How to solve one-step equations with decimals in pre-algebra - Math
Card 1 of 72
Michael buys two packs of pencils for 
each and three sketch pads for 
each. He pays for his purchase with 
. How much change should he get?
Michael buys two packs of pencils for
Tap to reveal answer
First, calculate how much he spends on pencils and pads.
Pencils: 
Pads: 
Therefore the total spent is 
.
Then the change is 
.
First, calculate how much he spends on pencils and pads.
Pencils:
Pads:
Therefore the total spent is
Then the change is
← Didn't Know|Knew It →
Solve for 
if 
Solve for
Tap to reveal answer
To solve for we must get all of the numbers on the other side of the equation as .
To do this in a problem where a number is being added to , we must subtract the number from both sides of the equation.
In this case the number is 
so we subtract 
from each side of the equation to make it look like this 
The numbers on the left side cancel to leave by itself.
To do the necessary subtraction we need to know how to subtract decimals from each other.
To subtract decimals you place the first decimal over the top of the other aligned by the decimal point.
Then go through each place and subtract the top number by the bottom number.
Subtract the numbers in each place like you would any number 
and 
Combine the numbers and keep the decimal in the same place to get 
The answer is 
To solve for
To do this in a problem where a number is being added to
In this case the number is
The numbers on the left side cancel to leave
To do the necessary subtraction we need to know how to subtract decimals from each other.
To subtract decimals you place the first decimal over the top of the other aligned by the decimal point.
Then go through each place and subtract the top number by the bottom number.
Subtract the numbers in each place like you would any number
Combine the numbers and keep the decimal in the same place to get
The answer is
← Didn't Know|Knew It →
Solve for 
if 
Solve for
Tap to reveal answer
To solve for 
we must get all of the numbers on the other side of the equation of 
.
To do this in a problem where 
is being multiplied by a number, we must divide both sides of the equation by the number.
In this case the number is 
so we divide each side of the equation by 
to make it look like this 
Then we must divide the decimals by each other to find the answer.
To divide decimals we line the decimals up like this 
.
Then ignoring all of the decimal places we divide the top number by the bottom number to get 
Then we must apply the decimals.
However many decimal places there are in the denominator will be subtracted from the number of decimal places in the numerator to get the final number of decimal places in our answer.
If the number is positive we move the decimal that number of places to the left of our number.
If the number is negative we move the decimal that number of places to the right of our number.
In this case it would be 
so we don't have any decimal places and the answer is 
.
To solve for
To do this in a problem where
In this case the number is
Then we must divide the decimals by each other to find the answer.
To divide decimals we line the decimals up like this
Then ignoring all of the decimal places we divide the top number by the bottom number to get
Then we must apply the decimals.
However many decimal places there are in the denominator will be subtracted from the number of decimal places in the numerator to get the final number of decimal places in our answer.
If the number is positive we move the decimal that number of places to the left of our number.
If the number is negative we move the decimal that number of places to the right of our number.
In this case it would be
← Didn't Know|Knew It →
Solve for if 
.
Solve for
Tap to reveal answer
We need to isolate x so that it is the only term on the left side of the equation.
To do this, add .16 to both sides of the equation:
The numbers on the left side cancel to leave 
by itself.
The answer is therefore 
.
We need to isolate x so that it is the only term on the left side of the equation.
To do this, add .16 to both sides of the equation:
The numbers on the left side cancel to leave
The answer is therefore
← Didn't Know|Knew It →
Solve for if 
.
Solve for
Tap to reveal answer
To solve for we must get all of the numbers on the other side of the equation of .
To do this in a problem where is being subtracted by a number, we must add the number to both sides of the equation.
In this case the number is 
so we add 
to each side of the equation to make it look like this 
The numbers on the left side cancel to leave by itself.
Then we must perform the necessary addition to get the answer.
To add decimals together you place the decimals one over the top of the other aligned by the decimal point.
If there are no numbers after a tens, hundredths, or thousandths place or further to the right of the decimal just add a zero in the required areas.
Then add each place with the appropriately aligned number to get a result for each number.
In this case the decimals will add together like this 
The answer is 
.
To solve for
To do this in a problem where
In this case the number is
The numbers on the left side cancel to leave
Then we must perform the necessary addition to get the answer.
To add decimals together you place the decimals one over the top of the other aligned by the decimal point.
