Mary Jane Sterling - Algebra I All-in-One For Dummies

A.Set up a proportion with words in the two numerators and the corresponding number of minutes in the denominators:

Divide both numerators by 60 and then cross-multiply to solve for x .

It will take her 67 minutes — just over an hour.

15 Solve for x :

16 Solve for x :

17 Solve for x :

18 Solve for x :

19 A recipe calls for 2 teaspoons of cinnamon and 4 cups of flour. You need to increase the flour to 6 cups. To keep the ingredients proportional, how many teaspoons of cinnamon should you use?

20 A factory produces two faulty tablets for every 500 tablets it produces. How many faulty tablets would you expect to find in a shipment of 1,250?

Before you can add or subtract fractions, you need to find a common denominator for them. Ideally, that common denominator is the least common multiple (the smallest number that each of the denominators can divide into without a remainder). A method of last resort, though, is to multiply the denominators together. Doing so gives you a number that the denominators divide evenly. You may have to work with larger numbers using this method, but you can always reduce the fractions at the end.

And then, there’s the box method . This method is especially helpful when you have three or more fractions to deal with — and they have relatively large denominators.

Common denominators (the same numbers in the denominators) are necessary for adding, subtracting, and comparing fractions. Carefully selected fractions that are equal to the number 1 are used to create common denominators because multiplying by 1 doesn’t change a number’s value.

Follow these steps to find a common denominator for two fractions and write the equivalent fractions:

1 Find the least common multiple of the two denominators — the smallest number that both denominators divide evenly.First, look to see if you can determine the common multiple by simple observation; you may know some multiples of the two numbers. If you find the common multiple by observation, go directly to Step 4. (Do not pass Go; do not collect $200.)

2 If the common multiple isn’t easily determined, start your search by choosing the larger denominator.Check to see if the smaller denominator divides the larger one evenly. If it does, then you’ve found the common denominator. Go to Step 4.

3 Check consecutive multiples of the larger denominator until you find one that the smaller one divides.That’s your common denominator.

4 When you find a common denominator, rewrite both fractions as equivalent fractions with that denominator.Multiply both numerator and denominator of each fraction by the equivalent of 1 that creates fractions with the common denominator.

Q.Find the least common denominator for the two fractions and .

A. 72.Look at the multiples of 24: 24, 48, 72, 96. You can stop with the multiple 72, because that’s also a multiple of 18. The LCD is 72.

Q.How would you write the fractions and with the same denominator?

A.The fractions and have denominators with no factors in common, so the least common denominator is 12, the product of the two numbers. Now you can write them both as fractions with a denominator of 12:

21 Rewrite the fractions and with a common denominator.

22 Rewrite the fractions and with a common denominator.

23 Rewrite the fractions and with a common denominator.

24 Rewrite the fractions and with a common denominator.

25 Rewrite the fractions , , and with a common denominator.

26 Rewrite the fractions , , and with a common denominator.