How to divide integers - Algebra

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Question

When evaluating the expression

$100 - 65 \times 7 + 23$ ,

in which order must you work the three operations?

Answer

By the order of operations, in the absence of grouping symbols, multplication must be worked before adding or subtracting. Then the addition and subtraction must be worked in left-to-right order; the subtraction is at left, so the subtraction is worked next, followed by the addition.

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Question

Divide: $96 \div 26$

Answer

In order to divide these two numbers, we will need to rewrite both numbers as a fraction and split the numbers by common factors.

$96 \div 26 = \frac{96}{26}= \frac{2 \times 48}{2 \times 13}$

The twos can be cancelled through division.

The answer is: $\frac{48}{13}$

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Question

What is $-48\div-16$ ?

Answer

Divide the absolute values to get the magnitude of the answer.

$48\div16=3$

Remember the following rules:

Positive divided by negative is negative.

Positive divided by positive is positive.

Negative divided by negative is positive.

Since we are dealing with two negatives, our answer will be positive.

$-48\div-16=3$

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Question

$-10+13-12\div{(16\div{2^{2}})}=$

Answer

This is a classic order of operations question, and if you are not careful, you can end up with the wrong answer!

Remember, the order of operations says that you have to go in the following order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction (also known as PEMDAS). In this equation, you will start with the parentheses. In the parentheses, we have

$(16\div2^{2})$ .

But within the parentheses, you still need to follow PEMDAS. First, we will solve the exponent, and the square of 2 is 4. Then, we'll divide 16 by 4, which gives us 4, so we can rewrite our original equation as

$-10+13-12\div4$ .

We can now divide into , which gives us

.

The last step is to add and subtract the numbers above, paying careful attention to negative signs. In the end, we end up with because added to equals , and minus equals .

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Question

Divide and express the quotient in scientific notation:

$\frac{ 1.5 \times 10^{16} }{ 6\times 10^{5} }$

Answer

All of these choices are equivalent to the correct answer. But only $2.5 \times 10^{10}$ is in scientific notation.

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Question

If a number is divisible by 9 and 12, it must also be divisible by...

I. 36

II. 48

III. 144

Answer

For a number A to be divisible by another number B, A must share all of the prime factors of B. For example, 100 is divisible by 10 because the prime factors of 10 (5 and 2) are found in the prime factors of 100 (2, 2, 5, and 5).

In this problem, we have a number A that is divisible by 9 and 12. First, find the prime factors of 9 and 12. The factors of 9 are (3, 3). The factors of 12 are (2,2,3). So, to be divisible by 9 and 12, the number A must have the factors (2,2,3,3). Multiply those together, and we get 223*3= 36.

So, A must be divisible by 36. It could be divisible by the other answer choices, but since the question asked which choice must be right, we can only choose 36.

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Question

Rewrite 100 as a number in base six.

Answer

One way to do this:

Divide 100 by 6. The remainder will be the last digit.

$100 \div 6 = 16 \textrm{ R } 4$

Now divide the quotient by 6. This remainder will be the second-to-last digit.

$16 \div 6 = 2 \textrm{ R } 4$

The quotient is less than 6, so it is the first digit. The base-six equivalent of 100 is $244_{\textrm{six}}$ .

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Question

Divide: $\frac{32}{84}$

Answer

Write the factors of the two numbers.

$\frac{32}{84}= \frac{4\times 8 }{4\times 21}= \frac{8}{21}$

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Question

If a number is divisible by , which of the following is always true?

I. Divisible by

II. Divisible by

III. Divisible by

Answer

If a number is divisble by some number , then it is also divisible by all of its factors. Hence, if a number is divisible by , it is also divisible by , and . Thus, I and II are both true.

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Question

What is $-25\div5$

Answer

When you are dealing with negative numbers, the following rules apply.

If there are no negative signs, the answer is positive.

If there is one negative sign, the answer is negative.

If there are two negative signs, the answer is positive.

