Gymathics 1: Basic Gymathics

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Fractions: Lesson 1

What is a fraction? Represents equal parts of a whole Represents parts of a set or a collection The word "fraction" has been derived from the Latin ‘fractus’ which means “broken”.

In the fraction 4/5, which is the numerator?

In the fraction 3/7, which is the denominator?

In a class of 50 students, 27 are girls and 23 are boys. Which fraction represents the girls in the class?

Jane's score in her Math exam is 17/20. Which of the following statements is correct?

Fractions: Lesson 2

What type of fraction is 5/6?

Which of the following fractions is an improper fraction?

Which of the following fractions has a value that is closest to 1?

Which of the following fractions has a value that is closest to 0?

Which of the following fractions has the greatest value?

Fractions: Lesson 3

Example 1: Convert 5/2 to mixed number Divide 5 by 2 The answer is 2 remainder 1 2 is the whole number, 1 is the numerator Final answer: 2 1/2

Example 2: Express 9/7 in mixed form. Divide 9 by 7 The answer is 1 remainder 2 1 is the whole number, 2 is the numerator Final answer: 1 2/7

Example 1: Convert 3 1/4 to improper fraction Multiply 3 (whole number) by 4 (denominator) The product is 12. Add 1 (numerator). The sum is 13. This is the "new" numerator. Final Answer: 13/4

Example 2: Convert 7 3/5 to improper fraction Multiply 7 (whole number) by 5 (denominator) The product is 35. Add 3 (numerator). The sum is 38. This is the "new" numerator. Final Answer: 38/5

19/3 in mixed form is 6 2/3

Which of the following improper fractions is equal to 3 1/2?

Which of the following improper fractions is equal to 4 3/7?

Fractions: Lesson 4

The simplest form of 7/21 is 1/3

The simplest form of 18/4 is 4 2/4.

The simplest form of 12/15 is 3/5

The simplest form of 27/36 is 3/4

Fractions: Lesson 5

Fractions: Lesson 6

Example 1: What is the product of 2/3 an 1/6? Multiply the numerators (2 and 1). The product is 2. Multiply the denominators (3 and 6). The product is 18. The answer is 2/18. Next, simplify the answer. The simplified form of 2/18 is 1/9.

Example 2: What is the product of 4/7 an 2/8? Multiply the numerators (4 and 2). The product is 8. Multiply the denominators (7 and 8). The product is 56. The answer is 8/56. Next, simplify the answer. The simplified form of 8/56 is 1/7.

Fractions: Lesson 7

Example 1: Divide 1/3 by 2/8 Get the reciprocal of the second fraction (2/8). The answer is 8/2. Multiply the reciprocal (8/2) by the first fraction (1/3). Multiply the numerators (8 and 1). The product is 8. Multiply the denominators (2 and 3). The product is 6. Simplify the answer (8/6). Final answer is 1 1/3.

Example 2: Divide 4/7 by 1/9 Get the reciprocal of the second fraction (1/9). The answer is 9/1. Multiply the reciprocal (9/1) by the first fraction (4/7). Multiply the numerators (9 and 4). The product is 36. Multiply the denominators (1 and 7). The product is 7. Simplify the answer (36/7). Final answer is 5 1/7.

The quotient of 1/4 divided by 1/5 is 1 1/4.

The quotient of 3/8 divided by 4/9 is 1/6.

Fractions: Lesson 8

Example 1: Convert 5/6 to decimal form. Divide the numerator (5) by the denominator (6). The answer is 0.83

Example 2: Convert 15/30 to decimal form. Divide the numerator (15) by the denominator (30). The answer is 0.5.

