Understanding Three-Fourths of a Number

When you hear the phrase “three-fourths of a number,” it essentially means you’re taking a portion of that number, specifically three out of every four parts. This concept is fundamental in understanding fractions and their applications in everyday life.

Visualizing Three-Fourths

Imagine a pizza cut into four equal slices. Three-fourths of the pizza would mean you have three of those slices. This visual representation helps us understand that three-fourths represents a part of a whole, and in this case, that part is three out of four.

Representing Three-Fourths

We can represent three-fourths in two ways:

  1. Fraction: The most common way to represent three-fourths is as a fraction: 3/4. The numerator (3) tells us how many parts we have, and the denominator (4) tells us the total number of parts in the whole.

  2. Decimal: We can also express three-fourths as a decimal: 0.75. This is obtained by dividing the numerator (3) by the denominator (4) : 3 ÷ 4 = 0.75.

Calculating Three-Fourths of a Number

To find three-fourths of a number, we need to perform multiplication. Here’s how:

  1. Fraction Method:

    • Multiply the number by the fraction 3/4.
    • For example, to find three-fourths of 20, we would calculate: (3/4) * 20 = 15

  2. Decimal Method:

    • Multiply the number by the decimal 0.75.
    • Using the same example, three-fourths of 20 would be: 0.75 * 20 = 15

Real-Life Applications

The concept of three-fourths is used in various real-life scenarios, including:

  • Cooking: Recipes often call for three-fourths of a cup of an ingredient.
  • Measurement: When measuring fabric or wood, you might need to cut a piece that’s three-fourths of a yard long.
  • Discounts: Stores often offer discounts of three-fourths off the original price of an item.
  • Statistics: When analyzing data, you might find that three-fourths of a population has a certain characteristic.

Examples

Let’s explore some examples to solidify our understanding:

Example 1: Find three-fourths of 12.

  • Fraction Method: (3/4) * 12 = 9
  • Decimal Method: 0.75 * 12 = 9

Example 2: A store offers a 3/4 discount on a $40 shirt. What is the discount amount?

  • Fraction Method: (3/4) * $40 = $30
  • Decimal Method: 0.75 * $40 = $30

Example 3: A survey found that three-fourths of the students in a school like chocolate ice cream. If there are 80 students in the school, how many students like chocolate ice cream?

  • Fraction Method: (3/4) * 80 = 60
  • Decimal Method: 0.75 * 80 = 60

Conclusion

Understanding three-fourths of a number is a fundamental concept in mathematics. It helps us grasp the idea of fractions, their representation, and their application in various real-life situations. By mastering this concept, we gain a stronger foundation for tackling more complex mathematical problems involving fractions and decimals.

Citations

  1. 1. Khan Academy – Fractions
  2. 2. Math is Fun – Fractions
  3. 3. Purplemath – Fractions

Related

(2) O3 + H → O2 + OH k2 = 1.78×10^-11 cm^3 s^-1 (3) O + OH → O2 + H k3 = 4.40×10^-11 cm^3 s^-1 (5) O + HO2 → O2 + OH k5 = 3.50×10^-11 cm^3 s^-1 (6) H + HO2 → O2 + H2 k6 = 5.40×10^-12 cm^3 s^-1 (9) OH + HO2 → O2 + H2O2 k9 = 4.00×10^-11 cm^3 s^-1 (10) HO2 + HO2 → O2 + H2O2 k10 = 2.50×10^-12 cm s^-1 (11) O + O2 + M → O3 + M k11 = 1.05×10^-34 cm^6 s^-1 (14) H + O2 + M → HO2 + M k14 = 8.08×10^-32 cm^6 s^-1 (15) H + H + M → H2O + M k15 = 3.31×10^-27 cm^6 s^-1 (16) O2 + hv → 2 O k16 = (1.26×10^-8 s^-1) φ (17) H2O + hv → H + OH k17 = (3.4×10^-6 s^-1) φ (18) O3 + hv → O2 + O k18 = (7.10×10^-5 s^-1) φ

