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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

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10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Real Numbers

Divide: $48 \div 14$

Possible Answers:

$\frac{13}{4}$

$\frac{24}{7}$

$\frac{14}{3}$

$\frac{17}{4}$

Correct answer:

$\frac{24}{7}$

Explanation:

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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Example Question #10 : Real Numbers

Divide the integers: $38 \div 14$

Possible Answers:

$\frac{9}{7}$

$\frac{11}{7}$

$\frac{19}{7}$

$\frac{7}{2}$

Correct answer:

$\frac{19}{7}$

Explanation:

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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Example Question #11 : Integer Operations

Divide: $88\div 20$

Possible Answers:

$\frac{16}{5}$

$\frac{22}{5}$

$\frac{23}{4}$

$\frac{13}{4}$

$\frac{21}{8}$

Correct answer:

$\frac{22}{5}$

Explanation:

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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Example Question #12 : Integer Operations

Divide: $96 \div 26$

Possible Answers:

$\frac{48}{13}$

$\frac{43}{2}$

$\frac{3}{2}$

$\frac{9}{2}$

$\frac{14}{5}$

Correct answer:

$\frac{48}{13}$

Explanation:

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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Example Question #3 : Division With Whole Numbers And Remainders

What is $-25\div5$

Possible Answers:

Correct answer:

Explanation:

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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Example Question #13 : Integer Operations

Divide the following numbers: $78\div 18$

Possible Answers:

$\frac{13}{3}$

$\frac{13}{6}$

$\frac{39}{4}$

$\frac{39}{8}$

$\frac{39}{2}$

Correct answer:

$\frac{13}{3}$

Explanation:

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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Example Question #14 : Integer Operations

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

Possible Answers:

$\frac{9}{2}$

$\frac{8}{3}$

$\frac{12}{7}$

$\frac{9}{4}$

$\frac{3}{2}$

Correct answer:

$\frac{9}{2}$

Explanation:

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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Example Question #11 : Real Numbers

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

Possible Answers:

$\frac{28}{11}$

$\frac{11}{2}$

$2\frac{7}{11}$

$\frac{7}{4}$

Correct answer:

$\frac{28}{11}$

Explanation:

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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Example Question #16 : Integer Operations

Divide the numbers: $98\div 32$

Possible Answers:

$\frac{12}{5}$

$\frac{49}{16}$

$\frac{27}{8}$

$\frac{32}{7}$

$\frac{11}{4}$

Correct answer:

$\frac{49}{16}$

Explanation:

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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Example Question #3 : Operations In Expressions

When evaluating the expression

$100 - 65 \times 7 + 23$ ,

in which order must you work the three operations?

Possible Answers:

Subtraction, addition, multiplication

Subtraction, multiplication, addition

Addition, subtraction, multiplication

Multiplication, addition, subtraction

Multiplication, subtraction, addition

Correct answer:

Multiplication, subtraction, addition

Explanation:

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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Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : Real Numbers

Example Question #10 : Real Numbers

Example Question #11 : Integer Operations

Example Question #12 : Integer Operations

Example Question #3 : Division With Whole Numbers And Remainders

Example Question #13 : Integer Operations

Example Question #14 : Integer Operations

Example Question #11 : Real Numbers

Example Question #16 : Integer Operations

Example Question #3 : Operations In Expressions

All Algebra 1 Resources

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