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Glencoe Math: Course 2, Volume 1

GM

Glencoe Math: Course 2, Volume 1 View details

2. Compare and Order Rational Numbers

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Exercise 10 Page 275

Begin by rewriting the decimal number as a mixed number. Then, rewrite the mixed numbers as improper fractions. How can you compare two fractions with different denominators?

2 56 > 2.8

Practice makes perfect

In this exercise, we are given a decimal number and a mixed number. 2 56 ? 2.8 First, we will rewrite the decimal number as a mixed numbers.

2.8

Write as a fraction

2 810

a/b=.a /2./.b /2.

2 45

Next, we will rewrite the mixed numbers as improper fractions. Let's begin with 2 56.

2 56

a bc=a* c+b/c

2* 6+5/6

Multiply

12+5/6

Add terms

17/6

Now, let's do the same for the second number.

2 45

a bc=a* c+b/c

2* 5+4/5

Multiply

10+4/5

Add terms

14/5

Next, we will compare these fractions. To compare fractions with different denominators, we should first find a common denominator. Since neither of the denominators is a factor of another, we will multiply the numerator and denominator of each fraction by the denominator of other. This will give us a common denominator.

17/6

a/b=a * 5/b * 5

17*5/6*5

Multiply

85/30

Let's do the same for the second fraction.

14/5

a/b=a * 6/b * 6

14*6/5*6

Multiply

84/30

Finally, we can make our comparison. Since 85 is more than 84, we know that the first value is more than the second value. 85/30 > 84/30 ⇔ 2 56 > 2.8 Let's draw it on a number line.

Subchapter links

Guided Practice p.274

Independent Practice p.275-276

H.O.T. Problems p.276

Standardized Test Practice p.276-278

Extra Practice p.277

Common Core Review p.278