Example 3: Convert 3 3/4 to decimal form. Divide the numerator (3) by the denominator (4). The answer is 0.75. Add the quotient (0.75) to the whole number (3). Final answer: 3.75

Fractions: Lesson 9

Example 1: What is 4/5 in percent? Divide the numerator (4) by the denominator (5). Multiply the quotient (0.8) by 100. Then add "%" symbol. Answer: 80%

Example 2: What is 7/9 in percent? Divide the numerator (7) by the denominator (9). Multiply the quotient (0.78) by 100. Then add "%" symbol. Answer: 78%

Percent: Lesson 1

Example 1: What is 30% of 60? Convert the percentage (30%) to decimal. Multiply the decimal (0.3) to the whole (60). Final answer: 18

Example 2: What is 78% of 520? Convert the percentage (78%) to decimal. Multiply the decimal (0.78) to the whole (520). Final answer: 405.6

Example 3: What is 150% of 45? Convert the percentage (150%) to decimal. Multiply the decimal (1.5) to the whole (45). Final answer: 67.5

Percent: Lesson 2

Example 1: In a class of 50 students, 32 are girls. What percent of the class are girls? Divide the part (32) by the whole (50). Multiply the quotient (0.64) by 100. Add the "%" symbol. Final answer: 64%

Example 2: Marcus got a score of 22 points out of a 30-item test correctly. What is his equivalent grade in percent? Divide the part (22) by the whole (30). Multiply the quotient (0.73) by 100. Add the "%" symbol. Final answer: 73%

Percent: Lesson 3

Example 1: There are 92 women who watched the musical play. If 40% of the audience are women, how many people are in the audience? Multiply the part (92) by 100. Divide the product (9,200) by the percent (40). Final answer: 230

Example 2: Vic has watched 25 Korean movies listed on Netflix. If he has watched only 5% of the movies on Netflix, how many movies are there in total? Multiply the part (25) by 100. Divide the product (2,500) by the percent (5). Final answer: 500

Integers: Lesson 1

Example 1: (-4) + (-5) Proceed with usual addition (4 + 5) Copy the sign of the numbers (-) Final answer: (-9)

Example 2: 9 + 11 Proceed with usual addition (9 + 11) Copy the sign of the numbers (+) Final answer: 20

Example 1: (-2) + 7 Subtract the numbers (7 - 2) Copy the sign of the greater number (+) Final answer: 5

Example 2: 5 + (-11) Subtract the numbers (11 - 5) Copy the sign of the greater number (-) Final answer: -6

Example 1: 7 - (-2) Change the sign of the second number (+2) Proceed to addition (7 + 2) Final answer: 9

Example 2: (-7) - 1 Change the sign of the second number (-1) Proceed to addition (-7 + -1) Final answer: -8

Integers: Lesson 2

Example 1: 5 x (-5) x (-2) The number of negative factors is EVEN (2 factors). The answer is 50.

Example 2: What is the quotient of (-2) x (-2) divided by 4 x (-1) The number of negative factors is ODD (3 factors). The answer is (-1).

Exponents: Lesson 1

Which of the following exponents is equal to 64?

Which of the following exponents is equal to 64?

Which of the following exponents is equal to 64?

Which of the following exponents is equal to 81?

Which of the following exponents is equal to 81?

Which of the following exponents is equal to 81?

Exponents: Lesson 2

To convert this to a regular number, shift the decimal place 6 places to the right. The exponent tells you how many times you would shift the decimal place

The answer is 2,000,000

To convert this to scientific notation, shift the decimal from the right to the left until it reaches the first digit. The number of shifts is the exponent.

The answer is

To convert this to a regular number, shift the decimal place 3 places to the left. The exponent tells you how many times you would shift the decimal place.

The answer is 0.0012.

To convert this to scientific notation, shift the decimal place to the left until it reaches the first non-zero digit (3). The number of shifts is the negative exponent.

The answer is

Radicals: Lesson 1

When simplifying radicals, write down all the factors of the number.

In simplifying square roots, find the numbers that appear THRICE in the factors.

Radicals: Lesson 2

Radicals: Lesson 3

Radicals: Lesson 4

Algebra: Lesson 1

Algebra: Lesson 2

Algebra: Lesson 3