# GED Math : Decimals and Fractions

## Example Questions

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### Example Question #1 : Decimals And Fractions

Convert the following decimal into a fraction:

Explanation:

The decimal, , is read as two-hundred forty-three thousandths, which translates to:

### Example Question #2 : Decimals And Fractions

Convert the following fraction to a decimal:

Explanation:

### Example Question #1 : Decimals And Fractions

Multiply:

Explanation:

Multiply numerators, then multiply denominators. We can cross-cancel the 9 and the 3 by dividing both by 3:

### Example Question #2 : Decimals And Fractions

Explanation:

To add fractions, you have to make sure that the fractions share a common denominator that the denominator of both numbers is the same. Because these fractions do not have a common denonominator, you use the Lowest Common Multiple rule to find a common denominator.

For these fractions, the lowest common multiple is  and .

For the fractions to remain the same, you have to multiply the numerator and the denominator in  by  and the numerator and the denominator in  by . Once you have found the common denominator and have multiplied the numerator and denominator for each fraction, you can add the fractions.

Because the numerator is larger than the denominator, you simplify the fraction to make it a mixed number.

### Example Question #53 : Numbers And Operations

Above is the menu for a coffee shop; there is no sales tax charged on purchases.

Hedwig wants to throw an informal party for herself and seventeen guests. She wants to serve a large espresso and a butter croissant to each attendee, including herself. As luck would have it, the shop is having a special - for every two croissants purchased, the third is free. How much change will Hedwig get back for a $100 bill? Possible Answers: Correct answer: Explanation: There will be eighteen people at the party, including Hedwig. She will spend for the large espressos. "Buy two get one free" means that only two-thirds of the eighteen croissants - twelve of them - will be bought at the regular price, and the remaining six will be free. She will therefore spend . The total purchase price will be The change from a$100 bill will be

.

### Example Question #3 : Decimals And Fractions

Divide:

Do not use a calculator.

Explanation:

### Example Question #6 : Decimals And Fractions

Evaluate:

Do not use a calculator.

Explanation:

which converts as follows:

,

so

### Example Question #7 : Decimals And Fractions

Jim has a total of $13.85 in nickels, dimes, and quarters. Suppose Jim has 47 nickels. How many dimes could he have? Possible Answers: Correct answer: Explanation: If Jim has 47 nickels, he has in nickels. Since he has$13.85 total, he has a total of  in dimes and quarters.

The number of dimes Jim has must leave an amount that can be made in quarters only - that is, a whole number multiple of . We try all four choices:

64 dimes:  in dimes

Amount in quarters:

Divide this by :

, which is not a whole number.

65 dimes:  in dimes

Amount in quarters:

Divide this by :

, which is a whole number.

66 dimes:  in dimes

Amount in quarters:

Divide this by :

, which is not a whole number.

67 dimes:  in dimes

Amount in quarters:

Divide this by :

, which is not a whole number.

65 dimes is the correct choice since it is the only one that allows for a whole number of quarters.

### Example Question #8 : Decimals And Fractions

Evaluate:

Do not use a calculator.

Explanation:

To divide numbers of unlike sign, divide their absolute values and affix a negative symbol. That is,

To divide a whole number by a decimal, move the decimal points in both numbers the same number of places until the divisor is a whole number.

Therefore, we move the (written or implied) decimal point in each two places:

This becomes a whole number division:

Since we must affix a negative sign, the quotient is .

### Example Question #58 : Numbers And Operations

Each student at an African-studies school is required to take one of three languages - Swahili,  Hausa, or Yoruba. Assume that no student takes more than one language.

One-third of the students have chosen Swahili, and two-fifths of the other students have chosen Hausa. What fraction of the students have chosen Yoruba?

Explanation:

of the students have chosen Swahili, so

have chosen Hausa or Yoruba.

Since  of these students have chosen Hausa,

of them have chosen Yoruba.

This is three-fifths of two-thirds, so we multiply these fractions:

Two-fifths of the students are taking Yoruba.

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