By LearningExpress Editors

Updated on Mar 23, 2011

Review these concepts if necessary:

- Fractions Study Guide: GED Math
- Adding, Subtracting, Multiplying, and Dividing Fractions Study Guide: GED Math
- Decimals Study Guide: GED Math
- Adding, Subtracting, Multiplying, and Dividing Decimals Study Guide: GED Math

### Problems

**F**RACTIONS AND DECIMALS are the most common ways that numbers are represented. An understanding of how to perform operations on these types of numbers is essential to your success on the GED

- 1,036.09 + 2.4 + 17 =
- 1,036.50
- 1,055.49
- 103.650
- 105.549
- 1,077.09

- 26.19 × 0.3 =
- 7.857
- 7,857
- 7.837
- 7,837
- 0.7857

- Which is greatest?
- 0.079
- 0.63
- 0.0108

- 540 ÷ 2.7 =
- 2
- 20
- 2,000
- 0.2
- 200

- Which is greatest?
- Which is smallest?
- 34.7 + 4.1 + 0.03 =
- 391
- 3.91
- 38.83
- 39.1
- 41.8

- 125.05 – 11.4 =
- 123.91
- 123.01
- 113.01
- 113.65
- 114.65

- 16.8 × 0.2 =
- 3.36
- 336
- 0.336
- 33.6
- 3.28

- 5.34 × 10 =
- 50.34
- 15.34
- 5.44
- 53.4
- 534

- 42.19 × 0.4 =
- 168.19
- 16.876
- 168.19
- 16876
- 1.6876

### Answers

**b.**The two fractions already have a common denominator, so combine the numerators and keep the denominator. Then simplify. , in lowest terms.**c.**First, find a common denominator, the LCM of 15 and 30. The LCM is 30. Convert the first fraction to have a denominator of 30: . Now combine to get .**a.**Change each mixed number to an improper fraction. . The fractions have the same denominator, so combine the numerators and keep the denominator: .**d.**When you multiply fractions, multiply straight across and then simplify: .**e.**Change and 6 to improper fractions. Then change the operation to multiply by the reciprocal of 6: . Multiply the numerators and the denominators straight across and simplify: = (14 × 1) ÷ (3 × 6) = .**c.**To divide fractions, change the problem to multiply by the reciprocal. Multiply straight across and then simplify: .**b.**Line up the decimal points, and add vertically:**a.**Multiply as you would with whole numbers; then count the number of digits to the right of the decimal points in the factors. There are three digits, so the decimal place is moved three places to the left in the product.**b.**The fractions are changed to decimals by dividing: = 7 ÷ 12 = 0.58 and = 5 ÷ 7 = 0.71. Change all numbers to decimal numbers with the same number of digits after the decimal point: 0.5800, 0.7100, 0.0790, 0.6300, 0.0108. The decimal 0.71 is the greatest, which was .**e.**Set up the problem as a long division problem. Because the divisor (2.7) has one digit to the right of the decimal point, you must move the decimal place one place to the right in both the divisor and the dividend (540). Add a trailing zero onto the dividend as a placeholder. Then, copy the decimal place straight up to the quotient.

**c.**To divide fractions, change the operation to multiplication and take the reciprocal of the second fraction. Multiply the numerators and denominators straight across: . Change this to an improper fraction by dividing 198 by 77. The result is 2 with remainder 44: . Simplify the fractional part: .**a.**First change the numerator to an improper fraction: . Then change the problem to be a fraction divided by a fraction: . Dividing fractions is the same as multiplying by the reciprocal of the second fraction. Multiply straight across the numerators and denominators: .**e.**This complex fraction means a fraction divided by a fraction. Change the problem to multiply by the reciprocal of the second fraction. . Put the fraction in lowest terms: .**b.**You can convert each fraction to an equivalent fraction, all of which have a common denominator. Find the least common multiple of the denominators: 40 is the LCM: . Now the numerators can be inspected for the greatest, which is .**e.**Convert all fractions to have a common denominator, which is the LCM = 12. . It is sufficient to compare the numerators to find the smallest because the denominators are the same.**c.**Add the numbers vertically; make sure to line up the decimal points and add trailing zeros when necessary:**d.**When subtracting decimals, it is easiest to do the problem vertically, remembering to line up the decimal points:**a.**Multiply without regard to the decimal points. 168 × 2 = 336. Because there are two digits to the right of the decimal points in the factors, place the decimal point two places from the right in the product.**d.**Use the shortcut when multiplying by 10. Move the decimal point one place to the right, to get the product of 53.4.**b.**Multiply without regard to the decimal point:

There are three digits to the right of the decimal points in the factors, namely 1, 9, and then 4. Place the decimal point three places from the right in the product.

From GED Math. Copyright © 2008 by LearningExpress, LLC. All Rights Reserved.

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