Algebra 1 : How to add integers

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #1 : How To Add Integers

Solve the expression  \displaystyle 13+(-3).

Possible Answers:

\displaystyle 13

\displaystyle 39

\displaystyle 16

\displaystyle -39

\displaystyle 10

Correct answer:

\displaystyle 10

Explanation:

Adding a negative is the same as subtraction.

\displaystyle 13+(-3)=13-3=10

Example Question #2 : How To Add Integers

What is the sum of all of the even integers from 2 to 2,000, inclusive?

Possible Answers:

\displaystyle 1,010,000

\displaystyle 990,000

\displaystyle 1,000,000

\displaystyle 1,001,000

\displaystyle 999,000

Correct answer:

\displaystyle 1,001,000

Explanation:

Pair the numbers as follows:

\displaystyle 2+2000=2,002

\displaystyle 4+1998=2,002

\displaystyle 6+1996=2,002

...

\displaystyle 1,000+1,002=2,002

There are 500 such pairs, so adding all of the even integers from 2 to 2,000 is the same as taking 2,002 as an addend 500 times. This can be rewritten as a multiplication.

\displaystyle 2,002* 500 = 1,001,000

Example Question #3 : How To Add Integers

Simplify

\displaystyle (-15)+12+(-4)+1

Possible Answers:

\displaystyle -7

\displaystyle -9

\displaystyle -6

\displaystyle 7

Correct answer:

\displaystyle -6

Explanation:

\displaystyle (-15)+12+(-4)+1

When adding integers first consider the signs of the numbers being added. Then simply work right to left. \displaystyle -15+12\rightarrow-3+(-4)\rightarrow-7+1=-6

So the answer is \displaystyle -6

 

Example Question #4 : How To Add Integers

Consider the expression:

\displaystyle \left ( 2 + y\right ) \div z ^{2} - 6

If you know the value of \displaystyle y and \displaystyle z, then in which order would you carry out the four operations in this expression in order to evaluate it?

Possible Answers:

Add, divide, subtract, square

Square, subtract, add, divide

Square, divide, add, subtract

Add, square, divide, subtract

Add, divide, square, subtract

Correct answer:

Add, square, divide, subtract

Explanation:

According to the order of operations:

Work any operation in parentheses first - here it would be the addition.

What remains would be an exponent (the squaring), a division, and a subtraction, which, according to the order of operations, would be worked in that order.

Example Question #5 : How To Add Integers

The Venn diagram depicts the number of students taking Spanish and Japanese classes. How many students in total are taking Japanese class?

Question_4

Possible Answers:

\displaystyle 63

\displaystyle 93

\displaystyle 48

\displaystyle 45

\displaystyle 40

Correct answer:

\displaystyle 63

Explanation:

There are 48 students taking only Japanese and 15 students taking both Japanese and Spanish. The total number taking Japanese classes is the sum of these two groups.

\displaystyle \small 48+15=63

Example Question #1 : How To Add Integers

Subtract:

\displaystyle (-1+5i)-(2-3i) 

 

Possible Answers:

\displaystyle -3+8i

\displaystyle -3+2i

\displaystyle 3-8i

\displaystyle -3-8i

\displaystyle -3-2i

Correct answer:

\displaystyle -3+8i

Explanation:

This is essentially the following expression after translation:

\displaystyle (-1+5i)-(2-3i)=-1-2+5i+3i

Now add the real parts together for a sum of \displaystyle -3, and add the imaginary parts for a sum of \displaystyle 8i.

Example Question #3 : Basic Operations With Complex Numbers

Multiply:

\displaystyle (2+3i)(1-i)

Answer must be in standard form.

Possible Answers:

\displaystyle 2-3i

\displaystyle 5-i

\displaystyle 5+i

\displaystyle 2+2i

\displaystyle 5

Correct answer:

\displaystyle 5+i

Explanation:

\displaystyle (2+3i)(1-i)

 The first step is to distribute which gives us:

\displaystyle 2-2i+3i-3i^{2}  

\displaystyle 2+i-3i^{2}=2+i+3=5+i

which is in standard form.

Example Question #3 : Adding And Subtracting Radicals

 \displaystyle What\: is \; 3\sqrt{7} + 4\sqrt{7}\, ?

Possible Answers:

\displaystyle 7\sqrt14

\displaystyle 7\sqrt7

\displaystyle 49

\displaystyle 12\sqrt7

Correct answer:

\displaystyle 7\sqrt7

Explanation:

 \displaystyle Think \: of\; x = \sqrt7

\displaystyle 3x + 4x = 7x

 \displaystyle Therefore, \: 3\sqrt{7} + 4\sqrt{7} = 7\sqrt7

 

Example Question #4685 : Algebra Ii

Add:

\displaystyle (2-3i)+(-1-2i)

Possible Answers:

\displaystyle -1+5i

\displaystyle 5+3i

\displaystyle 1+5i

\displaystyle 5-3i

\displaystyle 1-5i

Correct answer:

\displaystyle 1-5i

Explanation:

When adding complex numbers, add the real parts and the imaginary parts separately to get another complex number in standard form.

Adding the real parts gives \displaystyle 2-1=1, and adding the imaginary parts gives \displaystyle -5i.

 

Example Question #6 : How To Add Integers

Solve: \displaystyle 4016+98 

Possible Answers:

\displaystyle 4014

\displaystyle 5114

\displaystyle 4114

\displaystyle 5014

\displaystyle 4214

Correct answer:

\displaystyle 4114

Explanation:

To solve \displaystyle 4016+98, first add the ones digit.

\displaystyle 6+8=14

The ones digit is 4. Since 14 is ten or greater, carry the tens digit to the next number.

Add the tens digit with the one carried over.

\displaystyle 1+9+(1)=11

The tens digit is 1.  Since 11 is ten or greater, carry the tens digit to the next number.  There are no hundreds digit with 98.  Add both the thousands and hundreds digit to the carry over.

\displaystyle 40+1 =41

Combine this with the tens and ones digits.

The answer is:  \displaystyle 4114

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