How to multiply - ISEE Lower Level (grades 5-6) Mathematics Achievement
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Susie needs to buy new supplies for school. Pencils are sold for 23 cents a piece. Notebooks are sold in pairs, at $3.04 a pair. Folders are sold in packages of 4, and each package costs $2.12.
If Susie buys a 7 pencils, 8 notebooks, and a dozen folders with $25, how much change should she receive?
Susie needs to buy new supplies for school. Pencils are sold for 23 cents a piece. Notebooks are sold in pairs, at $3.04 a pair. Folders are sold in packages of 4, and each package costs $2.12.
If Susie buys a 7 pencils, 8 notebooks, and a dozen folders with $25, how much change should she receive?
Pencils are sold for $0.23 each.
If Susie buys 7 pencils, she is paying
7 x $0.23 =
$1.61 for pencils.
Notebooks are sold in pairs (or in packages of two), for $3.04 a pair.
If Susie buys 8 notebooks, that means that she bought
8 ÷ 2 =
4 pairs of notebooks.
So, 4 pairs of notebooks, at $3.04 a pair costs
4 x $3.04 =
$12.16.
Susie also buys a dozen, or 12, folders. Folders come in packages of 4.
This means that Susie buys
12 ÷ 4 =
3 packages of folders.
Because each package costs $2.12, Susie pays
3 x $2.12 =
$6.36 for a dozen folders.
If we add up the total cost of the pencils, notebooks, and folders we get
$1.61 + $12.16 + $6.36 =
$20.13.
Because Susie pays $25, she will be left with
$25 – $20.13 =
$4.87 in change.
Pencils are sold for $0.23 each.
If Susie buys 7 pencils, she is paying
7 x $0.23 =
$1.61 for pencils.
Notebooks are sold in pairs (or in packages of two), for $3.04 a pair.
If Susie buys 8 notebooks, that means that she bought
8 ÷ 2 =
4 pairs of notebooks.
So, 4 pairs of notebooks, at $3.04 a pair costs
4 x $3.04 =
$12.16.
Susie also buys a dozen, or 12, folders. Folders come in packages of 4.
This means that Susie buys
12 ÷ 4 =
3 packages of folders.
Because each package costs $2.12, Susie pays
3 x $2.12 =
$6.36 for a dozen folders.
If we add up the total cost of the pencils, notebooks, and folders we get
$1.61 + $12.16 + $6.36 =
$20.13.
Because Susie pays $25, she will be left with
$25 – $20.13 =
$4.87 in change.
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Solve using the order of operations: 
Solve using the order of operations:
The order of operations states that we must begin solving the mathematical expression by evaluating numbers in parentheses. In this expression, 
is in parentheses. When we solve this, we get 
. Our expression can now be rewritten as:
The order of operations states that the next step would be to evaluate any term with an exponent. Since there are no exponents in this expression, we move on to multiplication. In this expression we are asked to multiply 
, which is 
. Our expression can now be written as:
The order of operations would have us divide next, but seeing as there is no division in this expression, we move on to addition. 
.
The order of operations states that we must begin solving the mathematical expression by evaluating numbers in parentheses. In this expression,
The order of operations states that the next step would be to evaluate any term with an exponent. Since there are no exponents in this expression, we move on to multiplication. In this expression we are asked to multiply
The order of operations would have us divide next, but seeing as there is no division in this expression, we move on to addition.
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Find the product. Round to the nearest tenths place.
Find the product. Round to the nearest tenths place.
Multiply 
vertically.
After finding the product, don't forget to move the decimal in FOUR places because each number has 2 decimal places 
.
The product is 
.
Then, round to the nearest tenths place 
.
Multiply
After finding the product, don't forget to move the decimal in FOUR places because each number has 2 decimal places
The product is
Then, round to the nearest tenths place
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Read the following problem but do not solve it.
Acording to Mr. Smith's will, when he dies, each of his six children is to be left a parcel of land 510 acres in area. If these six parcels make up all of the farm, then how large is Mr. Smith's farm now?
Which of the following expressions must be evaluated in order to answer this question?
Read the following problem but do not solve it.
Acording to Mr. Smith's will, when he dies, each of his six children is to be left a parcel of land 510 acres in area. If these six parcels make up all of the farm, then how large is Mr. Smith's farm now?