Table 1 Reactions, rate constants and activation energies used in the model* No. Reaction kopt (M⁻¹ s⁻¹) 1 OH + H₂ → H + H₂O 3.74 x 10⁷ 2 OH + HO₂ → HO₂ + OH⁻ 5 x 10⁹ 3 OH + H₂O₂ → HO₂ + H₂O 3.8 x 10⁷ 4 OH + O₂ → O₂ + OH 9.96 x 10⁹ 5 OH + HO₂ → O₂ + H₂O 7.1 x 10⁹ 6 OH + OH → H₂O₂ 5.3 x 10⁹ 7 OH + e⁻aq → OH⁻ 3 x 10¹⁰ 8 H + O₂ → HO₂ 2.0 x 10¹⁰ 9 H + HO₂ → H₂O₂ 2.0 x 10¹⁰ 10 H + H₂O₂ → OH + H₂O 3.44 x 10⁷ 11 H + OH → H₂O 1.4 x 10¹⁰ 12 H + H → H₂ 1.94 x 10¹⁰ 13 e⁻aq + O₂ → O₂⁻ 1.9 x 10¹⁰ 14 e⁻aq + O₂ → HO₂⁻ + OH⁻ 1.3 x 10¹⁰ 15 e⁻aq + HO₂ 2.0 x 10¹⁰ 16 e⁻aq + H₂O₂ 1.1 x 10¹⁰ 17 e⁻aq + HO₂ → OH + OH⁻ 1.3 x 10¹⁰ 18 e⁻aq + H⁺ → H 2.3 x 10¹⁰ 19 e⁻aq + e⁻aq → H₂ + OH⁻ + OH⁻ 2.5 x 10⁹ 20 HO₂ + O₂ → O₂ + HO₂ 1.3 x 10⁹ 21 HO₂ + HO₂ → O₂ + H₂O₂ 8.3 x 10⁵ 22 HO₂ + HO₂ → O₂ + OH + H₂O 3.7 23 HO₂ + HO₂ → O₂ + O₂ + OH + H₂O 7 x 10⁵ s⁻¹ 24 H⁺ + O₂⁻ → HO₂ 4.5 x 10¹⁰ 25 H⁺ + O₂⁻ → O₂ 2.0 x 10¹⁰ 26 H⁺ + OH⁻ 1.4 x 10¹¹ 27 H⁺ + HO₂⁻ 2 x 10¹⁰ 28 H₂O₂ → HO₂ + H⁺ + OH⁻ 2.5 x 10⁻⁵ s⁻¹ 29 H₂O₂ → H⁺ + OH⁻ 1.4 x 10⁻⁷ s⁻¹ 30 O₂ + O₂ → O₂ + HO₂ + OH⁻ 0.3 31 O₂ + H₂O₂ → O₂ + OH + OH 16 32

(2) O3 + H → O2 + OH k2 = 1.78×10^-11 cm^3 s^-1 (3) O + OH → O2 + H k3 = 4.40×10^-11 cm^3 s^-1 (5) O + HO2 → O2 + OH k5 = 3.50×10^-11 cm^3 s^-1 (6) H2O + O → 2 OH k6 = 5.40×10^-12 cm^3 s^-1 (9) OH + HO2 → O2 + H2O k9 = 4.00×10^-11 cm^3 s^-1 (10) HO2 + HO2 → O2 + H2O2 k10 = 2.50×10^-12 cm s^-1 (11) O + O2 + M → O3 + M k11 = 1.05×10^-34 cm^6 s^-1 (14) H + O2 + M → HO2 + M k14 = 8.08×10^-32 cm^6 s^-1 (15) OH + H + M → H2O + M k15 = 3.31×10^-27 cm^6 s^-1 (16) O2 + hv → 2 O k16 = (1.26×10^-8 s^-1) φ (17) H2O + hv → H + OH k17 = (3.4×10^-6 s^-1) φ (18) O3 + hv → O2 + O k18 = (7.10×10^-8 s^-1) φ