If there are no numbers after a tens, hundredths, or thousandths place or further to the right of the decimal just add a zero in the required areas.
Then add each place with the appropriately aligned number to get a result for each number.
In this case the decimals will add together like this
The answer is
← Didn't Know|Knew It →
Solve for 
if 
Solve for
Tap to reveal answer
To solve for 
we must get all of the numbers on the other side of the equation of 
.
To do this in a problem where 
is being multiplied by a coefficient, we must divide both sides of the equation by the coefficient.
In this case the number is 
so we divide each side of the equation by 
to make it look like this 
Then we must divide the decimals by each other to find the answer.
To divide decimals we line the decimals up like this 
Then ignoring all of the decimal places we divide the top number by the bottom number to get 
Then we must apply the decimals.
The number of decimal places in the denominator will be subtracted from the number of decimal places in the numerator to get the number of decimal places we must change our answer.
If the number is positive we move the decimal that number of places to the left of our number.
If the number is negative we move the decimal that number of places to the right of our number.
In this case it would be negative so we move the decimal 
place to the right of 
to get 
.
The answer is 
.
To solve for
To do this in a problem where
In this case the number is
Then we must divide the decimals by each other to find the answer.
To divide decimals we line the decimals up like this
Then ignoring all of the decimal places we divide the top number by the bottom number to get
Then we must apply the decimals.
The number of decimal places in the denominator will be subtracted from the number of decimal places in the numerator to get the number of decimal places we must change our answer.
If the number is positive we move the decimal that number of places to the left of our number.
If the number is negative we move the decimal that number of places to the right of our number.
In this case it would be negative so we move the decimal
The answer is
← Didn't Know|Knew It →
What is 
?
What is
Tap to reveal answer
To solve 
, you can either plug it into your calculator or convert it to a fraction. Since 
, we can rewrite the equation as:
To solve
← Didn't Know|Knew It →
Solve for if 
.
Solve for
Tap to reveal answer
To solve for , we must isolate .
To do this in a problem where a number is being added to , we must subtract the number from both sides of the equation.
In this case the number is 
, so we subtract 
from each side of the equation to make it look like this: 
The numbers on the left side cancel to leave 
by itself.
The answer is then 
.
To solve for
To do this in a problem where a number is being added to
In this case the number is
The numbers on the left side cancel to leave
The answer is then
← Didn't Know|Knew It →
Solve for 
if 
.
Solve for
Tap to reveal answer
To solve for , we must move all of the constants to the other side of the equation as .
To do this in a problem where is being multiplied by a number, we must divide both sides of the equation by the number.
In this case the number is 
, so we divide each side of the equation by 
to make it look like this: 
Then we must divide the decimals by each other to find the answer.
To divide decimals we line the decimals up like this: 
Then, ignoring all of the decimal places, we divide the top number by the bottom number to get 
.
Then we must move the decimals.
The number of decimal places in the denominator will be subtracted from the number of decimal places in the numerator to get the number of places to move the decimal point.
If the number is positive, we move the decimal that number of places to the left of our number.
If the number is negative, we move the decimal that number of places to the right of our number.
In this case the subtraction yields 
, so we move the decimal 
place to the right of 
to get 
.
The answer is 
.
To solve for
To do this in a problem where
In this case the number is
Then we must divide the decimals by each other to find the answer.
To divide decimals we line the decimals up like this:
Then, ignoring all of the decimal places, we divide the top number by the bottom number to get
Then we must move the decimals.
The number of decimal places in the denominator will be subtracted from the number of decimal places in the numerator to get the number of places to move the decimal point.
If the number is positive, we move the decimal that number of places to the left of our number.
If the number is negative, we move the decimal that number of places to the right of our number.
In this case the subtraction yields
The answer is
← Didn't Know|Knew It →
Solve for 
.
Solve for
Tap to reveal answer
To solve 
, add 
to both sides.
To solve
← Didn't Know|Knew It →
Solve for 
.
Solve for
Tap to reveal answer
To solve 
, we need to isolate 
. That means we need to add 
to both sides.
To solve
← Didn't Know|Knew It →
Solve for 
.
Solve for
Tap to reveal answer
To solve 
, you can either plug it into your calculator or realize that 
. Therefore, we are looking for half of five, which is 
.
Mathematically, that means:
To solve
Mathematically, that means:
← Didn't Know|Knew It →
Solve for 
.
