How to find the whole from the part - ISEE Lower Level Quantitative Reasoning
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Jonathan ate 
of a carton of ice cream. This is equal to 1 pound of ice cream. How many pounds of ice cream were in the carton of ice cream before Jonathan started eating?
Jonathan ate
The fraction 
means that Jonathan has eaten 1 part out of a possible 4 parts of the carton of ice cream. So we can multiply the amount that he ate (1 pound) by 4 to see that there are 4 pounds of ice cream in a carton.
The fraction
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37 is 20% of what number?
37 is 20% of what number?
To find the whole from the part, divide the “part” by the percent. In order to do this, first change the percent into a decimal (20% becomes 0.2).
Therefore, 37 is 20% of 185.
To find the whole from the part, divide the “part” by the percent. In order to do this, first change the percent into a decimal (20% becomes 0.2).
Therefore, 37 is 20% of 185.
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Amanda and Adriana each ran four laps around the track in twelve minutes. At the same rate of speed, how long would they need to run twenty-eight laps?
Amanda and Adriana each ran four laps around the track in twelve minutes. At the same rate of speed, how long would they need to run twenty-eight laps?
To solve this problem, one must first determine how long it takes to run one lap. Since it takes twelve minutes to run four laps, divide twelve by four.
It takes three minutes to run one lap.
To determine how long it will take to run twenty-eight laps, multiply the original rate of speed by the new distance.
It will take eighty-four minutes to run twenty-eight laps if each lap is run in three minutes.
To solve this problem, one must first determine how long it takes to run one lap. Since it takes twelve minutes to run four laps, divide twelve by four.
It takes three minutes to run one lap.
To determine how long it will take to run twenty-eight laps, multiply the original rate of speed by the new distance.
It will take eighty-four minutes to run twenty-eight laps if each lap is run in three minutes.
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Brad is buying two appliances from a store: a microwave that costs $30 and a toaster that costs $25. He has two coupons: 10 percent off 1 item, and $5 off one item.
What is the most money that he can save with these coupons (in dollars)?
Brad is buying two appliances from a store: a microwave that costs $30 and a toaster that costs $25. He has two coupons: 10 percent off 1 item, and $5 off one item.
What is the most money that he can save with these coupons (in dollars)?
If Brad has 2 coupons, 10 percent off 1 item, and $5 off one item, he should use the 10 percent off coupon on the more expensive item to save more money.
Since the $30 microwave is more expensive, he should use the 10 percent off coupon on this item. This will save him $3 because 10 percent of $30 is $3.
He can then use the $5 off coupon on the $25 toaster, which saves him $5.
Therefore, the total savings is $8.
If Brad has 2 coupons, 10 percent off 1 item, and $5 off one item, he should use the 10 percent off coupon on the more expensive item to save more money.
Since the $30 microwave is more expensive, he should use the 10 percent off coupon on this item. This will save him $3 because 10 percent of $30 is $3.
He can then use the $5 off coupon on the $25 toaster, which saves him $5.
Therefore, the total savings is $8.
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What is 3.4 rounded to the nearest whole number?
What is 3.4 rounded to the nearest whole number?
A whole number is one in which the one's place is the smallest unit. Therefore, in a whole number, there is no decimal. While any number that ends in a .5 decimal or greater rounds up, anything that is smaller than .5 rounds down. Therefore, 
would round down to 
.
A whole number is one in which the one's place is the smallest unit. Therefore, in a whole number, there is no decimal. While any number that ends in a .5 decimal or greater rounds up, anything that is smaller than .5 rounds down. Therefore,
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A classroom contains 30 students, and there are the same number of boys as girls. If 
of the boys in the classroom are wearing sandals , how many boys are wearing sandals?
A classroom contains 30 students, and there are the same number of boys as girls. If
If the classroom of 30 students has an equal number of boys and girls, then there are 15 girls and 15 boys.
If 
of the boys are wearing sandals, then 
boys are wearing sandals.
If the classroom of 30 students has an equal number of boys and girls, then there are 15 girls and 15 boys.
If
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One fourth of the bananas that Beth bought are not ripe. The rest are ripe. She has 9 ripe bananas. How many bananas are there in total?
One fourth of the bananas that Beth bought are not ripe. The rest are ripe. She has 9 ripe bananas. How many bananas are there in total?