$25\div5=5$ , and since there is only one negative sign the answer is negative. is the solution.

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Question

Divide the following numbers: $78\div 18$

Answer

Rewrite this expression as a fraction.

$78\div 18 = \frac{78}{18}$

Rewrite both numbers using common factors.

$\frac{78}{18} =\frac{2 \times 3 \times 13}{2 \times 3\times 3}$

Cancel the common terms in the numerator and denominator.

The answer is: $\frac{13}{3}$

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Question

Divide $126 \div 36$ .

Answer

Rewrite the expression in fraction form.

$126 \div 36= \frac{126}{36}$

Write out the common factors of both the numerator and denominator.

$\frac{126}{36} = \frac{6\times 21}{6\times 6} =\frac{6\times 3\times 7}{6\times 3 \times 2}$

We can then see that the fraction can be reduced to $\frac{7}{2}$ without having to conduct long division.

The answer is $\frac{7}{2}$ .

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Question

Divide: $48 \div 14$

Answer

Rewrite the expression as a fraction.

$\frac{48}{14}$

Write out the multiples of the numerator and denominator.

$\frac{48}{14} =\frac{2 \times 3\times 8}{2 \times 7}$

The twos can be cancelled. Simplify what remains of the fraction.

$\frac{3\times 8}{7}= \frac{24}{7}$

The answer is: $\frac{24}{7}$

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Question

Divide the integers: $38 \div 14$

Answer

Rewrite the expression as a fraction.

$38 \div 14 = \frac{38}{14}$

Rewrite the fraction by common factors of two.

$\frac{38}{14} = \frac{2 \times 19}{2\times 7}$

Divide and cancel the twos, which will become one.

The answer is: $\frac{19}{7}$

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Question

Divide: $88\div 20$

Answer

Rewrite this expression into a fraction.

$88\div 20 = \frac{88}{20}$

Write the factors for the numerator and denominator.

$\frac{88}{20} = \frac{4\times 22}{4 \times 5}$

The fours are common and can be divided or cancelled.

The result is: $\frac{22}{5}$

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Question

Divide: $\frac{81}{18}$

Answer

Instead of using long division to solve, we can rewrite the numerator and denominator by their common factors.

$\frac{81}{18} = \frac{3\times 3 \times 3 \times 3}{3\times 3 \times 2}$

Cancel the common terms in the numerator and denominator.

Write the remaining terms.

$\frac{3 \times 3}{2} = \frac{9}{2}$

The answer is: $\frac{9}{2}$

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Question

Divide the numbers: $\frac{56}{22}$

Answer

Rewrite the numerator and denominator with common factors.

$\frac{56}{22} = \frac{2 \times 28}{2\times 11}$

Simplify the fraction.

The answer is: $\frac{28}{11}$

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Question

Divide the numbers: $98\div 32$

Answer

Rewrite the expression into a fraction.

$98\div 32 = \frac{98}{32}$

Write the numbers in terms of their common factors.

$\frac{98}{32} =\frac{2\times 49}{2 \times 16}$

Cancel the common terms. There are no common factors with the numbers 49 and 16.

The answer is: $\frac{49}{16}$

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Question

Divide twenty six by seventy eight.

Answer

Write the sentence as an expression.

$\frac{26}{78}$

Rewrite the fraction by common factors. Both numbers are divisible by two.

$\frac{26}{78} = \frac{2\times 13}{2\times 39}$

Cancel out the two.

Notice that the fraction $\frac{13}{39}$ can also be reduced further.

$\frac{13}{39} = \frac{13\times 1}{13 \times 3} = \frac{1}{3}$

The fraction is: $\frac{1}{3}$

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Question

Divide sixty with twenty five.

Answer

Write the expression as a fraction.

$\frac{60}{25}$

Rewrite the numerator and denominator with common factors.

$\frac{60}{25} = \frac{12\times 5}{5 \times 5}$

Cancel the common terms on the top and bottom.

The answer is: $\frac{12}{5}$

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