Solve for
Tap to reveal answer
To solve for 
, we first need to isolate it. That means we want ONLY 
on the left side of the equation.
Subtract 
from both sides.
To solve for
Subtract
← Didn't Know|Knew It →
Solve for when 
Solve for
Tap to reveal answer
To solve for we must get all of the numbers on the other side of the equation as .
To do this in a problem where a number is being added to , we must subtract the number from both sides of the equation.
In this case the number is 
so we subtract 
from each side of the equation to make it look like this
The numbers on the left side cancel to leave by itself.
To do the necessary subtraction we need to know how to subtract decimals from each other.
To subtract decimals you place the first decimal over the top of the other aligned by the decimal point.
Then go through each place and subtract the top number by the bottom number.
Subtract the numbers in each place like you would any number.
Then combine them keeping the decimal in the same place to get 
.
The answer is 
.
To solve for
To do this in a problem where a number is being added to
In this case the number is
The numbers on the left side cancel to leave
To do the necessary subtraction we need to know how to subtract decimals from each other.
To subtract decimals you place the first decimal over the top of the other aligned by the decimal point.
Then go through each place and subtract the top number by the bottom number.
Subtract the numbers in each place like you would any number.
Then combine them keeping the decimal in the same place to get
The answer is
← Didn't Know|Knew It →
Solve for 
when
Solve for
Tap to reveal answer
To solve for we must get all of the numbers on the other side of the equation as .
To do this in a problem where is being subtracted by a number, we must add the number to both sides of the equation.
In this case the number is 
so we add 
to each side of the equation to make it look like this 
The numbers on the left side cancel to leave by itself.
Then we must perform the necessary addition to get the answer.
To add decimals together you place the decimals one over the top of the other aligned by the decimal point.
Then add each place with the appropriately aligned number to get a result for each number.
In this case the decimals will add together like this 
The answer is 
.
To solve for
To do this in a problem where
In this case the number is
The numbers on the left side cancel to leave
Then we must perform the necessary addition to get the answer.
To add decimals together you place the decimals one over the top of the other aligned by the decimal point.
Then add each place with the appropriately aligned number to get a result for each number.
In this case the decimals will add together like this
The answer is
← Didn't Know|Knew It →
Solve for 
.
Solve for
Tap to reveal answer
To solve for 
, we need to isolate 
. That means we want only 
on the left side of the equation.
Divide both sides by 
.
To solve for
Divide both sides by
← Didn't Know|Knew It →
Solve for 
.
Solve for
Tap to reveal answer
To solve 
, we need to isolate 
. That means we want just 
on the left hand side.
To do that, we need to divide both sides by 
.
To solve
To do that, we need to divide both sides by
← Didn't Know|Knew It →
What number is 
of 
?
What number is
Tap to reveal answer
Verbal cues include "IS" means equals and "OF" means multiplication.
Verbal cues include "IS" means equals and "OF" means multiplication.
← Didn't Know|Knew It →
Michael buys two packs of pencils for each and three sketch pads for each. He pays for his purchase with . How much change should he get?
Michael buys two packs of pencils for
Tap to reveal answer
First, calculate how much he spends on pencils and pads.
Pencils:
Pads:
Therefore the total spent is .
Then the change is .
First, calculate how much he spends on pencils and pads.
Pencils:
Pads:
Therefore the total spent is
Then the change is
← Didn't Know|Knew It →
Solve for if
Solve for
Tap to reveal answer
To solve for we must get all of the numbers on the other side of the equation as .
To do this in a problem where a number is being added to , we must subtract the number from both sides of the equation.
In this case the number is so we subtract from each side of the equation to make it look like this
The numbers on the left side cancel to leave by itself.
To do the necessary subtraction we need to know how to subtract decimals from each other.
To subtract decimals you place the first decimal over the top of the other aligned by the decimal point.
Then go through each place and subtract the top number by the bottom number.
Subtract the numbers in each place like you would any number and
Combine the numbers and keep the decimal in the same place to get
The answer is
To solve for
To do this in a problem where a number is being added to
In this case the number is
The numbers on the left side cancel to leave
To do the necessary subtraction we need to know how to subtract decimals from each other.
To subtract decimals you place the first decimal over the top of the other aligned by the decimal point.
Then go through each place and subtract the top number by the bottom number.
Subtract the numbers in each place like you would any number
Combine the numbers and keep the decimal in the same place to get
The answer is
← Didn't Know|Knew It →