Simplify The Ratio $\frac{7}{8}: \frac{3}{4}$.

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**Simplify the Ratio $\frac{7}{8}: \frac{3}{4}$** =====================================================

What is a Ratio?

A ratio is a way to compare two or more numbers by division. It is often expressed as a fraction, with the first number being the numerator and the second number being the denominator. In this case, we have two ratios: 78\frac{7}{8} and 34\frac{3}{4}.

Why Simplify a Ratio?

Simplifying a ratio is important because it helps us to compare and contrast different quantities. By simplifying a ratio, we can make it easier to understand and work with. In this article, we will learn how to simplify the ratio 78:34\frac{7}{8}: \frac{3}{4}.

Step 1: Find the Least Common Multiple (LCM)

To simplify a ratio, we need to find the least common multiple (LCM) of the denominators. The LCM is the smallest number that both denominators can divide into evenly.

What is the LCM of 8 and 4?

To find the LCM of 8 and 4, we need to list the multiples of each number:

Multiples of 8: 8, 16, 24, 32, 40, ... Multiples of 4: 4, 8, 12, 16, 20, ...

As we can see, the smallest number that both lists have in common is 8. Therefore, the LCM of 8 and 4 is 8.

Step 2: Convert Both Ratios to Have the Same Denominator

Now that we have found the LCM, we can convert both ratios to have the same denominator.

How to Convert a Ratio to Have a Different Denominator

To convert a ratio to have a different denominator, we need to multiply the numerator and denominator by the same number. In this case, we need to multiply both ratios by 4/4 to get:

78×44=2832\frac{7}{8} \times \frac{4}{4} = \frac{28}{32}

34×44=1216\frac{3}{4} \times \frac{4}{4} = \frac{12}{16}

Step 3: Simplify the Ratios

Now that both ratios have the same denominator, we can simplify them by dividing both the numerator and denominator by their greatest common divisor (GCD).

What is the GCD of 28 and 12?

To find the GCD of 28 and 12, we need to list the factors of each number:

Factors of 28: 1, 2, 4, 7, 14, 28 Factors of 12: 1, 2, 3, 4, 6, 12

As we can see, the greatest number that both lists have in common is 4. Therefore, the GCD of 28 and 12 is 4.

How to Simplify a Ratio

To simplify a ratio, we need to divide both the numerator and denominator by their GCD.

Simplifying the Ratio 2832\frac{28}{32}

To simplify the ratio 2832\frac{28}{32}, we need to divide both the numerator and denominator by their GCD, which is 4.

2832÷44=78\frac{28}{32} \div \frac{4}{4} = \frac{7}{8}

Simplifying the Ratio 1216\frac{12}{16}

To simplify the ratio 1216\frac{12}{16}, we need to divide both the numerator and denominator by their GCD, which is 4.

1216÷44=34\frac{12}{16} \div \frac{4}{4} = \frac{3}{4}

Conclusion

In this article, we learned how to simplify the ratio 78:34\frac{7}{8}: \frac{3}{4}. We found the LCM of 8 and 4, converted both ratios to have the same denominator, and simplified them by dividing both the numerator and denominator by their GCD. The simplified ratio is 78:34\frac{7}{8}: \frac{3}{4}.

Frequently Asked Questions

Q: What is a ratio?

A: A ratio is a way to compare two or more numbers by division. It is often expressed as a fraction, with the first number being the numerator and the second number being the denominator.

Q: Why simplify a ratio?

A: Simplifying a ratio is important because it helps us to compare and contrast different quantities. By simplifying a ratio, we can make it easier to understand and work with.

Q: How do I find the LCM of two numbers?

A: To find the LCM of two numbers, you need to list the multiples of each number and find the smallest number that both lists have in common.

Q: How do I convert a ratio to have a different denominator?

A: To convert a ratio to have a different denominator, you need to multiply the numerator and denominator by the same number.

Q: How do I simplify a ratio?

A: To simplify a ratio, you need to divide both the numerator and denominator by their GCD.

Q: What is the GCD of two numbers?

A: The GCD of two numbers is the greatest number that both numbers have in common.

Q: How do I find the GCD of two numbers?

A: To find the GCD of two numbers, you need to list the factors of each number and find the greatest number that both lists have in common.