If one fourth of the bananas that Beth bought are not ripe, then three fourths are ripe. Therefore, the total number of bananas can be represented by 
in the equation below:
First, we cross multiply:
Next, we divide by 3:
Therefore, there are a total of 12 bananas.
If one fourth of the bananas that Beth bought are not ripe, then three fourths are ripe. Therefore, the total number of bananas can be represented by
First, we cross multiply:
Next, we divide by 3:
Therefore, there are a total of 12 bananas.
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Roman is ordering uniforms for the tennis team. He knows how many people are on the team and how many uniforms come in each box. Which equation can be used to solve for how many boxes 
Roman should order?
Roman is ordering uniforms for the tennis team. He knows how many people are on the team and how many uniforms come in each box. Which equation can be used to solve for how many boxes
The total number of uniforms needed equals the number of students divided by the number of uniforms per box.
The total number of uniforms needed equals the number of students divided by the number of uniforms per box.
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Find the whole from the part. Round to the nearest tenths place.
16 is 55% of what number?
Find the whole from the part. Round to the nearest tenths place.
16 is 55% of what number?
To find the whole from a part, divide the "part" by the percent. But first, change the percent into a decimal (55% = 0.55)
Round to the nearest tenths place = 29.1.
To find the whole from a part, divide the "part" by the percent. But first, change the percent into a decimal (55% = 0.55)
Round to the nearest tenths place = 29.1.
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is 
of what number?
Solve by setting up a proportion.
Cross multiply.
is 
of 
.
Solve by setting up a proportion.
Cross multiply.
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In Cody's class, there are 
boys for every 
girl. If there are 
boys in the class, how many students are there in the class altogether?
In Cody's class, there are
To find out how many students are in the class, we first need to find the number of girls in the class. For every 
boys, there will be 
girl. There are 
groups of 
in a group of 
(or, put another way, 
), so the class has 
groups of 
boys. That means we also have 
groups of 
girl. 
is 
, so altogether we have 
boys and 
girls. 
, so the correct answer is 
.
To find out how many students are in the class, we first need to find the number of girls in the class. For every
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52 is 25% of what number?
52 is 25% of what number?
To find the whole from the part, divide the “part” by the percent. In order to do this, first change the percent into a decimal (25% becomes 0.25).
Therefore, 52 is 25% of 208.
To find the whole from the part, divide the “part” by the percent. In order to do this, first change the percent into a decimal (25% becomes 0.25).
Therefore, 52 is 25% of 208.
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At a party, 
of the cake was eaten. If each of the 12 attendees had one piece of cake, how many pieces were in the whole cake?
At a party,
12 pieces of cake is equivalent to 
of the whole. Proportions can be used to determine how many pieces were in the entire cake. Let 
equal the number of pieces in the entire cake.
Using this set up, both fractions are equal to 
. Cross multiply.
12 pieces of cake is equivalent to
Using this set up, both fractions are equal to
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is 
of 
. Solve for 
.
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Which of the following numbers is a multiple of ten?
Which of the following numbers is a multiple of ten?
A multiple is a number that can be divided by another number without a remainder. 30 can be divided by 10 without a remainder.
It is the only number from the list of answer choices for which this is true. Therefore, it is the correct answer.
A multiple is a number that can be divided by another number without a remainder. 30 can be divided by 10 without a remainder.
It is the only number from the list of answer choices for which this is true. Therefore, it is the correct answer.
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Andrea and her three friends all pitched in to buy a puppy. Each person paid equal parts. If Andrea paid 20 dollars, what was the total cost of the puppy?
Andrea and her three friends all pitched in to buy a puppy. Each person paid equal parts. If Andrea paid 20 dollars, what was the total cost of the puppy?
We can solve this question with multiplication.
First, we know that Andrea paid 20 dollars and that each person paid equal parts. That means that each person paid 20 dollars.
Second, we know that there are four people total: Andrea and three additional friends.
Multiply the cost per person by the number of people to get the total cost.
We can solve this question with multiplication.
First, we know that Andrea paid 20 dollars and that each person paid equal parts. That means that each person paid 20 dollars.
Second, we know that there are four people total: Andrea and three additional friends.
Multiply the cost per person by the number of people to get the total cost.
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There are 4 canoes at a summer camp. Each canoe can hold a maximum of 6 campers, but each canoe must have an even number of campers in order to maintain balance.
Which of the following is NOT a possible number of campers who could have paddled from one end of the lake to the other using all 4 canoes?
