# 7th Grade Math : 7th Grade Math

## Example Questions

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### Example Question #1 : Number Sense

A sweater was originally , but the department store is running a  off sale. What is the sale price of the sweater?

Explanation:

In order to solve this problem, we need to calculate  of . The key word "of" is indicative of multiplication; however, we need to start by converting the percentage into a decimal because you cannot multiply a number by a percent.

We can convert a percent into a decimal by moving the decimal two places to the left:

Next, we can multiply:

Remember, we are taking  off the original price, which means we need to subtract.

### Example Question #2 : Number Sense

The rectangle provided is a scaled drawing of a rectangular yard. Given the scale of , what is the actual length of the yard?

Explanation:

This question is asking us to solve for the actual size of the length of the rectangle, therefore, we first need to recall which side is considered to be the length of the rectangle.

In this example, the length of the rectangle is . We can set up a proportion to solve for the actual length of the rectangle,

Next, we cross multiply and solve for

### Example Question #1 : Algebra

Billy makes  a week in allowance plus  for each lawn that he mows. This week Billy wants to make over . Select the inequality for the number of lawns he needs to mow.

Explanation:

We know that Billy needs to make more than  between his allowance and the lawns that he mows. This means our inequality should include

Also, since Billy will make  per lawn, that means we need to multiply  by the number of lawns he needs to mow, :

So far we have the following:

Next, we know that he makes  each week, on top of what he makes mowing each law.

This means we need to add the  to the

When we put all of these pieces together, we will get the following inequality:

### Example Question #1 : Operations

Andrew spends every Saturday at the gym working out. He can complete  of his workout in  of an hour. If he continues at this rate, how much of his workout does Andrew complete per hour?

Explanation:

The phrase "per hour" gives us a clue that we are going to divide. In this problem, we can replace the word "per" with a division sign; therefore, we will have the portion of his workout, , divided by hours, :

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

Therefore:

Andrew can complete  of his workout per hour.

### Example Question #2 : Operations

Solve:

Explanation:

In order to solve this problem, we need to start at  on the number line.

Next, we have  which means we need to move  places to the right on the number line. When we have an addition sign   we move to the right because that is towards the positive side of the number line. When we have a subtraction sign  we move to the left because that is towards the negative side of the number line.

The orange arrow moved  places to the right, and ended at ; thus,

### Example Question #1 : 7th Grade Math

Solve:

Explanation:

We know the following information:

In this particular case, do the negative numbers change our answer? . There are a couple of rules that we need to remember when multiplying with negative numbers:

• A negative number divided by a positive number will always equal a negative number, and a positive number divided by a negative number will always equal a negative number.
• A negative number divided by a negative number will always equal a positive number

Thus,

### Example Question #1 : Geometry

If a rectangle possesses a width of  and has a perimeter of , then what is the length?

Explanation:

In order to solve this problem, we need to recall the formula for perimeter of a rectangle:

We can substitute in our known values and solve for our unknown variable (i.e. length):

We want to isolate the  to one side of the equation. In order to do this, we will first subtract  from both sides of the equation.

Next, we can divide each side by

The length of the rectangle is

### Example Question #2 : Geometry

The figure represents a set of supplementary angles, solve for .

Explanation:

Supplementary angles are defined as two angles that when added together equal

From the question, we know that the two angles are supplementary, and thus equal , so we can set up the following equation:

Next we can solve for :

### Example Question #3 : Geometry

What is the area of the circle provided?

Explanation:

In order to solve this problem, we need to recall the formula for the area of a circle:

The circle in this question provides us with the diameter, so we first have to solve for the radius. Remember, the radius is half the diameter:

Now that we have the radius we can use the formula to solve:

Solve:

### Example Question #4 : Geometry

What is the area of the triangle pictured above?

12

60

24

40

30