Which of the following expressions must be evaluated in order to answer this question?
There are six parcels of equal size; the total size is therefore the product of the common size (510 acres) and the number of parcels (6). This is 
There are six parcels of equal size; the total size is therefore the product of the common size (510 acres) and the number of parcels (6). This is
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Evaluate 
for 
Evaluate
Substitute 7 for 
.
By order of operations, multiply, then subtract.
Substitute 7 for
By order of operations, multiply, then subtract.
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Evaluate 
for 
Evaluate
Substitute 8 for 
.
By order of operations, multiply, then add.
Substitute 8 for
By order of operations, multiply, then add.
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Evaluate: 
Evaluate:
To multiply two numbers of unlike sign, multiply their absolute values, then affix a negative symbol in front:
To multiply two numbers of unlike sign, multiply their absolute values, then affix a negative symbol in front:
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Evaluate: 
Evaluate:
To multply two negative numbers, just multiply their absolute values; the product will be positive:
To multply two negative numbers, just multiply their absolute values; the product will be positive:
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__ ?
There is a quick shortcut that you may notice in this problem (and problems like it) that will keep you from having to doing a lot of large computations. As you look at the left side of the equation, notice that you can factor out a 
from the 
, which gives you a 
on the left:
__ ?
__?
Now we can divide each side by 
, which leaves us with:
, which equals
, which equals 
There is a quick shortcut that you may notice in this problem (and problems like it) that will keep you from having to doing a lot of large computations. As you look at the left side of the equation, notice that you can factor out a
Now we can divide each side by
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Find the product.
Find the product.
When multiplying two negative numbers, the product will be positive. The correct answer is 324.
When multiplying two negative numbers, the product will be positive. The correct answer is 324.
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What expression is equivalent to:
What expression is equivalent to:
First, add the numbers in parentheses.
Now put the equation together.
First, add the numbers in parentheses.
Now put the equation together.
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Which story best fits the equation 
?
Which story best fits the equation
The equation has multiplication, so the story must have multiplication as well. Ignore the stories which just add or subtract candy bars.
The right answer involves boxes of candy bars:
The equation has multiplication, so the story must have multiplication as well. Ignore the stories which just add or subtract candy bars.
The right answer involves boxes of candy bars:
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What expression is equal to 24?
What expression is equal to 24?
Remember the order of operations with the help of the acronym PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Only one of the expressions in the answer choices which will give us the quantity we are looking for.
Remember the order of operations with the help of the acronym PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
Only one of the expressions in the answer choices which will give us the quantity we are looking for.
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If 
, what number does 
stand for?
If
There are two ways to solve this question: one is to try each answer in the place of 
, and another is to solve it with algebra.
To solve algebraically, first, divide both sides by 2:
Subtract 3 from both sides:
There are two ways to solve this question: one is to try each answer in the place of
To solve algebraically, first, divide both sides by 2:
Subtract 3 from both sides:
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Which expression is equal to 24?
Which expression is equal to 24?
Remember the order of operations, so work inside parentheses first:
Then everything else:
Remember the order of operations, so work inside parentheses first:
Then everything else:
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Find the product of 
and 
.
Find the product of
Find the product of two numbers by multiplying them together. 
, so the correct answer is 
.
Find the product of two numbers by multiplying them together.
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Multiply: 
Multiply:
We ignore the decimals for the time being, multiplying:
Since, between them, the two original factors have a total of three digits to the right of their decimal points, we place the decimal point in the product so that there are three digits to the right. This yields:
We ignore the decimals for the time being, multiplying:
Since, between them, the two original factors have a total of three digits to the right of their decimal points, we place the decimal point in the product so that there are three digits to the right. This yields:
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Which of the following is a valid approximation of the problem:
Which of the following is a valid approximation of the problem:
Round each of the numbers:
Multiply:
35 is a valid approximation for the problem. The precise answer is:
Round each of the numbers:
Multiply:
35 is a valid approximation for the problem. The precise answer is:
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Evaluate:
Evaluate:
A negative number taken to an odd-numbered power is negative, so:
A negative number taken to an odd-numbered power is negative, so:
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