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Chapter 4: Problem 48

Rewrite each fraction with the indicated denominators. $$\frac{7}{5}=\frac{ }{35}$$

Short Answer

Expert verified
\( \frac{49}{35} \)

Step by step solution

01

- Determine the multiplication factor

To rewrite the fraction \(\frac{7}{5}\) with a denominator of 35, determine the number by which to multiply 5 to get 35. This factor can be found by dividing 35 by 5.
02

- Calculate the factor

Divide 35 by 5: \(\frac{35}{5} = 7\). So, the factor needed is 7.
03

- Multiply the numerator and denominator

Multiply both the numerator (7) and the denominator (5) by the factor (7): \( \frac{7 \times 7}{5 \times 7} = \frac{49}{35} \).
04

- Write the final fraction

The fraction \(\frac{7}{5}\) can be rewritten with a denominator of 35 as \(\frac{49}{35}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

denominator
In fractions, the denominator is the bottom number. It shows how many equal parts the whole is divided into. For example, in the fraction \( \frac{7}{5} \), the denominator is 5. When converting fractions to have a common or different denominator, you keep the denominator consistent while adjusting the numerator accordingly. In our exercise, where we convert \( \frac{7}{5} \) to a fraction with a denominator of 35, we need to figure out the multiplication factor. Here, the original denominator (5) needs to become 35.
multiplication factor
The multiplication factor helps us change the size of the denominator while keeping the value of the fraction the same. To find this factor, divide the new denominator by the original denominator. In the exercise: \( \frac{7}{5} = \frac{ \) \text{ } {35} \), \( \ 35 = \frac \ 355. By dividing 35 by 5, our multiplication factor is 7. This factor will be used to adjust both the numerator and the denominator.
numerator
The numerator is the top part of the fraction. It indicates how many parts of the whole are being considered. In the fraction \( \frac{7}{5} \), the numerator is 7. Once we determine our multiplication factor, we multiply both the numerator and the denominator by that factor. For example, multiplying both parts by 7, we get \( \frac{7 \times 7}{5 \times 7} = \frac{49}{35} \). This keeps the fraction鈥檚 value the same but changes its form.
  • Original fraction: \ \frac{7}{5} \
  • Multiplication factor: 7
  • New numerator: 7 \ \times 7 = 49 \
  • New denominator: 5 \ \times 7 = 35 \
Using these steps ensures that the fraction \ \frac{7}{5} \ is correctly converted to \frac{49}{35}.

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