Questions and Answers
What is the prime factorization of 45?
3^2 x 5
Find the set of factors for 12.
{1, 2, 3, 4, 6, 12}
Find the set of multiples for 7.
{7, 14, 21, 28, 35,...}
Find the Least Common Multiple (LCM) of 6 and 8.
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Find the LCM of 15 and 12.
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What is the Greatest Common Factor (GCF) of 48 and 18?
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Add and simplify: 2/5 + 1/3.
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Convert to fractional notation (change to an improper fraction): 4 3/5.
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Simplify the fraction 22/4.
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Subtract and simplify: 4/5 - 1/4.
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Multiply and simplify: 2/3 x 4/5.
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Divide and simplify: 1/6 divided by 2/3.
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Divide and simplify: 3/4 ÷ 2/3.
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Without a calculator, add -15 + 4.
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Find the sum: -253 + 849.
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Without a calculator, subtract -8 - (-4).
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Without a calculator, multiply -8 x -6.
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The naturalist said that 43% of the 3400 plants in the park are flowering. How many plants are flowering?
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A store is having a 25% off sale. If a shirt normally costs $24, how much will it cost with the discount?
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When back-to-school shopping, a college student bought 5 packages of pencils for $2 each, 12 packages of lined paper for $1.50 each, and 6 notebooks for $3 each. How much did he spend in all?
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Study Notes
Prime Factorization and Factors
- Prime factorization of 45 is 3² x 5.
- Set of factors for 12 includes {1, 2, 3, 4, 6, 12}.
Multiples and LCM
- Multiples of 7 include {7, 14, 21, 28, 35,...}.
- Least Common Multiple (LCM) of 6 and 8 is 24.
- LCM of 15 and 12 is 60.
GCF
- Greatest Common Factor (GCF) of 48 and 18 is 6.
Fraction Operations
- Addition of 2/5 + 1/3 simplifies to 11/15.
- Convert 4 3/5 to improper fraction notation: 23/5.
- Simplification of the fraction 22/4 results in 5 1/2.
- Subtraction of 4/5 - 1/4 simplifies to 11/20.
- Multiplication of 2/3 x 4/5 equals 8/15.
- Division of 1/6 by 2/3 simplifies to 1/4.
- Division of 3/4 ÷ 2/3 equals 1 1/8.
Basic Arithmetic
- Without using a calculator, -15 + 4 equals -11.
- The sum of -253 + 849 is 596.
- Subtracting -8 - (-4) without a calculator gives -4.
- Multiplying -8 x -6 results in 48.
Real-Life Application Problems
- 43% of 3400 plants in a park that are flowering totals 1462 flowering plants.
- A 25% discount on a shirt originally costing $24 brings the price down to $18.
- Total expenditure for back-to-school shopping including pencils, lined paper, and notebooks is $46.
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Description
Test your understanding of basic pre-algebra concepts with this quiz. It covers essential topics such as prime factorization, factors, multiples, and least common multiples. Perfect for students preparing for more advanced mathematics.
