How to find the whole from the part - SSAT Middle Level Math
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Sarah, Robert, and Tristen each had the same number of cookies. Given the information below, which of the following could be the number of cookies each child had?
Sarah put her cookies into groups of 6 with none left over.
Robert put his cookies into groups 3 with none left over.
Tristen put his cookies into groups of 4 with none left over.
Sarah, Robert, and Tristen each had the same number of cookies. Given the information below, which of the following could be the number of cookies each child had?
Sarah put her cookies into groups of 6 with none left over.
Robert put his cookies into groups 3 with none left over.
Tristen put his cookies into groups of 4 with none left over.
This question is simply asking which number is divisible by 3, 4 and 6 with none left over. The only number that has 3, 4, and 6 as factors is 24.
This question is simply asking which number is divisible by 3, 4 and 6 with none left over. The only number that has 3, 4, and 6 as factors is 24.
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Angela bought 
of a pound of candy for $4.00. What was the price per pound?
Angela bought
If 
of a pound of candy costs $4 then the price of a full pound will be 4 times as much. Thus 4 times $4 is $16.
If
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500 is two-fifths of what number?
500 is two-fifths of what number?
Let 
be the number desired. The question can be rewritten as the multiplication statement:
Solve:
Let
Solve:
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Bernard is baking cookies. He has to bake 48 cookies and has 6 pounds of cookie dough to make them. After he bakes 8 cookies, how many pounds of cookie dough does he have left?
Bernard is baking cookies. He has to bake 48 cookies and has 6 pounds of cookie dough to make them. After he bakes 8 cookies, how many pounds of cookie dough does he have left?
If Bernard bakes 8 cookies, that means he has used one-sixth of the cookie dough because 48 divided by 8 equals 6. Thus, 8 is one-sixth of 48.
Therefore, he would have used one-sixth of the dough, or the equivalent of 1 pound.
This would leave 5 pounds of dough remaining.
If Bernard bakes 8 cookies, that means he has used one-sixth of the cookie dough because 48 divided by 8 equals 6. Thus, 8 is one-sixth of 48.
Therefore, he would have used one-sixth of the dough, or the equivalent of 1 pound.
This would leave 5 pounds of dough remaining.
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On Monday Beth created 
drawing. On Tuesday she created 
drawings. On Wednesday she created twice has many drawings as on Monday and Tuesday combined. She did not draw the rest of the week. How many drawings total did she create for the week?
On Monday Beth created
To calculate Beth's total drawings, we should add up the days:
Monday: 
drawing
Tuesday: 
drawings
Wednesday: 
, which is the total of Monday's drawings plus Tuesday's drawings, times 
. (Given that 
plus 
is equal to 
, and that 
times 
is 
, there were a total of 
drawings on Wednesday.)
The sum of 
plus 
plus 
is 
, which is therefore the correct answer.
To calculate Beth's total drawings, we should add up the days:
Monday:
Tuesday:
Wednesday:
The sum of
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In a rectangle, each corner has a value in degrees of A (first corner), B (second corner), C (third corner), and D (fourth corner).
What is the sum of corners A, B, and C?
In a rectangle, each corner has a value in degrees of A (first corner), B (second corner), C (third corner), and D (fourth corner).
What is the sum of corners A, B, and C?
In a rectangle, each corner is equal to 90 degrees. All corners are of equal degrees. Thus, the sum of any three corners would equal the product of 90 and 3, which is 270. Therefore, the correct answer is 270 degrees.
In a rectangle, each corner is equal to 90 degrees. All corners are of equal degrees. Thus, the sum of any three corners would equal the product of 90 and 3, which is 270. Therefore, the correct answer is 270 degrees.
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Which of the following numbers is divisible by 9 without a remainder?
Which of the following numbers is divisible by 9 without a remainder?
A number is divisible by 9 without a remainder when each of its digits add up to a number that is divisble by 9. When looking at the number 711, we can see that:
Given that 9 is divisble by 9, (equlaing 1, no remainder), 711 is divisble by 9.
A number is divisible by 9 without a remainder when each of its digits add up to a number that is divisble by 9. When looking at the number 711, we can see that:
Given that 9 is divisble by 9, (equlaing 1, no remainder), 711 is divisble by 9.
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Captain Hook, Captain Jack, and Captain James each had the same number of shipmates. Given the information below, which of the following could be the number of shipmates each captain had?
Captain Hook put his shipmates into groups of 
with none left over.
Captain Jack put his shipmates into groups of 
with none left over.
Captain James put his shipmates into groups of 
with none left over.
Captain Hook, Captain Jack, and Captain James each had the same number of shipmates. Given the information below, which of the following could be the number of shipmates each captain had?
Captain Hook put his shipmates into groups of
Captain Jack put his shipmates into groups of
Captain James put his shipmates into groups of
For this question we look at the multiples of each group and find the smallest factor that is common to all three groups.
Captain Hook: 
Captain Jack: 
Captain James: 
Therefore, the smallest number that is divisible by 
and 
is 
.
For this question we look at the multiples of each group and find the smallest factor that is common to all three groups.
Captain Hook:
Captain Jack:
Captain James:
Therefore, the smallest number that is divisible by
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Luke bought 
of a pound of cake for 
. What was the price per pound?
Luke bought
If 
is the price per pound, then the formula for this equation is 
Isolate 
by multiplying the inverse of 
, which is 
, to both sides.
If
Isolate
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Mark bought 
of an acre for 
. What was the price for the whole acre?
