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Chapter 2: Problem 2

(a) Express \(\frac{3}{5}\) as an equivalent fraction with a denominator of 40 . (b) Express \(\frac{9}{30}\) as an equivalent fraction with a denominator of 10 . (c) Express 6 as an equivalent fraction with a denominator of 4 .

Short Answer

Expert verified
Question: Express the following fractions as equivalent fractions with the given denominators: a) $\frac{3}{5}$ with a denominator of 40 b) $\frac{9}{30}$ with a denominator of 10 c) Express the whole number 6 as an equivalent fraction with a denominator of 4 and then simplify it. Answer: a) $\frac{24}{40}$ b) $\frac{3}{10}$ c) $\frac{24}{4} \implies \frac{6}{1}$ (which is the same as the whole number 6)

Step by step solution

01

(Part a - Find common denominator between 5 and 40)

Since the desired denominator is already given (40), we just need to find out how many times 5 needs to be multiplied to get 40. That is, \(5 \times ? = 40\). Learn that \(\frac{40}{5} = 8\). So, 5 should be multiplied by 8 to get 40 as the denominator.
02

(Part a - Express fraction with the new denominator)

Now that we know that the denominator 5 should be multiplied by 8, we need to do the same for the numerator (3). Multiply both the numerator and the denominator by 8: \(\frac{3 \times 8}{5 \times 8} = \frac{24}{40}\). Therefore, the equivalent fraction of \(\frac{3}{5}\) with a denominator of 40 is \(\frac{24}{40}\).
03

(Part b - Find common denominator between 30 and 10)

For this part, the desired denominator is already given (10). We need to find out how many times 30 should be divided by to get 10. That is, \(30 \div ? = 10\). Learn that \(\frac{30}{10} = 3\). So, 30 should be divided by 3 to get 10 as the denominator.
04

(Part b - Express fraction with the new denominator)

Now that we know that the denominator 30 should be divided by 3, we need to do the same for the numerator (9). Divide both the numerator and the denominator by 3: \(\frac{9 \div 3}{30 \div 3} = \frac{3}{10}\). Therefore, the equivalent fraction of \(\frac{9}{30}\) with a denominator of 10 is \(\frac{3}{10}\).
05

(Part c - Convert whole number 6 to an equivalent fraction with a denominator of 4)

To express the whole number 6 as a fraction with a denominator of 4, we need to find out what the numerator should be. That means, \(6 = \frac{?}{4}\). Since \(6 \times 4 = 24\), we can write 6 as a fraction with a denominator of 4 as follows: \(\frac{24}{4}\).
06

(Part c - Simplify the fraction)

Since \(\frac{24}{4}\) can be simplified, we need to find the greatest common divisor (GCD) for both the numerator (24) and the denominator (4). Since the GCD of 24 and 4 is 4, divide both the numerator and the denominator by 4: \(\frac{24 \div 4}{4 \div 4} = \frac{6}{1}\). Therefore, the equivalent fraction of 6 with a denominator of 4 is \(\frac{24}{4}\), which simplifies to \(\frac{6}{1}\), and it is the same as the whole number 6.

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Most popular questions from this chapter

Evaluate (a) \(6 \frac{2}{3} \div 4\) (b) \(10 \div 2 \frac{1}{3}\) (c) \(\left(\frac{1}{2}+\frac{1}{3}\right) \div\left(\frac{2}{3}+\frac{1}{5}\right)\) (d) \(\left(6-2 \frac{1}{3}\right) \times\left(4 \frac{1}{2}-1 \frac{3}{4}\right)\) (e) \(\frac{2 \frac{1}{2}+1 \frac{1}{3}}{6 \frac{2}{3}-2 \frac{1}{4}}\)

Calculate (a) \(\frac{1}{4}\) of 60 (b) \(\frac{2}{3}\) of 75 (c) \(\frac{3}{8}\) of 64 (d) \(\frac{2}{5}\) of \(\frac{15}{16}\) (e) \(\frac{3}{4}\) of \(\frac{20}{21}\) expressing each answer as a fraction in its simplest form.

Calculate the following, expressing your answer as a mixed fraction: (a) \(2 \frac{1}{4}+3 \frac{1}{3}\) (b) \(2 \frac{4}{5}-1 \frac{2}{3}\) (c) \(5 \frac{2}{3}-1 \frac{1}{2}+2 \frac{1}{5}\) (d) \(5-4 \frac{2}{7}+\frac{1}{3}\) (e) \(\frac{9}{10}+\frac{6}{7}-1 \frac{2}{5}\)

Calculate (a) \(\frac{6}{7} \times \frac{14}{27}\) (b) \(\frac{7}{10} \times \frac{4}{5} \times \frac{30}{49}\) (c) \(\frac{8}{9} \times \frac{18}{25}\) (d) \(\left(-\frac{4}{5}\right) \times\left(-\frac{3}{4}\right)\) (e) \(\frac{16}{21} \times\left(-\frac{3}{4}\right)\)

Consider the fractions \(\frac{2}{3}, \frac{5}{6}\) and \(\frac{7}{8}\). (a) Calculate the l.c.m. of their denominators. (b) Express each fraction as an equivalent fraction with the l.c.m. found in (a) as the denominator.
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