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Questions and Answers
What is the prime factorization of 45?
What is the prime factorization of 45?
3^2 x 5
Find the set of factors for 12.
Find the set of factors for 12.
{1, 2, 3, 4, 6, 12}
Find the set of multiples for 7.
Find the set of multiples for 7.
{7, 14, 21, 28, 35,...}
Find the Least Common Multiple (LCM) of 6 and 8.
Find the Least Common Multiple (LCM) of 6 and 8.
Find the LCM of 15 and 12.
Find the LCM of 15 and 12.
What is the Greatest Common Factor (GCF) of 48 and 18?
What is the Greatest Common Factor (GCF) of 48 and 18?
Add and simplify: 2/5 + 1/3.
Add and simplify: 2/5 + 1/3.
Convert to fractional notation (change to an improper fraction): 4 3/5.
Convert to fractional notation (change to an improper fraction): 4 3/5.
Simplify the fraction 22/4.
Simplify the fraction 22/4.
Subtract and simplify: 4/5 - 1/4.
Subtract and simplify: 4/5 - 1/4.
Multiply and simplify: 2/3 x 4/5.
Multiply and simplify: 2/3 x 4/5.
Divide and simplify: 1/6 divided by 2/3.
Divide and simplify: 1/6 divided by 2/3.
Divide and simplify: 3/4 ÷ 2/3.
Divide and simplify: 3/4 ÷ 2/3.
Without a calculator, add -15 + 4.
Without a calculator, add -15 + 4.
Find the sum: -253 + 849.
Find the sum: -253 + 849.
Without a calculator, subtract -8 - (-4).
Without a calculator, subtract -8 - (-4).
Without a calculator, multiply -8 x -6.
Without a calculator, multiply -8 x -6.
The naturalist said that 43% of the 3400 plants in the park are flowering. How many plants are flowering?
The naturalist said that 43% of the 3400 plants in the park are flowering. How many plants are flowering?
A store is having a 25% off sale. If a shirt normally costs $24, how much will it cost with the discount?
A store is having a 25% off sale. If a shirt normally costs $24, how much will it cost with the discount?
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?
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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