\(\frac{1}{2} = \frac{8}{16}\)[/tex].
To check this:
- Simplify [tex]\(\frac{8}{16}\)[/tex] to find that it reduces to [tex]\(\frac{1}{2}\)[/tex].
- Therefore, both fractions are equivalent as shown in the problem.
4. Problem 6:
We need to find the missing denominator in the equation [tex]\(\frac{9}{?} = \frac{27}{30}\)[/tex].
To solve for the missing denominator:
- Set up a proportion: [tex]\(\frac{9}{y} = \frac{27}{30}\)[/tex].
- Solve for [tex]\(y\)[/tex] by cross-multiplying:
- [tex]\(9 \times 30 = 27 \times y\)[/tex].
- Solve for [tex]\(y\)[/tex]:
- [tex]\(y = \frac{9 \times 30}{27}\)[/tex].
- Calculate [tex]\(y\)[/tex], which equals 10. So, [tex]\(\frac{9}{10} = \frac{27}{30}\)[/tex].
These are the detailed solutions for each part of the question.
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