There are 4 canoes at a summer camp. Each canoe can hold a maximum of 6 campers, but each canoe must have an even number of campers in order to maintain balance.
Which of the following is NOT a possible number of campers who could have paddled from one end of the lake to the other using all 4 canoes?
If each canoe requires an even number of campers, then it would have been impossible for 6 campers to have paddled across in all 4 canoes.
This is because if 6 campers used the canoes, 2 campers would have gone the first two canoes, while 1 camper would have gone in each of the 2 remaining canoes. Only having 1 camper per canoe would have been an odd number of campers, causing the canoe to be unbalanced.
6 campers:
Canoe 1 - 2, Canoe 2 - 2, Canoe 3 - 1, Canoe 4 - 1
In order for each canoe to have an even number of campers, there must be a minimum of 8 campers.
If there were 8 campers:
Canoe 1 - 2, Canoe 2 - 2, Canoe 3 - 2, Canoe 4 - 2
If there were 12 campers:
Canoe 1 - 2, Canoe 2 - 2, Canoe 3 - 2, Canoe 4 - 6
If there were 14 campers:
Canoe 1 - 2, Canoe 2 - 2, Canoe 3 - 4, Canoe 4 - 6
If there were 20 campers:
Canoe 1 - 4, Canoe 2 - 4, Canoe 3 - 6, Canoe 4 - 6
If each canoe requires an even number of campers, then it would have been impossible for 6 campers to have paddled across in all 4 canoes.
This is because if 6 campers used the canoes, 2 campers would have gone the first two canoes, while 1 camper would have gone in each of the 2 remaining canoes. Only having 1 camper per canoe would have been an odd number of campers, causing the canoe to be unbalanced.
6 campers:
Canoe 1 - 2, Canoe 2 - 2, Canoe 3 - 1, Canoe 4 - 1
In order for each canoe to have an even number of campers, there must be a minimum of 8 campers.
If there were 8 campers:
Canoe 1 - 2, Canoe 2 - 2, Canoe 3 - 2, Canoe 4 - 2
If there were 12 campers:
Canoe 1 - 2, Canoe 2 - 2, Canoe 3 - 2, Canoe 4 - 6
If there were 14 campers:
Canoe 1 - 2, Canoe 2 - 2, Canoe 3 - 4, Canoe 4 - 6
If there were 20 campers:
Canoe 1 - 4, Canoe 2 - 4, Canoe 3 - 6, Canoe 4 - 6
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Together, Patricia, Alex and Steve compose 25 percent of their math club. How big is the math club?
Together, Patricia, Alex and Steve compose 25 percent of their math club. How big is the math club?
If 3 people compose 25% of the math club, then 100% of the math club would consist of 4 times the number 3. This gives us a product of 12. Therefore, the correct answer is 12 people.
If 3 people compose 25% of the math club, then 100% of the math club would consist of 4 times the number 3. This gives us a product of 12. Therefore, the correct answer is 12 people.
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Bessy is making shirts for her daughters. If 2 square feet of fabric is enough for her to make 1 shirt, how many shirts can she make with 9 square feet of fabric?
Bessy is making shirts for her daughters. If 2 square feet of fabric is enough for her to make 1 shirt, how many shirts can she make with 9 square feet of fabric?
Given that 2 square feet of fabric is enough for Bessy to make 1 shirt, 9 square feet of fabric is 4.5 times the amount needed to make a shirt. This means that Bessy could make 4.5 shirts. Because making 0.5 shirts does not count as a full shirt, the correct answer is therefore 4 shirts.
Given that 2 square feet of fabric is enough for Bessy to make 1 shirt, 9 square feet of fabric is 4.5 times the amount needed to make a shirt. This means that Bessy could make 4.5 shirts. Because making 0.5 shirts does not count as a full shirt, the correct answer is therefore 4 shirts.
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There are 8 slices in a pie, and each slices weights 1.5 ounces. What is the total weight of the pie in ounces?
There are 8 slices in a pie, and each slices weights 1.5 ounces. What is the total weight of the pie in ounces?
If each slice of pie weighs 1.5 ounces and there are 8 slices total, then the total weight of the pie can be found by multiplying 8 by 1.5.
12 ounces is the weight of the entire pie.
If each slice of pie weighs 1.5 ounces and there are 8 slices total, then the total weight of the pie can be found by multiplying 8 by 1.5.
12 ounces is the weight of the entire pie.
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