Decimals and Fractions - GED Math
Card 1 of 285
Evaluate:
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Evaluate:
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Add vertically, aligning the decimal points:
Add vertically, aligning the decimal points:
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Convert the following decimal into a fraction:
Convert the following decimal into a fraction:
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The decimal, 
, is read as two-hundred forty-three thousandths, which translates to:
The decimal,
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Convert the following fraction to a decimal: 
Convert the following fraction to a decimal:
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Multiply: 
Multiply:
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Multiply numerators, then multiply denominators. We can cross-cancel the 9 and the 3 by dividing both by 3:
Multiply numerators, then multiply denominators. We can cross-cancel the 9 and the 3 by dividing both by 3:
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Add the fractiions below.
Add the fractiions below.
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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.
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
For the fractions to remain the same, you have to multiply the numerator and the denominator in
Because the numerator is larger than the denominator, you simplify the fraction to make it a mixed number.
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Above is the menu for a coffee shop. Today, the shop has a special - buy two iced coffees of any size, and get a third iced coffee of the same size free.
Jerry orders three large iced coffees; Elaine orders two large cappucinos; George orders three butter croissants. List the three customers in ascending order by money spent. (You may ignore tax.)
Above is the menu for a coffee shop. Today, the shop has a special - buy two iced coffees of any size, and get a third iced coffee of the same size free.
Jerry orders three large iced coffees; Elaine orders two large cappucinos; George orders three butter croissants. List the three customers in ascending order by money spent. (You may ignore tax.)
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Since the third large iced coffee is free, Jerry pays for two large iced coffees. He pays
.
Elaine pays for two large cappucinos. She pays
.
George pays for three butter croissants. He pays
.
In ascending order by amount spent, the three are George, Jerry, Elaine.
Since the third large iced coffee is free, Jerry pays for two large iced coffees. He pays
Elaine pays for two large cappucinos. She pays
George pays for three butter croissants. He pays
In ascending order by amount spent, the three are George, Jerry, Elaine.
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Above is the menu for a coffee shop; there is no sales tax charged on purchases.
David orders a large iced coffee, two large espressos, a small cafe latte, and four butter croissants. He hands the cashier two twenty-dollar bills. How much will he get back in change?
Above is the menu for a coffee shop; there is no sales tax charged on purchases.
David orders a large iced coffee, two large espressos, a small cafe latte, and four butter croissants. He hands the cashier two twenty-dollar bills. How much will he get back in change?
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Dave will spend $3.49 for the large iced coffee, $3.29 for each of the two large espressos, $3.09 for the cafe latte, and $2.29 for each of the butter croissants.
This is a total of:
Dave gives the cashier $40 and therefore gets back 
.
Dave will spend $3.49 for the large iced coffee, $3.29 for each of the two large espressos, $3.09 for the cafe latte, and $2.29 for each of the butter croissants.
This is a total of:
Dave gives the cashier $40 and therefore gets back
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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?
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?
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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
.
There will be eighteen people at the party, including Hedwig.
She will spend
"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
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What is 
as an improper fraction?
What is
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To convert a mixed number, (whole number and fraction), to an improper fraction, (a fraction whose numerator is greater than the denominator), the steps are as follows:
Multiply the whole number by the denominator of the fraction. In this example the whole number is 17 and the denominator is 5.
Then add the numerator to that total.
This total represents the numerator in the improper fraction. The denominator does not change.
Therefore the improper fraction would be 
To convert a mixed number, (whole number and fraction), to an improper fraction, (a fraction whose numerator is greater than the denominator), the steps are as follows:
Multiply the whole number by the denominator of the fraction. In this example the whole number is 17 and the denominator is 5.
Then add the numerator to that total.
This total represents the numerator in the improper fraction. The denominator does not change.
Therefore the improper fraction would be
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Divide:
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Divide:
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Evaluate:
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Evaluate:
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which converts as follows:
,
so
which converts as follows:
so
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Jim has a total of $13.85 in nickels, dimes, and quarters.
