Lesson 72: Fractions Chart

Definition

The S.O.S. method provides three steps for fraction arithmetic: Shape the problem correctly, Operate according to the rules, and Simplify the answer.

What’s next

This lesson provides the complete S.O.S. chart as your guide. Soon, we'll apply this structure to problems involving the multiplication of three fractions.

Property

To solve fraction problems, follow three steps: 1. Shape: Write the problem in the correct form (common denominators for +/−, fraction form for ×/÷). 2. Operate: Perform the calculation. 3. Simplify: Reduce the answer and convert improper fractions.

Examples

• Addition (Shape first): $\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}$
• Multiplication (Shape, Operate, Simplify): $1\frac{1}{2} \times \frac{2}{5} = \frac{3}{2} \times \frac{2}{5} = \frac{6}{10} = \frac{3}{5}$
• Division (Shape, Operate, Simplify): $\frac{5}{6} \div 2 = \frac{5}{6} \div \frac{2}{1} = \frac{5}{6} \times \frac{1}{2} = \frac{5}{12}$

Explanation

Think of S.O.S. as your secret code for acing fractions! It's a simple checklist to ensure you never miss a step. First, get the numbers in the right SHAPE. Then, OPERATE with math. Finally, SIMPLIFY your answer. It's a foolproof plan for any fraction problem!

Property

To multiply three or more fractions: 1. Write all numbers in fraction form. 2. Cancel common factors between any numerator and any denominator. 3. Multiply the remaining numerators and denominators.

Examples

• $\frac{1}{2} \times \frac{2}{3} \times \frac{3}{4} = \frac{1}{4}$
• $3 \times \frac{2}{5} \times \frac{1}{6} = \frac{1}{5}$
• $1\frac{1}{4} \times \frac{2}{5} \times 2 = 1$

Explanation

Multiplying three fractions is just a bigger version of multiplying two! The coolest part is canceling. You can cancel a numerator from the first fraction with a denominator from the last one. It’s a free-for-all that makes the final multiplication step way, way easier and faster!

Property

Before you can multiply, all mixed numbers must be converted into improper fractions. This is the first part of the "Shape" step for multiplication. You cannot multiply the whole numbers and fractions separately.

Examples

• To solve $2\frac{1}{2} \times \frac{3}{4}$, you must first change it to $\frac{5}{2} \times \frac{3}{4} = \frac{15}{8}$.
• $1\frac{1}{3} \times 6$ becomes $\frac{4}{3} \times \frac{6}{1}$, which simplifies to $8$.
• The problem $1\frac{3}{5} \times \frac{3}{4}$ must be shaped into $\frac{8}{5} \times \frac{3}{4}$ before you can solve it.

Explanation

Mixed numbers are like fancy guests who need to change into party clothes (improper fractions) before joining the multiplication fun. If you forget this crucial 'shape' step, you'll get the wrong answer every time. Always convert them into fractions before you even think about canceling or multiplying anything.