Test for Algebra, Fraction, and Decimal

Introduction
Algebra, fractions, and decimals are important concepts in mathematics. They provide a foundation for advanced mathematical topics and are frequently used in real-life situations. To assess your understanding of these concepts, here is a test that covers various aspects of algebra, fractions, and decimals.

Test Questions

1. Algebra:
a) Solve the equation: 2x + 5 = 15
b) Simplify the expression: 3(x + 2) - 2(x - 4)

2. Fractions:
a) Add the fractions: 1/4 + 3/8
b) Subtract the fractions: 5/6 - 2/3
c) Multiply the fractions: 2/5 * 3/4
d) Divide the fractions: 2/3 ÷ 4/5

3. Decimals:
a) Convert the decimal 0.75 to a fraction in simplest form.
b) Convert the fraction 4/5 to a decimal.
c) Multiply the decimals: 2.5 * 0.8
d) Divide the decimals: 1.2 ÷ 0.4

Explanation

1. Algebra:
a) To solve the equation 2x + 5 = 15, we need to isolate the variable x. Subtracting 5 from both sides gives us 2x = 10. Dividing both sides by 2, we find x = 5.
b) Simplifying the expression 3(x + 2) - 2(x - 4) involves applying the distributive property. This simplifies to 3x + 6 - 2x + 8, which further simplifies to x + 14.

2. Fractions:
a) To add the fractions 1/4 + 3/8, we find a common denominator, which is 8. Then, we convert 1/4 to 2/8 and add the numerators: 2/8 + 3/8 = 5/8.
b) To subtract the fractions 5/6 - 2/3, we also find a common denominator, which is 6. Then, we convert 2/3 to 4/6 and subtract the numerators: 5/6 - 4/6 = 1/6.
c) To multiply the fractions 2/5 * 3/4, we multiply the numerators and denominators: 2 * 3 = 6 and 5 * 4 = 20. Thus, the answer is 6/20, which simplifies to 3/10.
d) To divide the fractions 2/3 ÷ 4/5, we multiply the first fraction by the reciprocal of the second fraction: 2/3 * 5/4 = 10/12, which simplifies to 5/6.

3. Decimals:
a) To convert the decimal 0.75 to a fraction, we write it as 75/100 and simplify it to 3/4.
b) To convert the fraction 4/5 to a decimal, we divide the numerator by the denominator: 4 ÷ 5 = 0.8.
c) To multiply the decimals