Suppose Jim has 47 nickels. How many dimes could he have?
Jim has a total of $13.85 in nickels, dimes, and quarters.
Suppose Jim has 47 nickels. How many dimes could he have?
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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.
If Jim has 47 nickels, he has
The number of dimes Jim has must leave an amount that can be made in quarters only - that is, a whole number multiple of
64 dimes:
Amount in quarters:
Divide this by
65 dimes:
Amount in quarters:
Divide this by
66 dimes:
Amount in quarters:
Divide this by
67 dimes:
Amount in quarters:
Divide this by
65 dimes is the correct choice since it is the only one that allows for a whole number of quarters.
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Evaluate:
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Evaluate:
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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 
.
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
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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?
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?
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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.
have chosen Hausa or Yoruba.
Since
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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Three inches on a map represents 100 miles of real distance. The distance between Adams and Monroe on a map is seven and a half inches. How many miles separate the two cities in reality?
Three inches on a map represents 100 miles of real distance. The distance between Adams and Monroe on a map is seven and a half inches. How many miles separate the two cities in reality?
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Since three map inches represent 100 real miles, one inch represents
miles.
Seven and one half inches represents
miles,
the distance between the two cities.
Since three map inches represent 100 real miles, one inch represents
Seven and one half inches represents
the distance between the two cities.
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Each student at a classical studies school is required to take one of three languages - Latin, Greek, or Hebrew. Assume that no student takes more than one language.
One-fourth of the students decide to take Hebrew; half the remaining students decide to take Greek. What is the ratio of students who don't take Latin to those who do?
Each student at a classical studies school is required to take one of three languages - Latin, Greek, or Hebrew. Assume that no student takes more than one language.
One-fourth of the students decide to take Hebrew; half the remaining students decide to take Greek. What is the ratio of students who don't take Latin to those who do?
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of the students take Hebrew, so
of the students don't take Hebrew. Half of these students take Greek, so the other half must take Latin; this is
of the students.
Therefore,
of the students don't take Latin.
The ratio of those not taking Latin to those who are is
.
of the students don't take Hebrew. Half of these students take Greek, so the other half must take Latin; this is
of the students.
Therefore,
of the students don't take Latin.
The ratio of those not taking Latin to those who are is
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Evaluate: 
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Evaluate:
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is evaluated by first multiplying. 1.3 can be multiplied by ignoring the decimal point:
Since one digit of the first factor and no digits of the second are to the right of the decimal point, we can place the decimal point one place from the right in the product; this is 6.5.
Now, we add 2.5 to 6.5 as follows:
The correct response is 9.
Since one digit of the first factor and no digits of the second are to the right of the decimal point, we can place the decimal point one place from the right in the product; this is 6.5.
Now, we add 2.5 to 6.5 as follows:
The correct response is 9.
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What mixed number is represented by the shaded portion of the above diagram?
What mixed number is represented by the shaded portion of the above diagram?
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Three whole circles are shaded, so the integer part of the mixed number is 3.
The denominator of the fraction portion, on the bottom, is the number of pieces each whole circle is divided into, which is 8. The numerator, on the top, is the number of pieces of the fourth circle actually shaded in, which is 3.
Therefore, the diagram represents the fraction 
.
Three whole circles are shaded, so the integer part of the mixed number is 3.
The denominator of the fraction portion, on the bottom, is the number of pieces each whole circle is divided into, which is 8. The numerator, on the top, is the number of pieces of the fourth circle actually shaded in, which is 3.
Therefore, the diagram represents the fraction
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In lowest terms, what fraction of the above figure is red?
In lowest terms, what fraction of the above figure is red?
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Sixteen parts are colored red out of the twenty that make a whole, so one fraction that this represents is 
. This is not in lowest terms, however, since both numerator and denominator are divisible by 2.
which is the correct response.
Sixteen parts are colored red out of the twenty that make a whole, so one fraction that this represents is
which is the correct response.
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Evaluate 
for 
.
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Evaluate
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, so substitute 
for 
and follow the order of operations:
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