Numbers - GED Math
Card 0 of 950
What property of arithmetic is symbolized below?
If 
and 
, then 
.
What property of arithmetic is symbolized below?
If
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The symbols express the idea that two numbers equal to the same number are also equal to each other. This is the transitive property of equality.
The symbols express the idea that two numbers equal to the same number are also equal to each other. This is the transitive property of equality.
What property of arithmetic is symbolized below?
What property of arithmetic is symbolized below?
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The symbols express the idea that any number is equal to itself. This is the reflexive property of equality.
The symbols express the idea that any number is equal to itself. This is the reflexive property of equality.
Evaluate:
Do not use a calculator.
Evaluate:
Do not use a calculator.
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Add vertically, aligning the decimal points:
Add vertically, aligning the decimal points:
Which distance is greatest?
The distance between -2 and 1.
The distance between 1 and 7.
The distance between -2 and 5.
Which distance is greatest?
The distance between -2 and 1.
The distance between 1 and 7.
The distance between -2 and 5.
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Looking at a number line, you can visualize the distance between positive and negative numbers:
There are THREE units between -2 and 1
There are SIX units between 1 and 7.
There are SEVEN units between -2 and 5, so this is the greatest distance.
Looking at a number line, you can visualize the distance between positive and negative numbers:
There are THREE units between -2 and 1
There are SIX units between 1 and 7.
There are SEVEN units between -2 and 5, so this is the greatest distance.
A) The distance between -2 and 5 on a number line.
B) The distance between -1 and 3 on a number line.
A) The distance between -2 and 5 on a number line.
B) The distance between -1 and 3 on a number line.
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The first step is to find out the values of A and B by counting the units between the given numbers.
A) The distance between -2 and 5 on a number line is 7.
B) The distance between -1 and 3 on a number line is 4.
The first step is to find out the values of A and B by counting the units between the given numbers.
A) The distance between -2 and 5 on a number line is 7.
B) The distance between -1 and 3 on a number line is 4.
What property of arithmetic is symbolized below?
If 
and 
, then 
.
What property of arithmetic is symbolized below?
If
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The symbols express the idea that if a number is greater than a second number, which is greater than a third, then the first number is greater than the third. This is the transitive property of inequality.
The symbols express the idea that if a number is greater than a second number, which is greater than a third, then the first number is greater than the third. This is the transitive property of inequality.
What property of arithmetic is symbolized below?
What property of arithmetic is symbolized below?
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The symbols express the idea that if three numbers are added, the same sum results regardless of which numbers are added first. This is the associative property of addition.
The symbols express the idea that if three numbers are added, the same sum results regardless of which numbers are added first. This is the associative property of addition.
To how many of the following sets does the number 
belong?
I) The set of whole numbers
II) The set of integers
III) The set of rational numbers
To how many of the following sets does the number
I) The set of whole numbers
II) The set of integers
III) The set of rational numbers
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The whole numbers comprise 0 and the positive integers. 
is a negative integer, so it belongs to the set of integers, but not the set of whole numbers. Also, all integers are rational by definition, since every integer can be expressed as the quotient of two integers (the integer divided by 1, for example). Therefore, 
is an integer and a rational number, but not a whole number, and the correct response is two.
The whole numbers comprise 0 and the positive integers.
Convert 2.5 years to days. Assume that the years in question are not leap years. Round to the nearest day.
Convert 2.5 years to days. Assume that the years in question are not leap years. Round to the nearest day.
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Make sure that your units cross out properly.
Make sure that your units cross out properly.
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,
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:
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.
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.
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
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
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
Divide:
Do not use a calculator.
Divide:
Do not use a calculator.
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Evaluate:
Do not use a calculator.
Evaluate:
Do not use a calculator.
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which converts as follows:
,
so
which converts as follows:
so
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.