Mark bought
If 
is the price per acre, then the formula for this equation is 
Isolate 
by multiplying the inverse of 
, which is 
, to both sides.
If
Isolate
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is two-thirds of what number?
If 
be the number desired. The question can be rewritten as the multiplication statement:
Solve:
If
Solve:
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Mark is baking cupcakes. He has to bake 
cupcakes and has 
pounds of cake batter to make them. After he bakes 
cupcakes, how many pounds of cake batter does he have left?
Mark is baking cupcakes. He has to bake
If Mark bakes 
cupcakes, that means he has used one-eighth of the cake batter because:
.
Now we need to find out how much one-eighth of 
is:
From here we will find the difference between the amount of cake batter Mark started with and the amount he used for the 
cupcakes to find how many pounds of batter is left.
Therefore,
This would leave 7 pounds of cake batter remaining.
If Mark bakes
Now we need to find out how much one-eighth of
From here we will find the difference between the amount of cake batter Mark started with and the amount he used for the
Therefore,
This would leave 7 pounds of cake batter remaining.
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There is a bag of marbles and the three colors are red, blue, and green. If the green marbles equal 
times the amount of blue and blue is 
times the amount of red, what is the total amount of marbles when there are 
red marbles?
There is a bag of marbles and the three colors are red, blue, and green. If the green marbles equal
Since there are 
times as many blue marbles as there are red, you must multiple the red marbles by 
, Then you take the 
blue marbles and multiply by 
since there are 
times the green marbles as blue 
. Then you add them all together to get 
.
Since there are
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The ratio of blue to green lizards is 6:20. If there are 350 blue lizards, how many lizards are there total?
The ratio of blue to green lizards is 6:20. If there are 350 blue lizards, how many lizards are there total?
The easiest way to solve this problem is by using cross multiplication. First we need to determine how many green lizards there are and then add this to the number of blue lizards to get the total amount of lizards. Therefore,
(approx.) amount of green lizards
The easiest way to approximate this part of the problem is to notice that 6 is very close to 7. So if 
, 
. So if we are dividing by a slightly smaller number we will get a larger answer.
We then need to add this number to 350 blue lizards in order to get the total amount of lizards. Therefore, 
.
The easiest way to solve this problem is by using cross multiplication. First we need to determine how many green lizards there are and then add this to the number of blue lizards to get the total amount of lizards. Therefore,
The easiest way to approximate this part of the problem is to notice that 6 is very close to 7. So if
We then need to add this number to 350 blue lizards in order to get the total amount of lizards. Therefore,
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There are 6 parts root beer to 3 parts ice cream in a root beer float. If there is 18oz of root beer, how many total ounces make up the root beer float (ice cream+ root beer)?
There are 6 parts root beer to 3 parts ice cream in a root beer float. If there is 18oz of root beer, how many total ounces make up the root beer float (ice cream+ root beer)?
First, divide the 18oz of root beer by 6 parts in order to determine how many ounces per 1 part of root beer. Therefore, 
.
In order to determine the amount of ice cream, multiply 1 part (3 oz) by 3, since ice cream is comprised of 3 parts. Therefore, there are 9oz of ice cream. Add this to the 18oz of root beer in order to get the total ounces of the root beer float.
.
First, divide the 18oz of root beer by 6 parts in order to determine how many ounces per 1 part of root beer. Therefore,
In order to determine the amount of ice cream, multiply 1 part (3 oz) by 3, since ice cream is comprised of 3 parts. Therefore, there are 9oz of ice cream. Add this to the 18oz of root beer in order to get the total ounces of the root beer float.
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What is 
in expanded form?
What is
When we write a number in expanded form, we multiply each digit by its place value.
is in the ones place, so we multiply by 
.
is in the tenths place, so we multiply by 
.
is in the hundredths place, so we multiply by 
.
Then we add the products together.
When we write a number in expanded form, we multiply each digit by its place value.
Then we add the products together.
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What is 
in expanded form?
What is
When we write a number in expanded form, we multiply each digit by its place value.
is in the ones place, so we multiply by 
.
is in the tenths place, so we multiply by 
.
is in the hundredths place, so we multiply by 
.
Then we add the products together to check our answer:
When we write a number in expanded form, we multiply each digit by its place value.
Then we add the products together to check our answer:
Compare your answer with the correct one above
What is 
in expanded form?
What is
When we write a number in expanded form, we multiply each digit by its place value.
is in the ones place, so we multiply by 
.
is in the tenths place, so we multiply by 
.
is in the hundredths place, so we multiply by 
.
Then we add the products together.
When we write a number in expanded form, we multiply each digit by its place value.
Then we add the products together.
Compare your answer with the correct one above
What is 
in expanded form?
What is
When we write a number in expanded form, we multiply each digit by its place value.
is in the ones place, so we multiply by 
.
is in the tenths place, so we multiply by 
.
is in the hundredths place, so we multiply by 
.
Then we add the products together.
When we write a number in expanded form, we multiply each digit by its place value.
Then we add the products together.
Compare your answer with the correct one above
What is 
in expanded form?
What is
When we write a number in expanded form, we multiply each digit by its place value.
is in the ones place, so we multiply by 
.
is in the tenths place, so we multiply by 
.
is in the hundredths place, so we multiply by 
.
Then we add the products together.
When we write a number in expanded form, we multiply each digit by its place value.
Then we add the products together.
Compare your answer with the correct one above